Mathematical Epidemiology Subgroup (MEPI)

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Sub-group minisymposia

From Primate to Vectors to Humans: Understanding the underlying mechanisms of disease transmission and control

Organized by: Folashade Agusto (University of Kansas, United States), Majid Bani Yaghoub (University of Missouri Kansas City, United States)
Note: this minisymposia has multiple sessions. The second session is MS02-MEPI.

  • Amy Goldberg (Duke University, United States)
    "Model-based estimates of zoonotic malaria spillover in Atlantic Forest, Brazil"
  • Malaria was thought to have been eradicated from the Atlantic Coast of Brazil by the late 1970s. Previously thought to only infect non-human primates, recent molecular studies have identified the malaria parasite Plasmodium simium in humans along the Atlantic Coast of Brazil. Clinical symptoms present similarly to the common human-associated malaria parasite Plasmodium vivax, and the two parasites are difficult to distinguish with standard PCR assays or microscopy. Together, these observations raise the possibility that local monkey populations, particularly howler monkeys, act as reservoirs for zoonotic malaria that has been infecting human populations long-term. Here, we use a mathematical-modeling approach to estimate the rate of cryptic P. simiam infection that has been misdiagnosed as P. vivax in the Rio de Janiero state. We use coupled differential equations based on the Ross-MacDonald model, with two host populations representing humans and monkeys to model the infection rate of humans and howler monkeys with P. simiam. Based on elasticity analyses, we find that for the same intensity, interventions in the monkey patch reduces the overall number of human malaria cases more than interventions in the human patch. We simulate the model across a spatial grid, with the two-population system in each patch and migration between patches. Under various spillover scenarios, we compare results to clinical incidence rates of P. vivax and consider the impact on malaria elimination probability. Based on the frequency and spatial distribution of the cases, under our model, we expect spill over to be recurrent, with minimal human-to-human transmission.
  • Ibrahim M. ELMojtaba (Sultan Qaboos University, Oman)
    "The role of primates and human movement on the dynamics of zika virus"
  • We build a mathematical model to understand the role of human movement and primates in the dynamics of zika virus. The model considers the dynamics of the disease between four different populations, namely humans, primates, vectors in the rural areas, and vectors in urban areas. Our model possesses three different equilibrium, the disease-free equilibrium which is locally asymptotically stable when the basic reproduction number is less than unity, an axial equilibrium point (endemic with respect to human and vectors in urban areas, and disease-free with respect to primates and vectors in rural areas), and endemic equilibrium. The model exhibits very rich dynamics where there is a possibility of multiple bifurcations. Numerical simulations were carried out to study the effect of several parameters and to show the theoretical results.
  • Omar Saucedo (Virginia Polytechnic Institute and State University, United States)
    "Tick-borne Diseases in Virginia"
  • Ticks are known for being a source of disease infections and are cause of great concern within the public health community. Throughout the world, there are a variety of tick species that are associated with different tick-borne pathogens. Diseases such as Lyme Disease have surfaced in areas of the Commonwealth of Virginia where they previously have not been detected, and the incidence of these diseases have been steadily increasing. A better understanding of tick-borne viral pathogens is needed as this poses a threat to agriculture and livestock. In this talk, we will explore the relevant features of landscape and ecological influences on tick species and pathogen prevalence through mathematical modeling.
  • Sean Cavany (University of Notre Dame, United States)
    "The impacts of COVID-19 mitigation on dengue virus transmission: a modelling study"
  • The COVID-19 pandemic has induced unprecedented reductions in human mobility and social contacts throughout the world. Because dengue virus (DENV) transmission is strongly driven by human mobility, behavioral changes associated with the pandemic have been hypothesized to impact dengue incidence. By discouraging human contact, COVID-19 control measures have also disrupted dengue vector control interventions, the most effective of which require entry into homes. We used an agent-based model with a realistic treatment of human mobility and vector control to investigate how and why dengue incidence could differ under a lockdown scenario with a proportion of the population sheltered at home. We found that a lockdown in which 70% of the population sheltered at home led to a small average increase in cumulative DENV infections of up to 10%, depending on the time of year the lockdown occurred. Lockdown had a more pronounced effect on the spatial distribution of DENV infections, with higher incidence under lockdown in regions with high mosquito abundance. Transmission was also more focused in homes following lockdown. The proportion of people infected in their own home rose from 54% under normal conditions to 66% under lockdown, and the household secondary attack rate rose from 0.109 to 0.128, a 17% increase. When we considered that lockdown measures could disrupt regular, city-wide vector control campaigns, the increase in incidence was more pronounced than with lockdown alone, especially if lockdown occurred at the optimal time for vector control. Our results indicate that an unintended outcome of COVID-19 control measures may be to adversely alter the epidemiology of dengue. This observation has important implications for an improved understanding of dengue epidemiology and effective application of dengue vector control. When coordinating public health responses during a syndemic, it is important to monitor multiple infections and understand that an intervention against one disease may exacerbate another.

From Primate to Vectors to Humans: Understanding the underlying mechanisms of disease transmission and control

Organized by: Folashade Agusto (University of Kansas, United States), Majid Bani Yaghoub (University of Missouri Kansas City, United States)
Note: this minisymposia has multiple sessions. The second session is MS01-MEPI.

  • Wandi Ding (Middle Tennessee State University, United States)
    "Mathematical modeling and optimal control for malaria transmission"
  • We consider a malaria transmission model with SEIR (susceptible-exposed-infected-recovered) classes for the human population, SEI (susceptible-exposed-infected) classes for the wild mosquitoes and an additional class for sterile mosquitoes. We derive the basic reproduction number of infections. We formulate an optimal control problem in which the goal is to minimize both the infected human populations and the cost to implement two control strategies: the release of sterile mosquitoes and the usage of insecticide-treated nets to reduce the malaria transmission. Adjoint equations are derived and the characterization of the optimal controls is established. Finally, we quantify the effectiveness of the two interventions aimed at limiting the spread of Malaria. A combination of both strategies leads to a more rapid elimination of the wild mosquito population that can suppress Malaria transmission. Numerical simulations are provided to illustrate the results.
  • Eric Numfor (Augusta University, United States)
    "A malaria-HIV/AIDS co-infection model with treatment and insecticide-treated bednets"
  • Malaria and HIV, two of the world’s most deadly diseases, are endemic in several parts of the world, with overlapping distribution. The concurrent use of multiple strategies has been recommended as an effective strategy to reduce malaria and HIV prevalence. In this talk, we present a malaria-HIV/AIDS co-infection model with control in which malaria treatment, insecticide-treated bednets and HIV/AIDS treatment are incorporated. The local asymptotic stability of the disease-free equilibrium (DFE) of the malaria-only sub- model and co-infection model, and the global stability of the DFE of the HIV/AIDS-only sub-model are studied. The existence of a backward bifurcation and endemic boundary equilibria are established. Key parameters in determining the number of new cases of malaria-HIV/AIDS co-infection are identified. The impact of malaria treatment, insecticide-treated bednets and HIV/AIDS treatment are assessed by formulating and analyzing an optimal control problem. Our results present the importance of HIV/AIDS treatment in mitigating malaria and HIV prevalence.
  • Adeshina I. Adekunle (James Cook University, Australia)
    "Modeling drug-resistant tuberculosis amplification rates and intervention strategies in Bangladesh"
  • Tuberculosis (TB) is the seventh leading cause of morbidity and mortality in Bangladesh. Although the National TB control program (NTP) of Bangladesh is implementing its nationwide TB control strategies, more specific and effective single or combination interventions are needed to control drug-susceptible (DS) and multi-drug resistant (MDR) TB. In this study, we extended our two-strain mathematical model with amplification to account for the latent stage. The mathematical epidemiological properties of this extension follow from our previous analysis. Hence, we fit different variants of the model to the Bangladesh TB data to understand the transmission dynamics of DS and MDR TB. We further performed sensitivity analysis and evaluated the cost-effectiveness of varying combinations of four basic control strategies including distancing, latent case finding, case holding and active case finding, all within the optimal control framework. From our fitting, the model with different transmission rates between DS and MDR TB best captured the Bangladesh TB reported case counts. The estimated basic reproduction number for DS TB was 1.14 and for MDR TB was 0.54, with an amplification rate of 0.011 per year. The sensitivity analysis also indicated that the transmission rates for both DS and MDR TB had the largest influence on prevalence. To reduce the burden of TB (both DS and MDR), our finding suggested that a quadruple control strategy that combines distancing control, latent case finding, case holding and active case finding is the most cost-effective. Alternative strategies can be adopted to curb TB depending on availability of resources and policy makers’ decisions.
  • Hem Raj Joshi (Xavier University, United States)
    "Modeling transmission dynamics of rabies in Nepal"
  • We developed a mathematical model to describe the transmission dynamics of rabies in Nepal. In particular, this is an indirect interspecies transmission from jackals to humans through dogs, which is relevant to the context of Nepal. This indirect interspecies transmission dynamic is one of the novel features of our model. Our model utilizes annual dog-bite data collected from Nepal for a decade, allowing us to reasonably estimate parameters related to rabies transmission in Nepal. We calculated the basic reproduction number ($R_0$) as well as the intraspecies basic reproduction numbers for dogs ($R_0^D$) and jackals ($R_0^J$ ) in Nepal. We also applied the optimal control theory to identify an optimal control strategy for mitigating the rabies burden in Nepal. Our potential control strategies are human vaccination, dog vaccination, dog culling, dog sterilization, and jackal vaccination. We concluded that a combination of dog vaccination and dog culling is the most effective strategy to control rabies in Nepal. These results may be useful for designing effective prevention and control strategies for mitigating the rabies burden in Nepal and other parts of the world.

Control Interventions for New, Rare and Neglected Infectious Diseases

Organized by: Stacey Smith? (The University of Ottawa, Canada) & Aurelio A. de los Reyes V (University of the Philippines Diliman)

  • Hyojung Lee (National Institute of Mathematical Sciences,, South Korea)
    " Effects of social distancing on transmission dynamics of COVID19 in Republic of Korea"
  • The novel coronavirus outbreak has rapidly spread out from Wuhan, Hubei Province, China to other countries since December, 2019. The World Health Organization (WHO) declared the COVID-19 outbreak a global pandemic on March 11, 2020. The Korean government implemented the combined interventions including social distancing, and work-at-home policies. In this research, first, the epidemiological characteristics were analyzed in seven geographical areas in Korea. Second, we constructed a mathematical model to assess the control interventions including the social distancing. Third, the effective reproduction numbers by geographical area were estimated. Finally, we assessed the effect of the control strategies as time-dependent interventions using mathematical model approach on the COVID-19 spread to suggest the most effective intervention.
  • Stacey Smith? (The University of Ottawa, Canada)
    "Modelling the daily risk of Ebola in the presence and absence of a potential vaccine"
  • Ebola virus --- one of the deadliest viral diseases, with a mortality rate around 90% --- damages the immune system and organs, with symptoms including episodic fever, chills, malaise and myalgia. The Recombinant Vesicular Stomatitis Virus-based candidate vaccine (rVSV-ZEBOV) has demonstrated clinical efficacy against Ebola in ring-vaccination clinical trials. In order to evaluate the potential effect of this candidate vaccine, we developed risk equations for the daily risk of Ebola infection both currently and after vaccination. The risk equations account for the basic transmission probability of Ebola and the lowered risk due to various protection protocols: vaccination, hazmat suits, reduced contact with the infected living and dead bodies. Parameter space was sampled using Latin Hypercube Sampling, a statistical method for generating a near-random sample of parameter values. We found that at a high transmission rate of Ebola (i.e., if the transmission rate is greater than 90%), a large fraction of the population must be vaccinated ($>$80%) to achieve a 50% decrease in the daily risk of infection. If a vaccine is introduced, it must have at least 50% efficacy, and almost everyone in the affected areas must receive it to effectively control outbreaks of Ebola. These results indicate that a low-efficacy Ebola vaccine runs the risk of having vaccinated people be overconfident in a weak vaccine and hence the possibility that the vaccine could make the situation worse, unless the population can be sufficiently educated about the necessity for high vaccine uptake.
  • May Anne Mata (University of the Philippines Mindanao, Philippines)
    "Models of rabies incidence in Davao City, Philippines and their implications for policy makers"
  • Rabies is a fatal zoonotic disease and remains to be a priority health concern in the Philippines. The call to eradicate rabies in the Philippines by 2023 led Davao City public health officials to intensify the rabies control interventions. Despite the efforts done to mitigate the disease, rabies cases in dogs remain endemic. In this talk, I will present the status of canine rabies in Davao City as well as the modelling approaches we used to determine the associated factors affecting rabies incidence, explain the mechanisms behind the trend in monthly reported rabies cases, and to evaluate the impact of government-initiated interventions, climate variables, and dog information, which are known as potential disease drivers. Our results revealed that from model estimates, rabies in the city is not epidemic and in order to control the disease, the target vaccination coverage must be consistently met, and that dog population must be regulated. We recommend that the local government unit should consider our findings when conducting strategic planning sessions for achieving a rabies-free Davao City.
  • Victoria May Mendoza (University of the Philippines Diliman, Philippines)
    "A mathematical model and optimal control of Schistosomiasis in Agusan del Sur, Philippines"
  • Schistosomiasis is a neglected tropical disease and remains endemic in the Philippines, covering 28 provinces in 12 regions. Schistosomiasis in the Philippines is caused by textit{Schistosoma japonicum}, a zoonotic parasite which infects other mammalian hosts aside from humans. In this work, we develop a mathematical model to study the transmission dynamics of schistosomiasis in Agusan del Sur, Philippines and investigate strategies to control and possibly eliminate the disease. We consider humans and carabaos as definitive hosts, and snails as intermediate hosts. Using the available schistosomiasis data from the Philippine Department of Health, we estimate the transmission probability and contact rate between snails and humans, and infectivities from humans and carabaos to snails. Implementation of multiple control strategies highlight the significance of an integrated approach in mitigating the disease. Improved surveillance and monitoring of cases, and the importance of accurate and updated data are strongly emphasized.

Mathematical Modelling that Supported Australia and New Zealand’s COVID-19 Responses

Organized by: James Walker (The University of Melbourne, Australia)

  • Rebecca Chisholm (La Trobe University, Australia)
    "Modelling response strategies for potential COVID-19 outbreaks in remote Australian Aboriginal communities"
  • Remote Australian Aboriginal and Torres Strait Islander communities have potential to be severely impacted by COVID-19. Accordingly, the Aboriginal and Torres Strait Islander Advisory Group on COVID-19, co-chaired by the Australian Government Department of Health and the National Aboriginal Community Controlled Health Organisation led the development of specific guidance to support initial response to identified infections in these settings, and commissioned modelling to help inform this advice. We developed an individual-based model to represent remote communities of different sizes to consider alternative public health responses following the silent introduction of infection. The model included data-informed representation of extended family connections spanning multiple, often crowded dwellings, which are a key driver of infection spread. A range of strategies for case finding, quarantining of contacts, testing, and lockdown were examined. Our model suggests a SARS-CoV-2 outbreak will develop and spread rapidly in remote communities if an undetected infection is introduced. Prompt case detection with quarantining of extended-household contacts and a 14-day lockdown for all other residents, combined with exit testing for all, is the strategy most likely to achieve definitive initial containment.
  • Emily Harvey (ME Research & Te Pūnaha Matatini, Aotearoa New Zealand)
    "Modelling COVID-19 in Aotearoa NZ on a bipartite contact network of 5 million individuals"
  • Many of the models used for rapid policy advice during the COVID-19 pandemic have relied on simplifying assumptions about the homogeneity of individuals, however we know that risk factors for exposure, transmission, and poor outcomes are not evenly distributed across society. We have built a stochastic model of infection dynamics that runs on an empirically derived bipartite contact network of the ~5 million people in Aotearoa New Zealand. The contact network includes spatial information, and individual demographic information, along with distinct ‘transmission contexts’ including dwellings, workplaces, and schools, built from linked data in the Statistics NZ Integrated Data Infrastructure. This network is the underlying structure on which we run a stochastic contagion process to model the spread of COVID 19, which includes explicit representation of the testing and contact tracing processes. We have used this model to estimate the probable outcomes of COVID outbreaks in Aotearoa and to evaluate the effect of non-pharmaceutical interventions including 'Alert Level' changes. In particular, we find that this heterogeneity (network structure) means that the effect of different interventions does not combine linearly.
  • Michael Plank (University of Canterbury, Aotearoa New Zealand)
    "Modelling the risk of re-introduction of COVID-19 from border arrivals"
  • In an attempt to maintain the elimination of COVID-19 in New Zealand, all international arrivals are required to spend 14 days in government-managed quarantine and to return a negative test result before being released. We model the testing, isolation and transmission of COVID-19 within quarantine facilities to estimate the risk of community outbreaks being seeded at the border. We use a simple branching process model for COVID-19 transmission that includes a time-dependent probability of a false-negative test result. We show that the combination of 14-day quarantine with two tests is highly effective in preventing an infectious case entering the community, provided there is no transmission within quarantine facilities. Shorter quarantine periods, or reliance on testing only with no quarantine, substantially increases the risk of an infectious case being released. We calculate the fraction of cases detected in the second week of their two-week stay and show that this may be a useful indicator of the likelihood of transmission occurring within quarantine facilities. Frontline staff working at the border risk exposure to infected individuals and this has the potential to lead to a community outbreak. We use the model to test surveillance strategies and evaluate the likely size of the outbreak at the time it is first detected. We conclude with some recommendations for managing the risk of potential future outbreaks originating from the border.
  • Freya Shearer (The University of Melbourne, Australia)
    "Supporting the Australian response to COVID-19 through model-based situational assessment"
  • A key element of epidemic decision-making is situational awareness — that is, knowing the current and potential future status of the epidemic. Outputs from mathematical and statistical models have provided enhanced situational awareness to the Australian government throughout the course of the COVID-19 pandemic. Our response to COVID-19 required the rapid development of new methodologies and data streams for situational assessment, particularly with respect to monitoring changes in population behaviour and estimating transmission risk in the absence of cases. In this talk, I will describe Australia’s situational awareness modelling program for COVID-19. I will provide an overview of the modelling outputs reported to key government decision-making committees on a weekly basis (at least) since April 2020. Further, I will describe how our methods and the structure of our reporting has evolved over time, in response to changing epidemiology and response priorities.

Integrative Within-Host and Between-Hosts Modeling for Preparedness Against Infectious Diseases

Organized by: Esteban Hernandez-Vargas (Instituto de Matematicas, UNAM, Unidad Juriquilla, Queretaro, Mexico., Mexico), Jorge X. Velasco-Hernandez (Instituto de Matematicas, UNAM, Unidad Juriquilla, Queretaro, Mexico., Mexico)

  • Jan Fuhrmann (Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany, Germany)
    "Modeling the COVID-19 epidemic in Germany"
  • The novel corona virus SARS-CoV-2 that causes the disease COVID19 was first identified in Hubei province, China, in 2019 and has since spread around the globe. Its virulence and the morbidity associated with has caused the WHO to declare this new respiratory disease a pandemic in March 2020. From a modeling perspective this pandemic poses several challenges. As with most new infectious diseases, many parameters are not particularly well known. Alarmingly high numbers of known infectious and COVID-19 related deaths led to contact reductions among the population, partly by increased caution, partly mandated by authorities. And the infection often leading to mild, non-specific symptoms - or even no symptoms at all - makes it all but impossible to estimate the ratio of detected cases among all infections. We shall discuss some of the data available from public domain sources and show how ordinary differential equation models can be used to reproduce these data, generate short term forecasts, and simulate possible further courses of the epidemic for different scenarios. Particular emphasis will be put on the relevance of detection ratios and how they are affected by test strategies and case numbers.
  • Lubna Pinky (University of Tennessee Health Science Center, Memphis, TN 38163, USA, USA)
    "Quantifying Dose-, Strain-, and Tissue-Specific Kinetics of Parainfluenza Virus Infection"
  • Human parainfluenza viruses (HPIVs) are a leading cause of acute respiratory infection hospitalization in children, yet little is known about how dose, strain, tissue tropism, and individual heterogeneity affects the processes driving growth and clearance kinetics. Longitudinal measurements are possible by using reporter sendai viruses, murine parainfluenza counterpart, that express luciferase, where the insertion location yields a wild-type-like or attenuated phenotype. Bioluminescence measurements from individual animals infected with either strain suggests that there is a rapid increase in expression followed by a peak, biphasic clearance, and resolution. However, these kinetics vary between individuals and with dose, strain, and whether the infection was initiated in the upper and/or lower respiratory tract. To quantify the differences, we translated the bioluminescence measurements from the nasopharynx, trachea, and lung into viral loads and used a mathematical model together with nonlinear mixed effects approach to define the mechanisms distinguishing each scenario. The results confirmed a higher rate of virus production with the wild-type-like virus compared to its attenuated counterpart, and suggested that low doses result in disproportionately fewer infected cells. The analyses indicated faster infectivity and infected cell clearance rates in the lung and that higher viral doses, and concomitantly higher infected cell numbers, resulted in more rapid clearance. Infected cell clearance was also highly variable amongst individuals, which was particularly evident during infection in the lung. These critical differences provide important insight into distinct HPIV dynamics, and show how bioluminescence data combined with quantitative analyses can be used to dissect host-, virus-, and dose-dependent effects.
  • Fernando Saldaña (Instituto de Matematicas UNAM at Juriquilla, Mexico, Mexico)
    "A model for vaccine escape under unequal vaccine access"
  • Currently, there are concerns that without adequate vaccine distribution, the SARS-CoV-2 variants will grow and mutate, curbing the progress that has been made since the vaccine has been made available. In this work, we present a mathematical model to study vaccine escape evolution in structured host populations. We find that vaccine escape mutants are less likely to come from vaccinated regions where there is a strong selection pressure for vaccine escape and more likely to come from a neighboring unvaccinated region where there is no selection for escape.
  • Suneet Singh Jhutty (Frankfurt Institute for Advanced Studies, Frankfurt am Main, Germany., Germany)
    "Mapping of Influenza Infection from Blood Data with Machine Learning Methods"
  • Seasonal and pandemic influenza causes enormous economic loss, health complications and death. The measurement of clinical markers for influenza and its respective immune responses is time-consuming and almost impossible to perform. Here, we show for first time the proof applicability and implementation of machine learning algorithms to infer the viral load and immune markers in the lung compartment based on hematology data of mice infected with influenza H1N1. Our results show that even with high variability in the data, the model prediction to track the infection in the host is possible. Platelets and granulocytes play an essential role to track influenza infection. The proposed in silico tool paved the way towards a better prognosis of influenza infections and possibly other respiratory diseases.

Vector-borne Diseases: Data, Modeling, and Analysis

Organized by: Jing Chen (Nova Southeastern University, United States), Shigui Ruan (University of Miami, United States), Xi Huo (University of Miami, United States)
Note: this minisymposia has multiple sessions. The second session is MS13-MEPI.

  • Yijun Lou (The Hong Kong Polytechnic University, China)
    "Dynamics of a periodic tick-borne disease model with co-feeding and multiple patches"
  • This talk presents a mechanistic model for describing the spatial dynamics of tick-borne diseases by considering systemic transmission, seasonal climate impacts, host movement as well as the co-feeding transmission route. The net reproduction number for tick growth and basic reproduction number for disease transmission are derived, which predict the global dynamics of tick population growth and disease transmission. Further numerical simulations will also be presented in the talk to not only verify the analytical results, but also characterize the contribution of co-feeding transmission route on disease prevalence in a habitat and the effect of host movement on the spatial spreading of the pathogen.
  • Kaniz Fatema Nipa (University of Georgia, United States)
    "The Effect of Demographic and Environmental Variability on Disease Outbreak for a Dengue Model with a Seasonally Varying Vector Population"
  • Seasonal changes in temperature, humidity, and rainfall affect vector survival and emergence of mosquitoes and thus impact the dynamics of vector-borne disease outbreaks. Recent studies of deterministic and stochastic epidemic models with periodic environments have shown that the average basic reproduction number is not sufficient to predict an outbreak. We extend these studies to time-nonhomogeneous stochastic dengue models with demographic variability wherein the adult vectors emerge from the larval stage vary periodically. The combined effects of variability and periodicity provide a better understanding of the risk of dengue outbreaks. A multitype branching process approximation of the stochastic dengue model near the disease-free periodic solution is used to calculate the probability of a disease outbreak. The approximation follows from the solution of a system of differential equations derived from the backward Kolmogorov differential equation. This approximation shows that the risk of a disease outbreak is also periodic and depends on the particular time and the number of the initial infected individuals. Numerical examples are explored to demonstrate that the estimates of the probability of an outbreak from that of branching process approximations agree well with that of the continuous-time Markov chain. In addition, we propose a simple stochastic model to account for the effects of environmental variability on the emergence of adult vectors from the larval stage.
  • Necibe Tuncer (Florida Atlantic University, United States)
    "Determining Reliable Parameter Estimates for Within-host and Within-vector models of Zika Virus of Zika Epidemiological Models"
  • In this study, we introduce three within-host and one within-vector models of Zika virus. The within-host models are (i) the target cell limited model, (ii) the target cell limited model with natural killer cells class and (iii) a within-host-within-fetus model of a pregnant individual. The within-vector model includes the Zika virus dynamics in the midgut and the salivary glands. The within-host models are not structurally identifiable with respect to data on viral load and natural killer cell counts. After rescaling, the scaled within-host models are locally structurally identifiable. The within-vector model is structurally identifiable with respect to viremia data in the midgut and salivary glands. Using Monte Carlo Simulations we find that target cell limited model is practically identifiable from data on viremia; the target cell limited model with natural killer cell class is practically identifiable, except for the rescaled half saturation constant. The within-host-within-fetus model has all fetus related parameters not practically identifiable without data on the fetus, as well as the rescaled half saturation constant is also not practically identifiable. The remaining parameters are practically identifiable. Finally we find that none of the parameters of the within-vector model is practically identifiable.
  • Jianhong Wu (York University, Canada)
    "Multi-scale dynamic models for vector-borne disease transmission dynamics: infestation, co-feeding and systemic infection"
  • We present a series of collaborative studies on using structured models to understand the intertwined infestation (vector feeding on host), systemic and co-feeding transmission processes. We show how this multi-scale approach leads to a new class of nonlinearity, novel classes of dynamical systems, and interesting threshold dynamics including bistability and oscillation.

Celebrating Dr. Ngwa's 55th birthday with talks honoring his mathematical modeling work including malaria mosquitoes.

Organized by: Miranda Teboh-Ewungkem (Lehigh University, United States), Calistus N. Ngonghala, (University of Florida, Gainsville, FL, United States), Jude D. Kong (York University, Toronto, ON, Canada,, Canada)
Note: this minisymposia has multiple sessions. The second session is MS14-MEPI.

  • Philip Maini (Mathematical Institute, Oxford, UK)
    "Modelling collective leader-follower behaviour"
  • Collective movement is a very common occurrence in biology and ecology. I will review work in which I have been involved for the past few years on (i) angiogenesis (formation of new blood vessels) in wound healing and cancer growth; (ii) cranial neural crest migration in normal development. The models will range from coupled systems of partial differential equations to discrete cell-based systems. I will show how we have derived a new model for the classical snail-trail system and also how, working with experimental colleagues, we have generated new biological insights.
  • Nakul Chitnis (Swiss Tropical and Public Health Institute, Switzerland)
    "Modelling Mosquitoes and Malaria"
  • We present mathematical models of mosquito population dynamics and mosquito foraging behaviour and combine these with models of malaria transmission. We use these models to explore the dynamics of mosquito behaviour on malaria transmission and investigate the impact of vector control interventions on malaria transmission and disease burden.
  • Divine Wanduku (Department of Mathematics, Georgia Southern University, United States)
    "A Stochastic Multi-Population Behavioral Model to Assess the Roles of Education Campaigns, Random Supply of Aids, and Delayed ART Treatment in HIV/AIDS Epidemic"
  • The successful reduction in prevalence rates of HIV in many countries is attributed to control measures such as information and education campaigns (IEC), antiretroviral therapy (ART), and national, multinational and multilateral support providing official developmental assistance (ODAs) to combat HIV. However, control of HIV epidemics can be interrupted by limited random supply of ODAs, high poverty rates and low living standards. This study presents a stochastic HIV/AIDS model with treatment assessing the roles of IEC, the supply of ODAs and early treatment in HIV epidemics. The supply of ODAs is assessed via the availability of medical and financial resources leading more people to get tested and begin early ART. The basic reproduction number ( $mathfrak{R}_{0}$) for the dynamics is obtained, and other results for HIV control are obtained by conducting stability analysis for the stochastic SITRZ disease dynamics. Moreover, the model is applied to Uganda HIV/AIDS data, wherein linear regression is applied to predict the $mathfrak{R}_{0}$ over time, and to determine the importance of ART treatment in the dynamics.
  • Jacek Banasiak (Department of Mathematics and Applied Mathematics, University of Pretoria, South Africa)
    "Beyond the Next Generation Matrix Method"
  • The Next Generation Matrix method has been one of the most popular methods for establishing the stability of the disease-free equilibrium. It has, however, some drawbacks - for instance it is not directly applicable for problems with the immigration of infectives. In this talk, we shall discuss some ways of dealing with such problems, based on perturbation techniques.

Advances in Infectious Disease Modeling

Organized by: Lihong Zhao (University of California Merced, United States), Ling Xue (Harbin Engineering University, China), Suzanne Sindi (University of California Merced, United States)
Note: this minisymposia has multiple sessions. The second session is MS09-MEPI.

  • Folashade Agusto (Ecology and Evolutionary Biology, University of Kansas, United States)
    "Playing with fire: Modeling the effects of prescribed fire on Lyme disease"
  • Tick-borne illnesses are trending upward and are an increasing source of risks to people’s health in the United States; furthermore, the range of tick habitats is expanding due to climate change. Thus, it is imperative to find a practical and cost-efficient way of managing tick populations. Prescribed burns are a common form of land management, it can be cost efficient if properly managed. In this seminar, I will present a compartmental model for ticks carrying Lyme disease using an impulsive system, and then investigate the effect of prescribed fire intensity and the duration between burns. Our study found that fire intensity has a larger impact in reducing tick population than frequency between burns. Furthermore, burning at high intensity is preferable to burning at low intensity whenever possible, although high intensity burns may be unrealistic due to environmental factors. Annual burns resulted in the most significant reduction of infectious nymphs, which are the primary carriers of Lyme disease.
  • Fabian Santiago (Department of Applied Mathematics, University of California Merced, United States)
    "Mathematical Assessment of Intervention Strategies for Mitigating COVID-19 Transmission in a University Setting "
  • In March 2020, the University of California, Merced (UC Merced), along with other universities throughout the United States moved to an on-line only mode of course delivery to decrease the spread of SARS-CoV-2, the virus responsible for the COVID-19 disease. During that time, the UC Merced leadership focused on how to safely bring students back to the campus in the Fall. At UC Merced this involved using mathematical models to evaluate the effectiveness of proposed mitigation strategies for containing the spread of COVID-19 within the university setting. In this talk I will discuss the mathematical model we used to evaluate Fall 2021 re-opening strategies and present a global sensitivity analysis of the contact and infection model parameters that govern the transmission dynamics of COVID-19 within the university setting.
  • Zhuolin Qu (Department of Mathematics, The University of Texas at San Antonio, United States)
    "Modeling the invasion wave of Wolbachia in mosquitoes for controlling mosquito-borne diseases"
  • We develop and analyze partial differential equation (PDE) models to study the transmission and invasion dynamics of Wolbachia infection among the wild mosquitoes. Wolbachia is a natural bacterium that can infect mosquitoes and reduce their ability to transmit mosquito-borne diseases, such as Zika, Chikungunya, and dengue fever, and releasing Wolbachia-infected mosquitoes is a rising biological control to mitigate these diseases. Both field trials and previous modeling studies have shown that the Wolbachia infection among the mosquitoes needs to exceed a threshold level to persist in time. To give a realistic prediction of the threshold condition, it is critical to capture the spatial heterogeneity in the distributions of the infected and uninfected mosquitoes, which is created by the local introduction of the infection in the field release. We derive reaction-diffusion-type PDE models from the existing ordinary differential equation (ODE) models to better characterize the spatial invasion of Wolbachia infection into the native mosquitoes. The models account for both the complex vertical transmission parameters (inherited from the ODE models) and the horizontal transmission of infection (spatial diffusion). We analyze the threshold condition of establishing a successful invasion, the “critical bubble”, for the spatial models, and we compare it with the level in the spatially homogenous setting. We also show that the proposed PDE models can give rise to the traveling waves of Wolbachia infection. We then quantify how the magnitude of the diffusion coefficient can impact the threshold condition and the shape and velocity of the traveling front, and we numerically study different scenarios that may inform the design of the field release strategies.
  • Christopher Remien (Department of Mathematics and Statistical Sciences, University of Idaho, United States)
    "Reservoir population dynamics and pathogen epidemiology drive pathogen genetic diversity, spillover, and emergence"
  • When several factors align, pathogens that normally infect wildlife can spill over into the human population. If pathogen transmission within the human population is self-sustaining, or rapidly evolves to be self-sustaining, novel human pathogens can emerge. Although many factors influence the likelihood of spillover and emergence, the rate of contact between humans and wildlife is critical. Thus, for those pathogens inhabiting wildlife reservoirs with pronounced seasonal fluctuations in population density, it is broadly recognized that spillover risk also varies with season. What remains unknown, however, is the extent to which seasonal fluctuations in reservoir populations influence the evolutionary dynamics of pathogens in ways that affect the likelihood of emergence. Here, we use mathematical models and stochastic simulations to show that seasonal fluctuations in reservoir population densities lead to seasonal increases in genetic variation within pathogen populations and thus influence the waiting time for mutations capable of sustained human-to-human transmission. These seasonal increases in genetic variation also lead to elevated risk of emergence at predictable times of year.  

Advances in Infectious Disease Modeling

Organized by: Lihong Zhao (University of California Merced, United States), Ling Xue (Harbin Engineering University, China), Suzanne Sindi (University of California Merced, United States)
Note: this minisymposia has multiple sessions. The second session is MS08-MEPI.

  • Steve Krone (Department of Mathematics and Statistical Sciences, University of Idaho, United States)
    "The Timing and Nature of Behavioral Responses Affect the Course of an Epidemic"
  • During an epidemic, the interplay of disease and opinion dynamics can lead to outcomes that are different from those predicted based on disease dynamics alone. Opinions and the behaviours they elicit are complex, so modelling them requires a measure of abstraction and simplification. Here, we develop a differential equation model that couples SIR-type disease dynamics with opinion dynamics. We assume a spectrum of opinions that change based on current levels of infection as well as interactions that to some extent amplify the opinions of like-minded individuals. Susceptibility to infection is based on the level of prophylaxis (disease avoidance) that an opinion engenders. In this setting, we observe how the severity of an epidemic is influenced by the distribution of opinions at disease introduction, the relative rates of opinion and disease dynamics, and the amount of opinion amplification. Some insight is gained by considering how the effective reproduction number is influenced by the combination of opinion and disease dynamics.
  • Skylar Grey (University of Wisconsin Madison)
    "Contact Tracing during an Ebola Outbreak"
  • Be it Ebola, MERS, or SARS-CoV-2, contact tracing plays a key role in controlling an outbreak. To examine the role of contact tracers, we developed a system of ordinary differential equations to model the 2014-2016 Ebola outbreak in Sierra Leone. In the model we incorporated novel features of counting the total number of people being traced and tying this directly to the number of tracers doing this work. Utilizing data and simulations, we explore the role contact tracing played in eventually ending the outbreak and examine the potential impact of improved contact tracing on the death toll.
  • Lihong Zhao (Department of Applied Mathematics, University of California Merced, United States)
    "Association of Microbiome Dynamics with Chlamydia Infection"
  • Chlamydia trachomatics (C. trachomatics) is a major cause of bacterial sexually transmitted disease in the United States and is associated with adverse outcomes in the upper genital tract of women. It is unclear why some women are more likely to develop asymptomatic infection, have severe infection, or stay uninfected after exposure to C. trachomatics. Prior studies have shown a relationship between vaginal microbial composition and susceptibility to sexually transmitted infections including Chlamydia. However, little is known about the microbiome dynamics, especially in the upper genital tract, and its association with Chlamydia infection. We use mice as a model organism, seek to elucidate the association of genital tract microbiome dynamics with Chlamydia infection, and determining whether the time of infection affects the genital tract microbiome over time via analyzing the data collected before and over the course of infection.
  • Xiaotian Wu (College of Arts and Sciences, Shanghai Maritime University, China)
    "Modelling Triatomine Bug Population and Trypanosoma Rangeli Transmission: Co-feeding, Pathogenic Effect and Linkage with Chagas Disease"
  • A parasite of Trypanosoma rangeli is not pathogenic to human but pathogenic to the same vector species of Chagas disease. This parasite can induce the behavior changes of the infected vectors and subsequently impact the transmission dynamics of Chagas disease. In this talk, a mathematical model incorporating both systemic and co-feeding transmission routes and accounting for the pathogenic effect using infection-induced fecundity and fertility change of the triatomine bugs is presented. In terms of basic reproduction numbers R_v and R_0, the dynamical behaviors of the ecological and epidemiological systems are characterized. Moreover, when both R_v and R_0 are greater than unity, a unique parasite positive equilibrium E* appears which can be unstable and periodic oscillations can be observed where the pathogenic effect plays a significant role.

Models of COVID-19 Vaccination, Non-Pharmaceutical Interventions, and Relaxation

Organized by: Jane Heffernan (York University, Canada), Miranda Teboh Ewungkem (Lehigh University, USA), Zhilan Feng (Purdue University, USA), John Glasser (Centres for Disease Control, USA)
Note: this minisymposia has multiple sessions. The second session is MS16-MEPI. The third session is MS20-MEPI.

  • Bruce Mellado (University of Witwatersand, South Africa)
    "Modelling the COVID-19 pandemic in South Africa: the role of AI"
  • In this presentation work performed by the Gauteng Province Premier COVID-19 Advisory Committee in data analysis, modelling, predictions and vaccine roll-out straggles. The use of Artificial Intelligence through Machine Learning in devising smart algorithms will be highlighted. The challenges of interfacing advanced analytics with advising policy-makers will also be discussed.
  • Ellen Brooks Pollock (University of Bristol, England)
    "Mapping social distancing measures to the reproduction number during vaccine rollout"
  • Background: In the absence of a vaccine, SARS-CoV-2 transmission has been controlled by preventing person-to-person interactions via social distancing measures. As vaccination is rolled out and social distancing restrictions are lifted, policy-makers need to consider how combinations of measures will affect transmission and understand the trade-offs between them. Methods: We use age-specific social contact data collect in the UK in 2010, together with epidemiological data, to quantify the components of the COVID-19 reproduction number. We estimate the impact of social distancing policies and vaccination rollout on the reproduction number in the UK. Results: We demonstrate that pre-collected social contact data can be used to provide a time-varying estimate of the reproduction number (R). Transmission associated with primary schools is predicted to have a smaller impact on community prevalence than transmission in secondary schools. Prioritising older age groups for vaccination leads to modest initial indirect benefits of vaccination. Some levels of contact tracing and COVID security are required until the majority of the adult population are vaccinated. The results can be explored at Conclusions: Our approach has been widely used by policy-makers to project the impact of social distancing measures and assess the trade-offs between them. Effective social distancing, contact tracing and COVID-security are required while vaccination is rolled out.
  • Nick Golding (Curtin University, Australia)
    "Real-time tracking and forecasting of COVID-19 transmission potential in Australia"
  • The Australian COVID-19 pandemic experience has been characterised by long periods of no transmission interspersed with localised, and mostly small outbreaks linked to spillover from quarantine facilities for international arrivals. COVID-19 preparedness and response decision making in Australia has therefore been focused on the potential for outbreaks to take-off and the likely impact of interventions on preventing that. However in the absence of cases, standard models for estimating the reproduction rate of the virus cannot be used. We will detail a novel semi-mechanistic Bayesian statistical model developed to track COVID-19 transmission potential in Australia over time. This quantity can be tracked even in the absence of cases by drawing on mobility data streams, behavioural surveys, and data on health surveillance systems. The effects of lockdowns, varying adherence to hygiene measures, age-structured vaccination roll-out, variants with different transmissibility, and the effectiveness of health surveillance systems are all explicitly considered. This model is able to track the potential rate of transmission in the absence of cases, the realised rate of transmission in the presence of cases, and to move smoothly between these metrics. A particular advantage of this approach for the Australian context is the ability to derive estimates of transmission rates in the very early stages of an outbreak, when numbers of cases are still in the single figures. This model has informed the Australian response to COVID-19 throughout the pandemic - as discussed in a separate talk by Dr Freya Shearer at this conference.
  • Wilfred Ndifon (African Institute for the Mathematical Sciences, South Africa)
    "Vaccinating to Minimize COVID-19 Morbidity"
  • The morbidity caused by an acute infectious disease like COVID-19 is frequently measured only with respect to the short-term effects of infection. We consider an important longer-term effect, namely the deterioration of immune functioning due to accelerated senescence of pathogen-responsive T cells. Using both mathematics and data, we argue that this type of immune deterioration is negligible in young adults but substantial in older adults. A consideration that emerges in the current context of a limited COVID-19 vaccine supply is how to optimize vaccination in order to minimize such immune deterioration. We show that, compared to alternative vaccination strategies, prioritizing older adults as well as individuals who have an already significantly deteriorated immune functioning is optimal. Because, as we argue using data, the severity of SARS-CoV-2 infections increases with immune deterioration, this vaccination strategy would also save the most lives. Our mathematical framework offers a natural explanation for the higher risk of SARS-CoV-2 infection-induced death that has been observed in men compared to women.

Modeling containment and mitigation of COVID-19: experiences from different countries worldwide

Organized by: Andrei Akhmetzhanov (National Taiwan University College of Public Health, Taiwan), Natalie Linton (Hokkaido University, Japan)
Note: this minisymposia has multiple sessions. The second session is MS15-MEPI.

  • Michael Hochberg (Institute for Evolutionary Sciences, University of Montpellier, France)
    "Modeling COVID-19: Seeing the forest for the trees"
  • Given the pace of SARS-CoV-2 outbreaks, epidemiologists and mathematical biologists have had to apply their expertise in real time to understand COVID-19 epidemiology, sometimes modify traditional SEIR models, and evaluate how mitigation and suppression measures might impact outbreaks. This has produced a wide variety of mathematical and statistical models, from the overly simple to the extremely complex. I discuss the pros and cons of employing simple SEIR models for COVID-19 dynamics, and how simple but important constructs are often missed by more complex models. I then turn to how an SEIR model of intermediate complexity produces a rich range of outcomes when coupled with the optimization of stay-in-place decisions. These studies show how intuition and models combine to increase simulation and forecasting accuracy, and are integral in developing more effective control strategies.
  • Natalie Linton (Hokkaido University, Kyoto University, Japan)
    "Variation in serial interval distribution among reported cases in Japan"
  • This study looks how the serial interval of coronavirus disease 2019 (COVID-19) cases in Japan changed over time during 2020 and assesses whether differences in the length of the serial interval exists based on age, sex, and transmission context. We collected publicly reported data on cases in Japan and determined 758 likely transmission pairs based on the types and timings of exposures. The serial interval for pairs detected during the second wave and third waves of COVID-19 transmission in Japan was shorter than the serial interval of cases detected in the first wave. Serial interval length did not vary greatly by sex or transmission context, however serial intervals tended to be a bit shorter when infectors were under 30 years of age and when secondary transmission occurred in a household setting. Accounting for shortening of the serial interval compared to estimates from early in the pandemic may improve inference of transmission dynamics.
  • Robin Thompson (University of Warwick, U.K.)
    "Inferring the effectiveness of interventions during infectious disease outbreaks"
  • The effectiveness of interventions is assessed in real-time during outbreaks to guide public health policy. Estimates of quantities such as the time-dependent reproduction number and the epidemic growth rate help to provide a picture of an ongoing outbreak, alongside data describing incidence of cases, hospitalisations and deaths. In this talk, I will present a simple method for estimating the time-dependent reproduction number using disease incidence time series and an estimate of the serial interval distribution (the times between successive cases in chains of transmission). I will demonstrate some extensions of the simple method (including accounting for differences between infected individuals who acquired the pathogen locally and imported cases),and describe some challenges for improving estimates of the time-dependent reproduction number going forwards. Since, as described in another talk in this session, serial intervals can change during an outbreak, a key challenge is including up-to-date estimates of the serial interval (or generation time) when estimating the time-dependent reproduction number.
  • Sumire Sorano (London School of Hygiene and Tropical Medicine, U.K.)
    "The impact of COVID-19 from social and gender perspectives in Japan"
  • COVID-19 pandemic disproportionately affected vulnerable populations, revealing the weakness of society in the world. According to the Ministry of Health, Labor and Welfare in Japan, the number of suicides nationwide in 2020 exceeded 21,000, marking the first increase since 2009. While the number of male suicides decreased, female suicides showed a marked increase (6091 in 2019 to 7026 in 2020; an increase by 15%), especially among young age (44% increase among girls below 20 years and 32% increase among women in their 20s). Unemployment and economic hardship during COVID-19 pandemic affected women harder. and there was an increased concerns over unintended pregnancy as domestic violence and sexual violence increased. This presentation overviews the impact of COVID-19 from social and gender perspectives in Japan.

Vector-borne Diseases: Data, Modeling, and Analysis

Organized by: Jing Chen (Nova Southeastern University, United States), Shigui Ruan (University of Miami, United States), Xi Huo (University of Miami, United States)
Note: this minisymposia has multiple sessions. The second session is MS06-MEPI.

  • Rongsong Liu (University of Wyoming, United States)
    "Using Multiple Dose Pharmacokinetic Models to Predict Bioavailability of Toxins in Vertebrate Herbivores"
  • In the presented work, compartmental pharmacokinetic models are built to predict the concentration of toxic phytochemical in the gastrointestinal tract and blood following oral intake by an individual vertebrate herbivore. The existing single and multiple dose pharmacokinetic models are extended by inclusion of impulsive differential equations which account for an excretion factor whereby unchanged toxins are excreted in the feces due to gastrointestinal mobility. An index α is defined to measure the fraction of bioavailability attributed to the excretion factor of gastrointestinal motility. Sensitivity analysis was conducted and suggests, for any toxin, the bioavailability index α depends mostly on absorption rate of toxin from gastrointestinal tract into the blood, frequency of elimination due to gastrointestinal motility, and the frequency of toxin intake, under the model assumptions.
  • Yanyu Xiao (University of Cincinnati, United States)
    "Examine the dehydration effects on the behaviours of insects"
  • Current insights into the mosquito dehydration response rely on studies that examine specific responses but ultimately fail to provide an encompassing view of mosquito biology. Here, we examined underlying changes in the biology of mosquitoes associated with dehydration. Specifically, we show that dehydration increases blood feeding in the northern house mosquito, Culex pipiens, which was the result of both higher activity and a greater tendency to land on a host. Similar observations were noted for Aedes aegypti and Anopheles quadrimaculatus. RNA-seq and metabolome analyses in C. pipiens following dehydration revealed that factors associated with carbohydrate metabolism are altered, specifically the breakdown of trehalose. Suppression of trehalose breakdown in C. pipiens by RNA interference reduced phenotypes associated with lower hydration levels. Lastly, mesocosm studies for C. pipiens confirmed that dehydrated mosquitoes were more likely to host feed under ecologically relevant conditions. Disease modeling indicates dehydration bouts will likely enhance viral transmission. This dehydration-induced increase in blood feeding is therefore likely to occur regularly and intensify during periods when availability of water is low.
  • William Fitzgibbon (University of Houston, United States)
    "Mathematical Models for the Spatio Temporal Spread of Vector Born Disease in Highly Heterogeneous Domains: Part I"
  • This is a sequenced pair of talks. Part I will be given by the first alphabetically listed author and Part II will be given by the second alphabetically listed author. We are witnessing a global resurgence of vector-borne disease. The term vector-borne disease (VBD) refers to infectious disease that is transmitted between humans or and various animal species and vector arthropods (typically, mosquito, ticks, flies, mites). Among humans they can be potentially fatal and frequency feature a high level of morbidity. They also pose a major threat to livestock and wildlife. Common VBD’s affecting humans are malaria, dengue, yellow fever, Lyme disease, Zika, West Nile Virus, and of course the infamous plague. VBD’, perhaps less widely known than their human counterparts, include screwworm, blue tongue disease, cattle fever, equine encephalitis, and akabane. In these talks we will present a suite of distributed parameter models that describe the spatio-temporal spread of vector born disease. We will pay particular attention issues modelling and analytical issues associated with the incorporation of a high degree of spatial heterogeneity. Part I will focus primarily upon the development of the models while Part II will focus upon analytical issues and challenges presented by models involving this level of complexity.
  • Jeffrey Morgan (University of Houston, United States)
    "Mathematical Models for the Spatio Temporal Spread of Vector Born Disease in Highly Heterogeneous Domains: Part II"
  • This is a sequenced pair of talks. Part I will be given by the first alphabetically listed author and Part II will be given by the second alphabetically listed author. We are witnessing a global resurgence of vector-borne disease.  The term vector-borne disease (VBD) refers to infectious disease that is transmitted between humans or and various animal species and vector arthropods (typically, mosquito, ticks, flies, mites).  Among humans they can be potentially fatal and frequency feature a high level of morbidity.  They also pose a major threat to livestock and wildlife.  Common VBD’s affecting humans are malaria, dengue, yellow fever, Lyme disease, Zika,  West Nile Virus, and of course the infamous plague.  VBD’, perhaps less widely known than their human counterparts, include screwworm, blue tongue disease, cattle fever, equine encephalitis, and akabane. In these talks we will present a suite of distributed parameter models that describe the spatio-temporal spread of vector born disease. We will pay particular attention issues modelling and analytical issues associated with the incorporation of a high degree of spatial heterogeneity. Part I will focus primarily upon the development of the models while Part II  will focus upon analytical issues and challenges presented by models involving this level of complexity. 

Celebrating Dr. Ngwa's 55th birthday with talks honoring his mathematical modeling work including malaria mosquitoes.

Organized by: Miranda Teboh-Ewungkem (Lehigh University, United States), Calistus N. Ngonghala, (University of Florida, Gainsville, FL, United States), Jude D. Kong (York University, Toronto, ON, Canada,, Canada)
Note: this minisymposia has multiple sessions. The second session is MS07-MEPI.

  • Ian Frigaard (University of British Columbia, Canada)
    "Yield stress fluids and G.A. Ngwa"
  • Yield stress fluids have broad applications in industrial and geophysical flows, ranging from food processing to industrial slurries and river-bed mud. They also come into play biologically in the lung pathways, in mammalian reproduction, in mucus barriers and in blood flow. Here we review key dynamical features of these fluids, difficulties in application and their biological relevance.
  • Abba B. Gumel (Arizona State University, School of Mathematical and Statistical Sciences, United States)
    "Mathematics of population biology of malaria mosquitoes and disease: a genetic-epidemiology modeling framework"
  • Malaria, a deadly infectious disease caused by the Plasmodium parasite transmitted to humans via the bite from infected adult female Anopheles mosquitoes, continues to exude significant public health and socio-economic burden globally (causing over 200 million cases and in excess of 400,000 deaths annually). In his pioneering work on modeling population abundance of mosquitoes, G. Ngwa noted, in the early 1990s, that deep understanding of the population dynamics of mosquitoes is very crucial to providing insight and understanding on the transmission dynamics and control of the diseases they cause. In line with the Ngwa ``follow the mosquito' philosophy, I will present mathematical models, mostly of the form of genetic-epidemiology, deterministic system of nonlinear differential equations, for understanding the population ecology and control of malaria mosquitoes and disease, using insecticide-based and biological interventions. We will explore the feasibility of achieving the concerted global effort to eradicate malaria by 2040 using currently available mosquito control and management strategies.
  • Gwendolyn B. Fru (University of Buea, Cameroon)
    "Mathematical modelling of the pharmacokinetics of antimalarial drugs under different treatment regimes"
  • Mathematical models are used to study how antimalarial drugs interact with the human body when administered through different modes. The developed models capture the parameters which identify with the way antimalarial drugs cure humans during treatment. Drug administration by intravenous infusion and oral therapy are considered, with the classification of antimalarial drugs into two categories; drugs which exhibit their antimalarial activity in their primary form and drugs which together with their metabolites exhibit antimalarial activity. The models also consider the drug concentration in the different compartments comprising the gut (solely in the case of oral administration of drug), plasma and red blood cells, with the considerations of drug diffusing out of the red blood cells solely as byproducts of metabolism and in another case, diffusing both as byproducts of metabolism and in their original form. Results display the variations in drug concentrations in the respective compartments when the drugs are administered. A simple within human host model for the Plasmodium parasite is developed and treatment is eventually added to the model giving a Drug Model. It is shown that both in the Drug - free and Drug Models, the disease free steady state always exists and is globally stable. The disease steady state of the Drug Model is parameterized as functions of drug concentration in the infected red blood cells, and it is shown that if drug concentration in the infected red blood cells exceed the minimum therapeutic level the densities of the infected red blood cells as well as the free floating parasites vanish. Thus curing of the infection has taken place.
  • Kristan Alexander Schneider (Hochschule Mittweida, University of Applied Sciences, Germany)
    "Modelling COVID-19 in Africa"
  • With the massive COVID-19 crisis in India, worries were raised that Africa could be affected similarly in the near future. More infectious SARS-CoV-2 variants that are more likely to cause symptomatic episodes in younger people and are emerging and spreading. This is particularly dangerous since some of the approved vaccines do not properly immunize against new variants. Hence, such mutations have potentially catastrophic effects for the African continent, characterized by a young population. Predictive SEIR models can be employed as decision support tools for COVID-19 management. Realistic models, applicable for the African continent, must take the age and spatial structures of the countries into account as well as the possibilities of different viral variants and available vaccines. Here, we introduce an age and spatially stratified COVID-19 model that explicitly takes the age-dependent contact behavior, different SARS-CoV-2 variants, and vaccination strategies into account.

Modeling containment and mitigation of COVID-19: experiences from different countries worldwide

Organized by: Andrei Akhmetzhanov (National Taiwan University College of Public Health, Taiwan), Natalie Linton (Hokkaido University, Japan)
Note: this minisymposia has multiple sessions. The second session is MS12-MEPI.

  • Jonathan Dushoff (McMaster University, Canada)
    "Defining, estimating and applying transmission-interval distributions"
  • The spread of epidemics is structured by delay distributions, including the now-famous “serial interval” between the symptom-onset times of an infector and an infectee (often conflated with the “generation interval” between infection times). Defining these time distributions clearly, and describing how they relate to each other, and to key parameters of disease spread, poses interesting theoretical and practical questions, some of which are still open. I will discuss how transmission intervals link the “speed” and “strength” of epidemics, issues in their estimation, and their role in helping monitor changes in the parameters underlying the spread of COVID-19 disease.
  • Sarah Kada (Centers for Disease Control and Prevention (CDC), U.S.A.)
    "Early assessment of SARS-CoV-2 controllability with contribution of asymptomatic and pre-symptomatic individuals"
  • Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the infectious agent responsible for coronavirus disease 2019 (COVID-19), is readily transmitted person to person. Optimal control of COVID-19 depends on directing resources and health messaging to mitigation efforts that are most likely to prevent transmission. We used an analytical model to assess the proportion of SARS-CoV-2 transmissions in the community that likely occur from persons without symptoms. This model assessed the relative amount of transmission from pre-symptomatic, asymptomatic, and symptomatic individuals across a range of scenarios in which the proportion of transmission from people who never develop symptoms (i.e., remain asymptomatic) and the infectious period were varied according to published best estimates. We used multiple scenarios of proportions of asymptomatic individuals with COVID-19 and infectious periods to estimate that transmission from asymptomatic individuals most likely accounted for more than half of all transmissions. In addition to identification and isolation of persons with symptomatic COVID-19, effective control of spread therefore require reducing the risk of transmission from people with infection who do not have symptoms. These findings suggested that measures such as wearing masks, hand hygiene, social distancing, and strategic testing of people who are not ill would be foundational to slowing the spread of COVID-19 until safe and effective vaccines are available and widely used.
  • Hao-Yuan Cheng (Epidemic Intelligence Center, Taiwan CDC, Taiwan)
    "Experience of COVID-19 elimination in Taiwan"
  • In my presentation I will review prevention and control measures against COVID-19 spread in Taiwan that have been centered on stringent border control, obligatory quarantine of all incoming travelers, and intensified contact tracing.
  • Ta-Chou Ng (National Taiwan University, Taiwan)
    "Comparison of Estimated Effectiveness of Case-Based and Population-Based Interventions on COVID-19 Containment in Taiwan"
  • Taiwan is one of the few countries with initial success in COVID-19 control without strict lockdown or school closure, yet reasons remain to be fully elucidated. This comparative effectiveness study evaluated the effectiveness of case-based (including contact tracing and quarantine) and population-based (including social distancing and facial masking) interventions for COVID-19 in Taiwan. We used a stochastic branching process model using COVID-19 epidemic data from Taiwan for model development and calibration. Effective reproduction number of COVID-19 cases and the probability of outbreak extinction were used to evaluate the effectiveness of each combination of interventions. Case detection, contact tracing, and 14-day quarantine of close contacts (regardless of symptoms) was estimated to decrease the reproduction number from the counterfactual value of 2.50 to 1.53 (95% CrI 1.50-1.57), which would not be sufficient for epidemic control, which requires a value of less than 1. In our estimated analysis, voluntary population-based interventions, if used alone, were estimated to have reduced the reproduction number to 1.30 (95% CrI 1.03-1.58). Combined case-based and population-based interventions were estimated to reduce the reproduction number to below unity (0.85; 95% CrI 0.78-0.89). Results were similar for additional analyses with influenza data and sensitivity analyses. We showed that only the combination of case-based and population-based interventions (with wide adherence) may explain the success of COVID-19 control in Taiwan in 2020. Either category of interventions alone would have been insufficient, even in a country with an effective public health system and comprehensive contact tracing program. Mitigating the COVID-19 pandemic requires the collaborative effort of public health professionals and the general public. Full article is available at:

Models of COVID-19 Vaccination, Non-Pharmaceutical Interventions, and Relaxation

Organized by: Jane Heffernan (York University, Canada), Miranda Teboh Ewungkem (Lehigh University, USA), Zhilan Feng (Purdue University, USA), John Glasser (Centres for Disease Control, USA)
Note: this minisymposia has multiple sessions. The second session is MS11-MEPI. The third session is MS20-MEPI.

  • Jeff Shaman (Columbia University, USA)
    "Overall Burden and Characteristics of COVID-19 in the US"
  • The COVID-19 pandemic disrupted health systems and economies throughout the world during 2020 and was particularly devastating for the United States, which experienced the highest numbers of reported cases and deaths during 2020. Many of epidemiological features responsible for observed rates of morbidity and mortality have not been comprehensively quantified. Here we use a data-driven model-inference approach to simulate the pandemic at county-scale in the United States during 2020 and estimate critical, time-varying epidemiological properties underpinning the dynamics of the virus, in particular the ascertainment rate, population susceptibility, community infection rates and the infection fatality rate. The results provide a county-resolved depiction of conditions until the end of 2020 when COVID-19 vaccine administration began. The implications for ongoing control of the virus are also investigated.
  • David Dick (York University, Canada)
    "A Model of COVID-19 Vaccination and Waning Immunity in Canada"
  • We have developed an age- and immunity-structured model of COVID-19 infection and vaccination. The model assumes rates of waning immunity from infection and vaccination. It also includes different non-pharmaceutical interventions, including work-from-home, school closure, social distancing and mask wearing. In this talk I will discuss different outcomes of a Canadian-informed COVID-19 vaccination program given different types of vaccines and rollout strategies. I will also discuss scenarios for relaxation and mitigation strategies needed to inhibit a Fall 2021 resurgence.
  • Toby Brett (University of Georgia, USA)
    "How mathematical modeling reveals the impracticality of COVID-19 herd immunity strategies"
  • Confronted with escalating COVID-19 outbreaks, countries at the leading edge of the pandemic have resorted to imposing drastic social distancing measures, with serious societal and economic repercussions. Establishing herd immunity in a population by allowing the epidemic to spread, while mitigating the negative health impacts of COVID-19, has presented a tantalizing resolution to the crisis. Using an ODE-based transmission model, parameterized to simulate SARS-CoV-2 transmission in the United Kingdom, we assessed the long-term prospects of achieving herd immunity without mass vaccination. We studied a range of different nonpharmaceutical intervention scenarios incorporating social distancing applied to differing age groups using a combination of numerical simulations and analytical techniques. Our modeling confirmed that suppression of SARS-CoV-2 transmission is possible with plausible levels of social distancing over a period of months, consistent with observed trends. Our findings show that achieving herd immunity without overwhelming hospital capacity leaves little room for error. Intervention levels must be carefully manipulated in an adaptive manner for an extended period, despite acute sensitivity to poorly quantified epidemiological factors. Specifically, we found that 1) social distancing must initially reduce the transmission rate to within a narrow range, 2) to compensate for susceptible depletion, the extent of social distancing must be adaptive over time in a precise yet unfeasible way, and 3) social distancing must be maintained for an extended period to ensure the healthcare system is not overwhelmed. Such fine-tuning of social distancing renders this strategy impractical.
  • Daniel Larremore (University of Colorado, USA)
    "Vaccine prioritization strategies with age, serostatus, and immunosenescence"
  • Limited initial supply of SARS-CoV-2 vaccine raised the question of how to prioritize available doses. One might reason, intuitively, that doses should be prioritized to directly protect those who are most vulnerable. Yet one might also intuitively argue that we should use vaccination as a means to break chains of transmission by prioritizing early doses to those most responsible for transmission, thereby indirectly protecting the vulnerable by reducing prevalence. Unfortunately, these two intuitive solutions make orthogonal recommendations. Here, we introduce a family of mixed discrete and differential equation models to resolve the tension between these recommendations, and compare five age-stratified vaccine prioritization strategies. By considering the demographics and contact patterns in the country of interest, transmission rates, vaccine properties, and the accumulated immunity in the population due to prior infection with SARS-CoV-2, we show how one can use differential equation models to quantify the tradeoffs between vaccine rollout strategies in a context-specific ways. We also highlight ways in which these models can help ameliorate existing pandemic-related inequities in access to healthcare and protection. In this talk, we will cover both the high-level results and recommendations, as well as vaccine-related modeling choices that complicate the more typical and standard 'SIR' type disease model.

Modelling the transmission of COVID-19 in indoor spaces

Organized by: Raquel González Fariña (Cardiff University, United Kingdom), Katerina Kaouri (Cardiff University, United Kingdom)

  • Christian Kähler (Universität der Bundeswehr München, Germany)
    "From droplets to pandemic – how to prevent SARS-CoV-2 infections via droplets and aerosols"
  • The SARS-CoV-2 pandemic is currently presenting humanity with major challenges. Containing the spread of the virus requires enormous financial, technical and social efforts, and it is impossible to predict how well humanity will cope with the problem. Since the infectious disease not only has an acute course, but can also cause long-lasting systemic damage to infected individuals, prevention of infection is most important. It is generally accepted that the transmission of viruses is largely via droplets and aerosol particles. Therefore, the question of how these aerosol particles are generated and released and how they spread through the room and cause infection is particularly important to answer. Next, there is the question of how to best protect against infection. The answer to this question depends on the areas for which protection is to be established, because different protective measures have to be taken in a pedestrian zone than in buses and trains or in offices, schools and restaurants. To address these two problems, the first part of the talk will present the formation of aerosol particles in the body, their ejection by breathing, speaking, singing and coughing, and their dispersion in space. In the second part, the effectiveness of different protective measures is analyzed experimentally using laser based measurement data. In particular, the effectiveness of different masks for individual protection, as well as the usefulness of room air cleaners and protective walls, is demonstrated quantitatively. A deeper understanding of the spread processes and the protection options is imperative to effectively limit the spread of the pandemic and thus the costs for the state, the economy and society. Whether society is finally ready to protect itself effectively depends on the insight of the population, but also on the way the measures are implemented politically. This will also be discussed during the lecture, because this pandemic can only be contained if science, technology, politics and the population pull together.
  • Chenfeng Li (Swansea University, United Kingdom)
    "CFD simulation of airborne virus transmission aided by a machine learning surrogate model"
  • In this study, the airborne virus transmission is investigated using computational fluid dynamics simulation. The study is carried in three steps. First, a standard boxroom scenario is considered, and different conditions in relation to the door, window and mechanical ventilation are investigated using OpenFOAM, a well-established CFD simulator. The resulting data are organized a series of relation curves to reveal the sensitivity of virus transmission with respect to the change of ventilation conditions. Next, a machine-learning based surrogate model is constructed from the simulation data obtained from the first step. The experiment shows at an acceptable level of accuracy, the surrogate model can quickly predict the flow field and the associated airborne virus transmission for the boxroom scenario at different environmental and ventilation conditions. In the last step, the study focuses on the impact of having people in the room. To achieve this, a coupled CFD-DEM approach is adopted, where the air flow is captured by the CFD solver, and the moving objects are captured by the DEM (discrete element method) solver. The two solvers are fully coupled, representing accurately the influence of people on the air flow, thereby the airborne virus transmission. In all these studies, we assume the virus particles are sufficiently small, such that they do not have a significant impact on the air flow and merely get transported by the air. The information obtained this investigation quantify the relative risks of virus transmission with respect to changing environmental and ventilation conditions, as well as the impact from human activities.
  • Simon Parker (Defence Science and Technology Laboratory, United Kingdom)
    "Transmission of virus in carriages - development of a multiroute viral exposure model for public transport"
  • Understanding the potential exposure of passengers during the use of public transport is of particular interest for transport planning. The Transmission of Virus on Carriages model has been developed to address this need. This stochastic model estimates passenger exposure to SARS-CoV-2 on an underground train carriage via three routes: close range droplet, small aerosol and surface contact. Passenger input data reflects realistic ridership at different stations on the journey. In addition to the effect of ventilation details, the effect of airborne and surface viral decay and surface deposition are accounted for. Touching of high-touch surfaces within the carriage is included and is used to study the transfer of fomite contamination between surfaces and passengers. Variation in passenger density throughout a journey contributes to different close range exposures. Stochastic representation of infectious passenger boarding and other events allow the model to be used to explore key parameters such as disease prevalence in the travelling population, carriage loading and adherence to mask wearing rules. The results from the model clearly show the relative importance of different routes of exposure and the value of different mitigation measures. Future work is focused on improving the representation of multiple respiratory activities and on extending the model to other types of public transport.
  • Raquel González Fariña (Cardiff University, United Kingdom)
    "Predicting the spatiotemporal risk of airborne infection in indoor spaces using an advection-diffusion-reaction equation"
  • Probabilistic models for indoors airborne transmission of viruses, such as the Wells-Riley model (Riley et al., 1978) and its extensions applied to COVID-19, for example (Buonanno et al., 2020), assume that the concentration of infectious particles in the room is uniform in space. We have developed a spatially dependent generalisation to such models to determine the infection risk in indoor spaces. We model the concentration of airborne infectious particles using an advection-diffusion-reaction equation where the particles are emitted by an infected person, advected by airflow, diffused due to turbulence, and removed due to the room ventilation, biological inactivation of the virus and gravitational settling. The model is quasi-three-dimensional and incorporates a recirculating flow due to air-conditioning. We are able to obtain a semi-analytic solution which allows for very fast simulations. An important aspect of our work is that we include realistic particle size distributions. We consider that the particle emission rate and the gravitational settling rate depend on the size of the particles. Most airborne transmission models only account for a single particle size and, thus, assume a constant settling rate. We find that this simplifying assumption may significantly alter the predicted infection risk in a room. We also quantify the effect of several ventilation settings and different activities such as breathing, talking and coughing, on the particle concentration and the infection risk. Finally, we determine the time to probable infection (TTPI), at any location in a room, paving the way for formulating recommendations. Good agreement with CFD models and existing data is obtained.

Women in Mathematical Epidemiology

Organized by: Katharine Gurski (Howard University, United States), Kathleen Hoffman (University of Maryland, Baltimore County, United States)
Note: this minisymposia has multiple sessions. The second session is MS19-MEPI.

  • Zhilan Feng (Purdue University, United States)
    "Applications of mathematical models in epidemiology"
  • Mathematical modeling of infectious diseases has affected disease control policy throughout the developed world. Policy goals vary with disease and setting, but preventing outbreaks is common. In this talk, I will present several examples to demonstrate how various models can be used to answer questions related to disease control and prevention for specific diseases in real populations. These models are systems of integral and/or differential equations. The mathematical results are motivated to address specific biological questions.
  • Marissa Renardy (Applied BioMath, United States)
    "Structural identifiability analysis of PDEs: A case study in continuous age-structured epidemic models"
  • Identifiability analysis is crucial for interpreting and determining confidence in model parameter values and to provide biologically relevant predictions. Structural identifiability analysis, in which one assumes data to be noiseless and arbitrarily fine-grained, has been extensively studied in the context of ordinary differential equation (ODE) models, but has not yet been widely explored for age-structured partial differential equation (PDE) models. These models present additional difficulties due to increased number of variables and partial derivatives as well as the presence of boundary conditions. In this work, we establish a pipeline for structural identifiability analysis of age-structured PDE models using a differential algebra framework and derive identifiability results for specific age-structured models. We use epidemic models to demonstrate this framework because of their wide-spread use in many different diseases and for the corresponding parallel work previously done for ODEs. In our application of the identifiability analysis pipeline, we focus on a Susceptible-Exposed-Infected model for which we compare identifiability results for a PDE and corresponding ODE system and explore effects of age-dependent parameters on identifiability. We also show how practical identifiability analysis can be applied in this example.
  • Olivia Prosper (University of Tennessee Knoxville, United States)
    "Within-mosquito parasite heterogeneity and its impact on population-level malaria transmission"
  • The malaria parasite Plasmodium falciparum requires a vertebrate host and a female Anopheles mosquito to complete a full life cycle, with sexual reproduction occurring in the mosquito. This sexual stage of the parasite life cycle allows for the production of genetically novel parasites. In the meantime, a mosquito’s biology creates bottlenecks in the infecting parasites’ development. In earlier work, we developed a stochastic model of within-mosquito parasite dynamics and the generation of parasite diversity within a mosquito. We demonstrated the importance of heterogeneity in parasite dynamics across a population of mosquitoes on estimates of parasite diversity. Here, we investigate the implications of this heterogeneity on population-level transmission dynamics of malaria.
  • Miranda Teboh-Ewungkem (Lehigh University, Lehigh University)
    "Using Continuous-time Systems of Non-Linear Ordinary Differential Equations to study Removal of Mosquito-Breeding Site Density Under Community Action and Temperature Effects"
  • : A system of two first order nonlinear ordinary differential equations is used to model and theoretically investigate the dynamics of the formation of mosquito breeding sites in a uniform environment. The model captures the dynamic interplay between community action, climatic factors, and the availability of mosquito breeding sites. The developed model is analysed using standard methods in nonlinear dynamical systems' theory. Model results show that it is possible to attempt the problem of the dynamics of formation of breeding sites by considering the level of human consciousness as measured through human response to community action. Different feedback response functions are used to excite the breeding site removal and community action. For the case where the response functionals are both constants, we identify an indicator function whose size can indicate whether in the long run, community action can lead to the removal and elimination of breeding sites near human habitats. Using a predictor-corrector procedure that fits real climatic data to a continuous periodic function, we demonstrate how climatic variables can be included in the model and how models for the time variation of temperature and precipitation in a given area can be constructed just by appropriately choosing the parameters of a sinusoidal function and then correcting the output using nonlinear least squares analysis. Numerical simulation results are used to complement our analytical results.

Women in Mathematical Epidemiology

Organized by: Katharine Gurski (Howard University, United States), Kathleen Hoffman (University of Maryland, Baltimore County, United States)
Note: this minisymposia has multiple sessions. The second session is MS18-MEPI.

  • Christina Edholm (Scripps College, United States)
    "Stochastic Models and Superspreaders: Effects of Environmental Variability"
  • The importance of host transmissibility in disease emergence has been demonstrated in historical and recent pandemics that involve infectious individuals, known as superspreaders, who are capable of transmitting the infection to a large number of susceptible individuals. To investigate the impact of superspreaders on epidemic dynamics, we formulate deterministic and stochastic models that incorporate differences in superspreaders versus nonsuperspreaders. In particular, continuous-time Markov chain models are used to investigate epidemic features associated with the presence of superspreaders in a population. We parameterize the models for two case studies, Middle East respiratory syndrome (MERS) and Ebola. In this talk, we will explore how superspreaders and environmental variability impact important epidemiological measures via mathematical analysis and numerical simulations.
  • Angela Peace (Texas Tech University, United States)
    "Spatial influences on Ebola and MERS epidemic dynamics: an agent-based modeling approach"
  • For many communicable diseases, superspreaders are defined as specific infected individuals that transmit disproportionately to more susceptible individuals than other infected individuals, which may result from increased contact with susceptible individuals, higher pathogen shedding or increased strain virulence. Epidemiological studies show that epidemics such as EBOV and MERS were largely driven and sustained by superspreaders that are ubiquitous throughout the outbreak. Hence understanding the dynamics of superspreaders can facilitate devising individually-targeted control measures. Studies have identified host heterogeneity (e.g.,~behavioral and immunological differences), population density and urbanization as underlying factors in disease outbreaks, therefore to capture disease transmission dynamics, we need a spatial modeling approach which can incorporate social phenomenons associated with human interactions. We developed an agent-based model (ABM) for simulating the actions and interactions of autonomous agents (both individual or collective entities such as organizations or groups) during an epidemic. We show that ABMs of infectious disease dynamics can provide additional insights by incorporating individual heterogeneity and spatial information.
  • Carrie Manore (Los Alamos National Laboratory, United States)
    "COVID-19 modeling and forecasting to inform decision makers"
  • We will present mathematical and statistical models for COVID-19 spread and impacts including hospital capacity, case counts, and deaths. Different methods are needed for supporting decision making depending on if we need accurate forecasting or exploration of 'what-if' scenarios. We will show how detailed agent based models, differential equation, and high level statistical models can be used together to support modeling of an ongoing pandemic.
  • Sylvia Gutowska (University of Maryland, Baltimore County, United States)
    "Effects of PrEP on the spread of HIV in the MSM population"
  • talk will describe the convergence-divergence model and discuss some

Models of COVID-19 Vaccination, Non-Pharmaceutical Interventions, and Relaxation

Organized by: Jane Heffernan (York University, Canada), Miranda Teboh Ewungkem (Lehigh University, USA), Zhilan Feng (Purdue University, USA), John Glasser (Centres for Disease Control, USA)
Note: this minisymposia has multiple sessions. The second session is MS11-MEPI. The third session is MS16-MEPI.

  • Melanie Prague (University of Bordeaux, France)
    "Multi-level modeling of COVID-19 epidemic dynamics in French regions, estimating the combined effects of multiple non-pharmaceutical interventions"
  • We developed a multi-level model of the French COVID-19 epidemic at the regional level. We rely on a global extended Susceptible-Exposed-Infectious-Recovered (SEIR) mechanistic model as a simplified representation of the average epidemic process, with the addition of region specific random effects. We estimate region-specific key parameters of epidemics dynamics such as the transmission rate conditionally on the mechanistic model through Stochastic Approximation Expectation Maximization (SAEM) optimization using Monolix software. Using French dataset of hospitalisation in France over a course of one year, we estimate the effect of non-pharmaceutical interventions adjusting for weather, vaccination and apparition of more transmissible variants. The proposed novel methodology, consisting in using population approach to compartmental epidemic models, allows to compare with satisfactory efficiency the different effects of intervention and derive informative epidemics parameters such as region-specific effective reproductive numbers and attack rates.
  • Gerardo Chowell (Georgia State University, USA)
    "Ensemble modeling approaches for forecasting infectious disease spread"
  • The ongoing COVID-19 pandemic presents with an unprecedented opportunity to evaluate the performance of mathematical modeling frameworks for forecasting the trajectory of the pandemic at different spatial and temporal scales. I will present new ensemble modeling approaches that can outperform individual models in short-term forecasts without substantially increasing model complexity.
  • Iain Moyles (York University, Canada)
    "Cost and Social Distancing Dynamics in a Mathematical Model of COVID-19"
  • We present an SEIAR mathematical model of COVID-19 which includes social distancing and relaxation. Our model has a dynamic behavioural influence where the decision for susceptible people to isolate is a function of the total and active cases, but the decision to stop isolating is a function of the perceived cost of isolation. Along with this social distancing cost, we define an overburden healthcare cost due to the strain placed on the healthcare system with a high caseload. We demonstrate that, non-intuitively, increasing either isolation activity or incentive to isolate do not always lead to optimal health outcomes. We further demonstrate that an increase in the frequency of isolation events, each of shorter duration, can lead to improved outcomes compared to sustained isolation activity.
  • Seyed Moghadas (York University, Canada)
    "Effectiveness of COVID-19 Vaccines in the Context of Emerging Variants"
  • Newly emerged SARS-CoV-2 variants represent a challenge for current vaccines as preliminary results suggest increased transmissibility as well as variable levels of cross-reaction depending on the viral strain. These selection advantages along with constraints in vaccine supply and distribution may drive certain immune escape variants to dominance in the near future, hampering the ability of vaccination to control the pandemic. In our research, we utilize dynamic transmission models to evaluate COVID-19 vaccination strategies including evaluating the effects of a delayed second dose and projected the shifting dynamics of viral circulation in the presence of emerging variants.

Sub-group contributed talks

MEPI Subgroup Contributed Talks

  • Michael Irvine Simon Fraser University
    "Quantifying transmissibility of COVID-19 and the impact of intervention in long-term care facilities"
  • Estimates of the basic reproduction number (R0) for Coronavirus disease 2019 (COVID-19) are particularly variable in the context of transmission within locations such as long-term health care (LTHC) facilities. We sought to characterise the heterogeneity of R0 across known outbreaks within these facilities. We used a unique comprehensive dataset of all outbreaks that have occurred within LTHC facilities in British Columbia, Canada. We estimated R0 with a Bayesian hierarchical dynamic model of susceptible, exposed, infected, and recovered individuals, that incorporates heterogeneity of R0 between facilities. We further compared these estimates to those obtained with standard methods that utilize the exponential growth rate and maximum likelihood. The total size of an outbreak varied dramatically, with a range of attack rates of 2%-86%. The Bayesian analysis provides more constrained overall estimates of R0 = 2.83 (90% CrI 0.25--7.19) than standard methods, with a range within facilities of 0.66 - 10.06. We further estimated that intervention led to 67% (56%-73%) of all cases being averted within the LTHC facilities. Understanding the risks and impact of intervention are essential in planning during the ongoing global pandemic, particularly in high-risk environments such as LTHC facilities.
  • Carlo Davila-Payan Centers for Disease Control and Prevention
    "Analysis of the yearly transition function in measles disease modeling"
  • Globally, there were an estimated 9.8 million measles cases and 207,500 measles deaths in 2019. As the worldwide effort to eliminate measles continues, modeling remains a valuable tool for public health decision makers and program implementers. This study presents a novel approach to the use of a yearly transition function to account for the effects of the timing of vaccination (based on vaccination schedules for different age groups) and disease seasonality on the yearly number of measles cases in a given country.Our methodology adds to and expands on the existing modeling framework of Eilertson et al. (Stat. Med. 2019; 38: 4146-4158) by developing explicit functional expressions for each underlying component of the transition function in order to adjust for the temporal interaction between vaccination and exposure to disease. Assumption of specific distributional forms provides multipliers that can be applied to estimated yearly counts of cases and vaccine doses to estimate impacts more precisely on population immunity. These new model features provide the ability to forecast and compare the effects of different vaccination timing scenarios and seasonality of transmission on the expected disease incidence. Although this application is to measles, the method has potential relevance to modeling other vaccine-preventable diseases.
  • Luis Manuel Munoz-Nava Center for Research and Advanced Studies
    "‘Learning Bubbles’ are an effective and safe alternative to schools reopening during the COVID-19 pandemic"
  • According to estimates of the UNESCO, the COVID-19 pandemic has affected more than 1.4 billion (aprox. 84 %) students worldwide. In many countries, schools have remained closed for more than a year and this situation is likely to persist for several additional months before local vaccination programs start to slow down virus propagation. While policymakers debate on how and when children should go back to school buildings, closures are expecting to have a profound and long-term impact in children education, nutrition, social skills, and mental health, as well as in the economy and psychosocial behavior of students and their families. As an alternative to reopening of schools, 'Learning Bubbles' are groups of a few children that their parents voluntarily set-up for in-person instruction either from one of the parents or an external tutor. 'Learning bubbles' were very popular in the United States started remotely the academic year in the Fall of 2020, but to the best of our knowledge, a report on the effectiveness of 'learning bubbles' in mitigating the propagation of the COVID-19 disease has not been analyzed. We developed a mathematical model of 'learning bubbles' and discuss its effectiveness in mitigating the disease compared with schools reopening.
  • Glenn Ledder University of Nebraska-Lincoln
    "A Model for COVID-19 with Limited Vaccination"
  • Now that vaccines for COVID-19 are available and distribution has begun, a critical question arises: To what extent do protective measures need to be maintained as more people are vaccinated? Addressing this question requires careful attention to the way vaccination is incorporated into the model. We augment our SEAIHRD (Susceptible, Exposed, Asymptomatic, (symptomatic) Infectious, Hospitalized, Recovered, Deceased) model by breaking up the susceptible class into a standard (S)usceptible class and a (P)re-vaccinated class, with proportions determined by a vaccine acceptance parameter. Susceptible and pre-vaccinated individuals move to the Exposed through infection in the standard way. In addition, a vaccination process moves individuals directly out of the pre-vaccinated class at a rate that follows a Michaelis-Menten mechanism; that is, the rate is linear when the pre-vaccinated class is small but quickly saturates due to limitations in the distribution speed. The most recent update accounts for prioritization of high-risk people. Most individuals who leave the pre-vaccinated class move into the recovered class, but a small fraction move back to the standard susceptible class, representing the probability of failing to mount a proper immune response. We use the model to investigate the impact of reduced compliance with protective measures.

MEPI Subgroup Contributed Talks

  • Beryl Musundi Technical University of Munich
    "An immuno-epidemiological model linking within-host and between-host dynamics of cholera"
  • Cholera is a severe diarrheal infection caused by the Vibrio cholerae bacterium. It affects millions of people globally with an estimated 2.9 million cases reported annually. In this study, we formulate a multi-scale model linking the between-host and within-host dynamics of cholera to gain new perspectives on the spread of the infection. We conduct a time-scale analysis for the within-host system, where the dynamics of the immune response and the pathogen are differentiated using time scales. The approach used allows for the elimination of the pathogen after a defined time, which is contrary to other within-host models. We use the within-host system as a basis for the formulation of the epidemic model which takes into account direct human-to-human transmission as well as transmission via the environment. The epidemic model is a physiologically structured model based on the immune status, which is a function derived from the within-host immune response. The basic reproduction number is derived and the steady states analysed. Analysis of the endemic equilibrium reveals conditions that may lead to its stability as well as its destabilisation through the occurrence of a Hopf bifurcation. Without loss of immunity, the environmental transmission route is necessary for periodic orbits to occur.
  • Josephine Tetteh Goethe University
    "Modelling Therapy Scheduling Based on the Collateral Susceptibility of Drugs"
  • The development of drug resistance remains a major challenge in the treatment of chronic infections as there are little to no new drugs being discovered and mortality due to such infections are on the increase. To address this, the concept of collateral sensitivity cycling was proposed as a plausible therapy scheduling approach whereby drugs are sequentially used based on their collateral susceptibility profiles. Using control engineering approaches, we develop strategies aimed at minimizing the appearance of drug-resistant pathogens within the host whilst considering their collateral susceptibilities. With a generalized mathematical model based on bacteria population, we develop switching drug strategies which can be used to ensure the stability of the eradication equilibrium. Our numerical simulations compare different switching drug strategies and validate their use for mitigation against bacterial resistance.
  • Dana Kleimeier Institut for Bioinformatics, University Medicine Greifswald
    "Mathematical modeling of 1-MT-induced production of the ant-inflammatory metabolite KYNA in pigs"
  • Treatment with the drug 1-methyltryptophan (1-MT) has been shown to modulate immune responses by targeting several immunologically relevant pathways. One potential mode of action of 1-MT is a shift towards production of the tryptophan (TRP) metabolite kynurenic acid (KYNA), which mediates crucial immunomodulatory effects under inflammatory conditions. It is still unknown whether 1-MT is metabolized to KYNA directly or via intermediate metabolites such as TRP or kynurenine (KYN). To answer this question, this study employs mathematical modeling to evaluate six different hypothetical mechanisms. We developed models based on system of ordinary differential equations, and compare simulations to data measured in an experiment pig model investigating in vivo effects of 1-MT. We in silico evaluate the feasibility of assumptions made by comparing model dynamics with kinetic experimental data, and are thus able to direct further experimental work to the most promising explanatory mechanisms, facilitating further experimental verification. Based on analysis of the computational model, we conclude that a direct degradation of 1-MT to KYNA is the most probable metabolic pathway which best explains the experimentally observed kinetics.
  • Louise Dyson University of Warwick
    "SARS-CoV-2 variants and potential escape from vaccine-derived and pre-existing immunity"
  • The heterogeneity in vaccine coverage both locally and worldwide represents a large potential for SARS-CoV-2 variants that escape existing immunity both from vaccines and prior infections. As countries with high vaccine coverage prepare to relax other control measures, such variants could have a devastating effect. We demonstrate that, even when the variant is less transmissible than the locally dominant variant, reduced immunity can lead to a significant wave of infection. We use an SEIR ODE model of infection with two variants and three potential vaccines, and assume asymmetric immunity granted by prior infection between the two variants. We apply our model to the context in the UK, which had given first doses to 57% of its population by 29th March, with a combination of AstraZeneca and Pfizer vaccines. Initial doses focussed on older age groups and doses were given 12 weeks apart. As of 29th March, cases were dominated by the B.1.1.7 (UK) variant and the primary concern was importations of the B.1.351 (South African) variant. We show that if the B.1.351 variant significantly evades vaccine-derived and prior immunity then planned relaxations could lead to a large wave of B.1.351 infections.

MEPI Subgroup Contributed Talks

  • Harry Saxton Heriot-Watt
    "Considering the effect reinfected asymptomatic individuals have on malaria transmission"
  • In this paper we will consider a mathematical model that aims to better describe the transmissionof malaria. The transmission model is an interaction model between mosquitoes and humans thatdescribes the progress of the infectious disease malaria in the human population. It accounts for thedifferent stages of the disease, showing how the infection develops in both humans and mosquitoes,together with treatment of both sick and partially immune humans. Partially immune humans, whichare termed as asymptomatic, have recovered from the worst stages of the infection, but can still passon the disease to other humans. I will present a mathematical model that consists of a system ofordinary differential equations that describes the evolution of humans and mosquitoes in a range ofdifferent stages of the disease.A new part of the model that I have added, in what turns out to be a key part of the system, is the consideration of asymptomatic humans that have been reinfected again with malaria. Studying the model I will be able to provide a better timeframe in which possible interventions, in the infected region, may produce better results.
  • Nico Stollenwerk BCAM, Basque Center of Applied Mathematics, Bilbao, Spain
    "The interplay between subcritical fluctuations and import: understanding COVID-19 epidemiological dynamics"
  • A question of major importance at this moment in time of the ongoing COVID-19 epidemic is the momentary growth rate (exponential growthwith positive growth factor or restriction to limited spreading subcritically), in the public discussed as momentary epidemiological reproduction ratio above or belowunity. In the presentation we investigate stochastic processes which are in their community spreading still controlled, but close to the epidemiologicalthreshold. Such models show large fluctuations, mimicking variations of reproduction numbers oscillating around the threshold of unity, sometimes below,sometimes above threshold due to large fluctuations expected from theories of percolation. Any transition from susecptible individuals to infected not mediatedby the currently infected persons in the study community, here called 'import', will lead to an epidemiological situation under community control but proneto large subcritical fluctuations. We analyse simple models and transfer the notion to well calibrated models of COVID-19, e.g. in the Basque Country, whereexcellent data can be obtained. Reference: medRxiv preprint doi:, and updates.
  • Alun Lloyd North Carolina State University
    "Honeymoons, Divorces, Flu and Dengue: The Underappreciated Importance of Susceptible Dynamics on Control of Endemics"
  • Modelers of an emerging pathogen can typically assume that a population is entirely susceptible to the infection. In contrast, the dynamics of an endemic infection are highly dependent on the fraction of the population that is susceptible. This has important implications for the short and long-term success of control measures targeting an endemic infection (the ''honeymoon effect'') and can lead to perverse outcomes of transient non-immunizing control measures (the ''divorce effect''). We discuss recent examples of these phenomena in the context of the impacts of non-pharmaceutical interventions aimed at COVID-19 on other directly transmitted respiratory infections, and on the interpretation of large-scale trials of non-vaccine controls of mosquito-borne viral infections.
  • Leonardo Souto Ferreira Universidade Estadual Paulista
    "Assessing optimal vaccination scenarios in two-dose regimen with delay differential equations"
  • We propose and analyse a mathematical model of epidemiological dynamics coupled with vaccination to assess under which conditions delaying the application of the second dose in a two-dose vaccination effort during an ongoing epidemic reduces the number of cases and deaths. We use delay differential equations to accurately describe the timing between doses, and calculate optimal vaccination rate under several scenarios of production and maximum vaccination rates, and initial vaccine storage. Vaccine parameters are based on published second dose efficacy values of three main vaccine platforms - inactivated virus, adenovirus and mRNA - and the key parameter related to first dose efficacy is varied to assess the critical value over which it is better to delay the application of the second dose. We evaluate the dependency of this critical value on vaccine production and maximum rate of vaccination, as well as the initial growth rate of the epidemic.

MEPI Subgroup Contributed Talks

  • Tuğba Akman Yildiz University of Turkish Aeronautical Association
    "Modeling vaccination against COVID-19 in Turkey with effective reproduction number"
  • A mathematical model with the compartments of susceptible, exposed, mildly infected individuals, patients staying in intensive care units (ICUs) and ventilation units is developed and fitted with the daily reported symptomatic cases, deaths, patients staying in ICUs and ventilation units in Turkey for the period 11 March-31 May 2020. Then, this model has been modified after May 31, 2020 due to updated public restrictions and a time-dependent contact rate is derived via the effective reproduction number Rt, which is calculated using the daily reported cases, to capture the dynamics of the outbreak until vaccination. With the start of vaccination on January 13, 2021, the model is extended and COVID-19 outbreak in Turkey is successfully simulated and it is observed that vaccination rate is a more critical parameter than the vaccine efficacy to eliminate the disease successfully.
  • Joshua C. Macdonald University of Louisiana at Lafayette
    "Modeling COVID-19 outbreaks in United States with distinct testing, lockdown speed and fatigue rates"
  • Each state in the United States exhibited a unique response to the COVID-19 outbreak, along with variable levels of testing, leading to different actual case burdens in the country. In this study, via per-capita testing dependent ascertainment rates, along with case and death data, we fit a minimal epidemic model for each state. We estimate infection-level responsive lockdown entry and exit rates (representing government and behavioral reaction), along with the true number of cases as of May 31, 2020. Ultimately we provide error corrected estimates for commonly used metrics such as infection fatality ratio and overall case ascertainment for all 55 states and territories considered, along with the United States in aggregate, in order to correlate outbreak severity with first wave intervention attributes and suggest potential management strategies for future outbreaks. We observe a theoretically predicted inverse proportionality relation between outbreak size and lockdown rate, with scale dependent on the underlying reproduction number and simulations suggesting a critical population quarantine ``half-life'' of 30 days independent of other model parameters.
  • Aurod Ounsinegad Tarleton State University Department of Mathematics
    "Dynamics of Eastern Equine Encephalitis Infection Rates: A Mathematical Approach"
  • The Eastern Equine Encephalitis Virus (EEEV) is an erratic and deadly neurological disease that spans across the northeastern coast of the United States. To determine the rate at which the virus is spread between the Black-Tailed Mosquito (Culiseta melanura) and select avian species we began by analyzing the migration patterns of both the mosquito and the avian species. It was found that certain species of avians shared similar, or even identical, flight patterns with the Black-Tailed Mosquito. Through this research, we develop and analyze a system of Ordinary Differential Equations (ODEs) to gain insight into how and when transmission of the virus to avians is at its highest. We incorporate a host stage-structured model where the avian host group is split into two categories, adults and young-of-the-year birds (YOY). Using this we explored the extent to which fluctuations occurred in transmission rates according to host/vector abundances, mosquito biting rate, and type of host. We evaluate the hypothesis that YOY avians are more readily exposed to the mosquito vector as they lack a defense mechanism, unlike their adult counterpart using the compartmental model.

MEPI Subgroup Contributed Talks

  • Kamuela Yong University of Hawaii - West Oahu
    "A Mathematical Model of the Transmission of Rat Lungworm Disease"
  • The parasite Angiostrongylus cantonensis (AC), known as the rat lungworm hasa complex life cycle that begins when adult worms found in rats reproduce. Larvae exitthe rats through their feces where terrestrial gastropods such as snails and slugsbecome infected after consuming the rat feces. The life cycle is complete when ratsconsume infected snails and slugs. In this paper, we develop a mathematical model torepresent the transmission of AC through its life cycle. Numerical simulations areconducted to determine the factors that have the most impact on the transmission ofAC.
  • Artem Novozhilov North Dakota State University
    "Parametric heterogeneity in epidemiological models and modeling of COVID-19"
  • The theory of heterogeneous populations with parametric heterogeneity is a well developed area of mathematical modeling in biology. We say that our mathematical models describe parametric heterogeneity if we assume that the individuals in populations are heterogeneous with respect to some unchangeable with time parameter, such as birth of death rates or individual's susceptibility to an infectious disease for instance. In particular, the applications of this theory to epidemiological modeling yield very tractable analytically but also quite profound general results (e.g., that the epidemics is always less severe in heterogeneous populations compare to a homogeneous one). Recently, the observed avalanche of data related to the spread of COVID-19 around the world prompted the revival of interest in such heterogeneous models, a number of old results were rediscovered in different contexts, and also new results were obtained. In my talk I aim to present most of the known analytical results about heterogeneous populations with parametric heterogeneity from the general point of theory of heterogeneous populations and also discuss the dangers and pitfalls of applying this theory to the observed data. References: [1] Novozhilov, Math Biosc, 2008; [2] Novozhilov, Math Mod Nat Phen, 2012, Karev and Novozhilov, Math Biosc, 2019
  • Taeyong Lee School of Mathematics and Computing (Mathematics), Yonsei University, Seoul, Republic of Korea
    "The impact of control strategies for COVID-19 in South Korea"
  • The COVID-19 (Coronavirus disease) has spread since the first occurrence on 20 Jan 2020 in South Korea. To mitigate the transmission, KDCA (Korea Disease Control and Prevention Agency) has taken various types of control measures including school-closure and social-distancing. We developed an age-stratified compartmental model considering quarantine and isolation to describe the disease dynamics, which has been calibrated to the newly confirmed data from 20 Jan to 2 Apr 2020. The effectiveness of intervention measures was investigated under several scenarios through the simulation of the proposed model.The results predict that the epidemic threshold for increase of contacts is 1.6 times, which brings the net reproduction number to 1. A second outbreak is expected if the contacts between teenage increase more than 3.3 times when school opens. The reduction of average time until isolation and quarantine from three days to two would decrease cumulative cases by 60% and 47%, respectively. We also study the impact of control strategies considering transmission from asymptomatic or mild symptomatic people, because the infectiousness of those has been controversial.
  • Anjana Pokharel Tribhuvan University Kathmandu, Nepal
    "Modeling the Impact of Vaccination on the Transmission Dynamics of Measles in Nepal"
  • Measles is one of the highly contagious human viral diseases caused by the virus of paramyxovirus family. Despite availability of successful vaccine, measles outbreaks occur presumably due to the lack of compliance of vaccination. In this work, we will develop a deterministic mathematical model that explains the transmission dynamics of measles in Nepal. We will perform the numerical simulation to explore the impact of the vaccinations. We will also explain the qualitative behavior of the model.

MEPI Subgroup Contributed Talks

  • Daniel Sanchez-Taltavull University of Bern
    "Regular testing of asymptomatic healthcare professionals identifies cost-efficient SARS-CoV-2 preventive measures"
  • Protecting health professionals is crucial to maintain a functioning healthcare system. However, little is known about the risk factors affecting healthcare personnel during the COVID-19 pandemic. We implemented a weekly testing regime on the cohort to identify pre- and asymptomatic individuals at a department of Bern University Hospital among a cohort of 330 healthcare professionals. We have developed a mathematical model of SARS-CoV-2 transmission that integrates the infection dynamics among the cohort. We used our model to study how regular testing and a shift work protocol are effective in preventing transmission of COVID-19 infection at work, and compared both strategies in terms of workforce availability and cost-effectiveness. We showed that case incidence among health workers is higher than would be explained solely by community infection. Furthermore, while both strategies are effective in preventing nosocomial transmission, regular testing allows work productivity to be maintained while keeping implementation costs lower than shift work.
  • Emma Southall University of Warwick
    "Time-of-detection: alerting upcoming critical transitions"
  • Early-warning signals are widely used in many fields to anticipate a critical threshold prior to reaching it. A systems undergoes the phenomenon known as critical slowing down as it crosses through a bifurcation. Theory predicts that fluctuations away from the mean will recover more slowly as the system approaches a critical transition. This is key in infectious disease modelling to assess when the basic reproduction number is reduced below the threshold of one. Theoretical advances have shown indicators of critical transitions in epidemiology, such as measuring the rising lag-1 autocorrelation in synthetic disease data. An effective early-warning signal would be able to predict an impending critical transition of this type with a suitable 'lead time' in order to act on the current path of the disease.We validate several empirical studies which offer lead time predictions for ecological and infectious diseases systems when using this theory practice. Our work highlights several challenges when applying lead time methodologies to simulated models. We find poor specificity, falsely reporting a critical transition in simulations at steady state.In this talk we present an extension to these methods and our results show promising potential for calculating early-warning signals of elimination on real-world noisy data.
  • Maira Aguiar Basque Center for Applied Mathematics
    "Modeling COVID19 in the Basque Country: from introduction to control"
  • In March 2020, a multidisciplinary task force (so-called Basque Modelling Task Force, BMTF) was created to assist the Basque health managers and Government during the COVID-19 responses. BMTF is a modelling team, working on different approaches, including stochastic processes, statistical methods and artificial intelligence. Here we describe the efforts and challenges to develop a flexible modeling framework able to describe the dynamics observed for the tested positive cases, including the modelling development steps. The results obtained by a new stochastic SHARUCD model framework are presented. Our models differentiate mild and asymptomatic from severe infections prone to be hospitalized and were able to predict the course of the epidemic, providing important projections on the national health system's necessities during the increased population demand on hospital admissions. Short and longer-term predictions were tested with good results adjusted to the available epidemiological data. We have shown that the partial lockdown measures were effective and enough to slow down disease transmission in the Basque Country. This framework is now being used to monitor disease transmission while the country lockdown was gradually lifted, with insights to specific programs for a general policy of “social distancing” and home quarantining.
  • Kyle Dahlin University of Georgia
    " Predicting reservoirs of mosquito-borne zoonoses: Modelling interactions between temperature and pace of host life history"
  • The “pace” of host life history is an important driver of pathogen transmission dynamics in wildlife populations. Populations of species with a faster pace-of-life (generally associated with more frequent reproduction and a shorter lifespan) are often the most competent reservoirs for zoonoses and present a greater risk of spillover to human populations. However, the role of pace in systems of mosquito-borne pathogen transmission, where temperature also plays a crucial role in the population dynamics of mosquitoes, has not been previously studied. By considering a compartmental model of pathogen transmission, which incorporates important features of mosquito and vertebrate life history, we investigate how temperature and pace interact to determine zoonotic potential in these systems, measured through the basic reproduction number. We determine that the relationship between zoonotic potential, pace, and temperature as predicted by the “pace-of-life” and “warmer-means-sicker” hypotheses occurs only in some cases, depending on how host traits vary with the pace of their life history. Overall, incorporating realistic assumptions about mosquito-host contact rates and variations in host life history, pace and temperature interact in complex ways to drive transmission dynamics.

MEPI Subgroup Contributed Talks

  • Marcelo Eduardo Borges Observatório COVID-19 BR
    "Impact of school reopening and contact tracing strategies in covid-19 epidemiological dynamics in Brazilian capitals"
  • In Brazil, school closure was one of the first interventions adopted to contain the spread of Sars-Cov-2. While maintaining this intervention for an extended period presents increasing social costs, there is a reasonable concern regarding the epidemiological consequences of reopening schools during the pandemic. Here, we model the epidemiological dynamics in scenarios of school reopening for 3 capitals of Brazil, and how mitigation measures such as contact tracing can contribute to reduce the risk of transmissions. We implement an extended SEIR model stratified by age and contact networks at different environments (school, home, work, and others), and the transmission rate is affected by distinct intervention measures. After fitting epidemiological and demographic data, we simulate scenarios of increasing school transmission due to school reopening. The effects of contact tracing strategies in reducing transmission in school contacts are explored. Our results indicate that a flexibilization in the school closure intervention results in a non-linear increase of reported cases and deaths, that is dependent on the previous prevalence of cases in the population. Also, when contact tracing is restricted to school settings, a large number of daily tests are required to produce significant effects in reducing the total number of infections and deaths.
  • Cole Butler North Carolina State University
    "Density-dependence and the effectiveness of gene drives in controlling prevalence of mosquito-borne infections"
  • A gene drive is a genetic mechanism that can spread a gene through a population. Gene drives have the potential to significantly change the way we control vector-borne diseases, most notably dengue and malaria, with mathematical models having demonstrated their potential effectiveness. A key consideration absent from the mathematical modeling literature is the influence of density-dependence on target populations. Density-dependence is a natural ecological process that can counteract population suppression by a gene drive. The purpose here is then to study gene drive performance in a population of mosquitoes with density-dependent characteristics and determine how this affects infectious disease control. We use a mathematical framework in which a model for mosquito population genetics and dynamics is coupled to an epidemiological model. We explore a variety of different scenarios relating to the type of transgene released (e.g. varying sex-specific lethality). We undertake a sensitivity analysis to explore performance over a wide range of scenarios and to identify key parameters that influence the effectiveness of the approach. In each situation, results of system analysis with and without density-dependence is compared, and to what extent such factors influence certain quantities of interest such as disease prevalence in a human population.
  • Jonathan Forde Hobart and William Smith Colleges
    "The tradeoff between sensitivity and frequency in COVID-19 testing"
  • Control strategies that employ real-time polymerase chain reaction (RT-PCR) tests for the diagnosis and surveillance of COVID-19 epidemic are inefficient in fighting the epidemic due to high cost, delays in obtaining results, and the need of specialized personnel and equipment for laboratory processing. Cheaper and faster alternatives have been proposed, which return results rapidly, but are less sensitive in detecting virus. To quantify the effects of the tradeoffs between sensitivity, cost, testing frequency, and delay in test return on the overall course of an outbreak, we built a multi-scale immuno-epidemiological model that connects the virus profile of infected individuals with transmission and testing at the population level. For fixed testing capacity, lower sensitivity tests with shorter return delays slightly flatten the daily incidence curve and delay the time to the peak daily incidence. However, compared with RT-PCR testing, they do not always reduce the cumulative case count at half a year into the outbreak. When testing frequency is increased to account for the lower cost of less sensitive tests, we observe a large reduction in cumulative case counts. We predict that surveillance testing that employs low-sensitivity tests at high frequency can be an effective tool for epidemic control.
  • Iraj Yadegari Postdoctoral fellow
    "Updating the herd-immunity threshold under multiple-vaccine strategies"
  • Several vaccines with different efficacies are currently being distributed across the world to control COVID-19. Having enough doses from the most efficient vaccines in a short time is not possible for all countries. Hence, policy-makers may propose using various combinations of available vaccines to eliminate the disease quickly by achieving herd immunity. The classic herd-immunity threshold suggests that we can eliminate outbreaks from a population by vaccinating a fraction of the population. However, that classic threshold is for a single vaccine and is invalid and biased when we have multiple-vaccine strategies for a disease. Therefore, making decisions for vaccine-allocation policies based on this threshold may be costly. Here, we formulate the problem and find the exact threshold for the case with multiple-vaccine strategies for a single disease and show that there is more than one strategy to achieve herd immunity. Unlike the single-vaccine case, herd immunity can be achieved with an unlimited number of vaccine-allocation policies when multiple vaccines are available. Moreover, we propose methods to find the optimal strategy in a set of multiple-vaccination strategies.

MEPI Subgroup Contributed Talks

  • Wongyeong Choi Department of Mathematics, Soongsil University
    " Mathematical modeling and optimal intervention strategies to control COVID-19"
  • The ongoing outbreak of the novel coronavirus disease (COVID-19) has considerably affected public health and the economy worldwide.Optimizing control measures is urgent given the substantial societal and economic impacts associated with infection and interventions. We established mathematical models to determine the optimal strategies. We used game theory to identify the individually optimal strategy, and optimal control theory to find optimal strategies that minimize the costs associated with infection and intervention. When social distancing and testing with contact tracing are considered as intervention strategies, the results demonstrate that testing should be maintained at a maximum level in the early phases and after the peak of the epidemic, whereas social distancing should be intensified when the prevalence of the disease is greater than 15%. After the peak of the pandemic, it would be optimal to gradually relax social distancing and switch back to testing. Additionally, we identified the individually optimal strategy based on the Nash strategy when social distancing and vaccination are available as control strategies. We determined the relative costs of control strategies at which individuals preferentially adopt vaccination over social distancing (or vice versa).
  • David Wu University of Auckland
    "Likelihood-based estimation and prediction for misspecified epidemic models: an application to measles in Samoa"
  • Prediction of the progression of an infectious disease outbreak in a population is an important task. Differential equations are often used to model an epidemic outbreak's behaviour but are challenging to parametrise. Furthermore, these models can suffer from misspecification, which biases the estimates. In this talk we present our recent work on an explicitly likelihood-based variation of the generalised profiling method as a tool for prediction and inference under model misspecification. Our approach allows us to carry out identifiability analysis and uncertainty quantification using profile likelihood-based methods without the need for marginalisation. Rather than introduce an explicit stochastic process model, generalised profiling uses a deterministic model as an approximately enforced `smoothing penalty' term and uses maximisation rather than integration to handle nuisance parameters. We provide additional justification for this approach by introducing a novel interpretation of the model approximation component as a stochastic constraint, and preserves the rationale for using profiling rather than integration to remove nuisance parameters while still providing a link back to explicitly stochastic models. We present results applying our approach to data from an outbreak of measles in Samoa and show that fast, accurate prediction is possible.
  • Jiyeon Suh School of Mathematics and Computing (Computational Science and Engineering), Yonsei University, Seoul, Republic of Korea
    "Cost-benefit analysis of tafenoquine for the relapse prevention of Plasmodium vivax malaria in South Korea"
  • Plasmodium vivax malaria has not been eradicated in South Korea since 1993 and the government is aiming to grant certification for malaria elimination from the WHO in 2024. P. vivax malaria has a dormant liver-stage, and this can cause relapse. Tafenoquine has been proven to effectively prevent relapse as an alternative to primaquine. In this study, we developed a model for P. vivax malaria using delay differential equations to estimate the impact of tafenoquine introduction on malaria burden. We also conducted a cost-benefit analysis of tafenoquine from the payer's perspective based on the cost and benefit extracted from the national health insurance data and performed probabilistic sensitivity analysis. The results showed that the introduction of tafenoquine could prevent 77.78% of relapse and 12.27% of total malaria cases over 10 years compared to primaquine. And the cost-benefit analysis provided an incremental cost of $13,115 and an incremental benefit of $165,520 resulting in an incremental benefit-cost ratio of 12.26. Furthermore, the sensitivity analysis showed a consistent result with a probability of 98.3%. Hence, the introduction of tafenoquine can reduce the malaria burden and is beneficial over primaquine. These findings support the introduction of tafenoquine to step toward malaria elimination in South Korea.
  • Andrew Nugent University of Warwick
    "Analysing early warning signals of disease elimination by approximating the potential surface"
  • The theory of critical slowing down states that a system displays increasing relaxation times as it approaches a critical transition. Such changes in relaxation times can be seen in statistics generated from data timeseries, which can be used as early warning signals of a transition. While analytic equations have been derived for various early warning signals in a variety of epidemiological models, there is frequent disagreement with the general theory of critical slowing down, with some indicators performing well when used in prevalence data but not when applied to incidence data. We investigate this effect in an SIS model by reconstructing the potential surface for different types of data. By modelling prevalence, incidence and the rate of infection as stochastic differential equations, then using an equation-free method to approximate their drift functions from simulated timeseries, we reconstruct the potential surface for each data type. Slowly varying parameters provides insight into how the shape of the potential surface changes. Analytic equations for the drift functions are also derived for comparison with simulated results, showing that the potential surface for all data types becomes shallower upon the approach to a critical transition from either direction, as predicted by critical slowing down.

MEPI Subgroup Contributed Talks

  • Andrew Oster Eastern Washington University
    "A New Model for Rat-Flea–Driven Plague Transmission"
  • Rats have long been thought to drive plague epidemics, specifically bubonic plague. However an alternative theory for plague transmission has been posited by Dean et al. (PNAS 2018) where ectoparasites living on human hosts drive spread. This talk will present a new mathematical model for the spread of the plague based on rat-flea interactions with the human population and compare our results to existing models. Our results suggest that rat-flea transmission of the plague is still a plausible explanation.
  • Katia Vogt-Geisse Universidad Adolfo Ibáñez
    "An SIR-type model incorporating social distancing dynamics based on point prevalence and socio-behavioral factors"
  • Modeling human behavior within mathematical modeling of infectious diseases is key to understand and control disease spread. We present a mathematical compartmental model of Susceptible - Infectious - Removed to compare the infected curves given by four different functional forms describing the transmission rate. These depend on social-distance, which varies according to the balance between two opposite thrives: the self-protecting reaction of individuals upon the presence of disease to increase social distancing and their necessity to return to a culturally dependent natural social distance that occurs in the absence of disease. We present results for different society types on point prevalence, the peak size of a first epidemic outbreak and the time of occurrence of that peak, for four different transmission rate functional forms and parameters of interest related to distancing behavior. We observe the vulnerability to disease spread of close contact societies, and also that certain social distancing behavior may provoke an early occurring small peak of a first epidemic outbreak, observing differences in this regard between society types. We discuss the appearance of oscillations of the transmission rates and how these oscillations are impacted through social distancing; breaking the unimodality of the actives-curve produced by the classical SIR-model.
  • Edward Hill University of Warwick
    "A network modelling approach to assess non-pharmaceutical disease controls against SARS-CoV-2 in a worker population"
  • As part of a concerted pandemic response to protect public health, businesses can enact non-pharmaceutical controls to minimise exposure to pathogens in workplaces and premises open to the public. Amendments to working practices can lead to the amount, duration and/or proximity of interactions being changed, ultimately altering the dynamics of disease spread.We use a data-driven approach to parameterise an individual-based network model for transmission of SARS-CoV-2 amongst the working population, stratified into work sectors. The network comprises layered contacts to consider risk of spread in multiple encounter settings (workplaces, households, social and other). We analyse several interventions targeted towards working practices: mandating a fraction of the population to work from home; using temporally asynchronous work patterns; and introducing 'COVID-secure' workplaces. We also assess the general role of adherence to (or effectiveness of) isolation and test and trace measures and demonstrate the impact of these interventions on epidemiological metrics.Given the heterogeneity of demographic attributes across worker roles, in addition to the individual nature of controls such as contact tracing, we demonstrate the utility of a network model approach to investigate workplace-targeted intervention strategies and the role of test, trace and isolation in tackling disease spread.
  • Jeffery Demers University of Maryland
    "Optimal allocation of limited testing resources for flattening the COVID-19 curve"
  • Insufficient testing capacity has proven to be a critical bottleneck in the fight against COVID-19, especially during the early stages of the pandemic. Prioritizing allocation of limited testing resources based on symptom severity (among other factors) has therefore emerged has a key component of public policy ripe for mathematical analysis and optimization, but the typical testing rate expressions utilized in compartmental disease models are inadequate for describing severely constrained resource scenarios. Here, we propose a testing model which flexibly accounts for both limited and plentiful resources, and we use a modified SEIR model with quarantine to find optimal allocations of testing capacity for flattening the epidemic curve. We balance resources between two testing strategies: clinical testing focused only on severely symptomatic individuals and non-clinical testing focused on mild and asymptomatic individuals, where contact tracing and case monitoring are incorporated by an information parameter. We find that purely clinical testing is optimal at very low testing capacities, supporting early guidance to ration tests for the sickest patients. Additionally, we find that a mix of clinical and non-clinical testing becomes optimal as testing capacity increases. Further, we find that reduction of our model's R0 is an unreliable metric for epidemic peak reduction.

Sub-group poster presentations

MEPI Posters

MEPI-1 (Session: PS01)
Michael Eguia Subido University of the Philippines, Diliman
"Assessing the Effect of Temperature on Multi-Strain Dengue Transmission Dynamics in the Philippines"

Dengue is one of the most important infectious diseases with more than 55% of the world population at risk of acquiring the infection. Recent climate changes related to global warming have increased the potential risk of dengue outbreaks in the world. In this paper, we propose an SEIR model for the human population and an SEI model for the vector population by incorporating temperature-dependent parameters to describe the transmission dynamics of a multi-strain dengue model. Sensitivity analysis of both the constant and temperature-dependent parameters are performed to explore the effects of the changes in temperature on the multi-strain dengue transmission dynamics. The adapted model will then be investigated to describe the dengue epidemics that occurred in the Philippines in the year 2015-2018 using Philippine epidemiological and climatological data. We then test the identifiability of the proposed multi-strain dengue model using the reported dengue cases by morbidity week in the Philippines for the same year.

MEPI-11 (Session: PS01)
Peter Rashkov Institute of mathematics and informatics, Bulgarian Academy of Sciences
"Viable controls in models for vector-borne diseases"

Analysis of transient dynamic behaviour of controlled trajectories is a novel problem in the context of vector-borne diseases. Epidemiological modelling focuses often on investigation of local or global asymptotic stability of equilibria or on trajectories corresponding to optimal resource allocation if control is introduced. The study is motivated by the application of mosquito repellents as protective measure in textiles, paints and other household items. The model for a vector-borne disease is SIR for the host and SI for the vector with time-dependent controls. We determine the viability kernel comprising those initial states for the dynamical system such that the proportion of infected individuals is kept below a certain maximum level for all future times, and the respective viable trajectories. Analysis of viable controls has been done earlier for a SIS model for the host (DeLara & Salcedo 2016), which has properties of a quasi-monotone system. Our results (Rashkov 2021) extend the analysis to a more complex model system. We compute numerical approximations of the viability kernels and the viable trajectories using a variational framework.This work is partially supported by the Bulgarian National Science Fund within the National Science Program 'Petar Beron i NIE' [contract number KP-06-DB-5].

MEPI-12 (Session: PS01)
Dimitris A. Goussis Khalifa University
"Time-scale analysis of population dynamics models for the COVID-19 pandemic"

The identification of the various factors influencing the spread of the COVID-19 outbreak, especially during the early stages of the pandemics, is critical to determine appropriate interventions to control the outbreak and prevent its resurgence. In this regard, it is demonstrated here that the time scale characterizing various phases of the COVID-19 outbreak provides most useful information. The analysis is based on a number of popular population dynamics models and data from various countries. It is further demonstrated that this characteristic time scale is robust, when considering (i) different population models, (ii) fitting the parameters of a model to data spanning different periods of the growth phase and (iii) different parameters sets resulting from different fittings of the same data sets. This time scale characterizes the largest portion of the epidemic-growth period and is promoted by the infecting paths of the models and is opposed by the recovery ones. This approach provides a robust and systematic framework for the assessment of the control measures of the COVID-19 outbreak.

MEPI-13 (Session: PS01)
María Gamboa Pérez Complutense University of Madrid
"Measures to asses an optimal vaccination coverage in a stochastic SIV model with imperfect vaccine"

This communication is framed within the area of epidemic modelling in a stochastic approach. An additional compartment of vaccinated individuals is considered in a stochastic SIS model within a not isolated, homogeneous, and uniformly mixed population. The vaccine is not 100% effective and individuals are partially protected against the disease. The propagation of a contagious disease is modelled in terms of a continuous time Markov chain where individuals evolve among susceptible, S, vaccinated, V, and infected, I; compartments.A well-known measure of the initial transmission potential is the basic reproduction number R_0, which determines the herd immunity threshold or the critical proportion of immune individuals required to stop the spread of a disease when a vaccine offers a complete protection. Assuming that the vaccine is imperfect, alternative measures to R_0 are defined in order to study the influence of the initial coverage on the transmission of the epidemic. The talk is based on the paper: Gamboa, M., and Lopez-Herrero, M. J. (2020). Measuring infection transmission in a stochastic SIV model with infection reintroduction and imperfect vaccine. Acta biotheoretica, 1-26.

MEPI-14 (Session: PS01)
Salisu Garba Department fo Mathematics and Applied Mathematics, University of Pretoria
"Modeling the transmission dynamics of yellow fever with optimal control"

In this presentation, a model for yellow fever transmission dynamics in a human-mosquito setting is constructed and analyzed. The model incorporates vertical transmission within mosquito population. Threshold quantities (such as the basic offspring and the type reproduction numbers) and their interpretations for the models are presented. Analysis of the mosquito-only component shows that the reduced model has a mosquito-extinction equilibrium, which is globally-asymptotically stable whenever the basic offspring number is less than unity. Optimal control theory is applied to the model to characterize the controls parameters. Using Pontryagin's maximum principle and modified forward-backward sweep technique, the necessary conditions for existence of solutions to the optimal control problem is determined. The effect of various control strategies (bed nets, adulticides and vaccination) were assess via numerical simulations.

MEPI-15 (Session: PS01)
Christopher Overton University of Manchester
"Data driven compartmental modelling of the COVID-19 hospital burden in England"

The COVID-19 pandemic in England has put considerable strain on the national healthcare system. To predict the effect of the pandemic on hospital capacity in England, we used a variety of data streams to inform the construction and parameterisation of a hospital progression model, which was coupled to a model of the generalised epidemic. Data from a partially complete patient-pathway line-list was used to provide initial estimates of the mean duration that individuals spend in the different hospital compartments. We then fitted the model using complete data on hospital occupancy and hospital deaths, enabling estimation of the proportion of individuals that follow different clinical pathways, and the reproduction number (Rt) of the generalised epidemic. The construction of the model makes it straightforward to adapt to different patient pathways and settings beyond England. As part of the UK response to the pandemic, this model has provided weekly forecasts to the NHS for hospital bed occupancy in England, Wales, Scotland and Northern Ireland, and formed part of the UK combined reproduction number estimates.

MEPI-3 (Session: PS01)
Elba Raimúndez University of Bonn
"COVID-19 outbreak in Wuhan demonstrates the limitations of publicly available case numbers for epidemiological modeling"

Mathematical models are standard tools for understanding the underlying mechanisms of biological systems. Generally, the parameters of these models are unknown and they need to be inferred from experimental data using statistical methods. Most common measurement techniques only provide relative information about the absolute molecular state and often data is noise-corrupted. Therefore, introducing scaling and noise parameters in the model observables is necessary. Since frequently these parameters are also unknown, the dimensionality of the estimation problem is augmented. Sampling methods are widely used in systems biology to assess parameter and prediction uncertainties. However, the evaluation of sampling methods is usually demanding and often on the border of computational feasibility. Hence, efficient sampling algorithms are required.We propose a marginal sampling scheme for estimating the parameter uncertainties of mechanistic models with relative data. We integrate out the scaling and noise parameters from the original problem, leading to a dimension reduction of the parameter space. Herewith, only reaction rate constants have to be sampled. We find that the marginal sampling scheme retrieves the same parameter probability distributions and outperforms sampling on the full parameter space by substantially increasing the effective sample size and smoothing the transition probability between posterior modes.

MEPI-4 (Session: PS01)
Uljana Apel Technical University of Munich
"How long is long enough? The impact of the contact tracing interval"

Contact tracing is one of the most important non-pharmaceutical control measures for infectious diseases. The corona epidemic revealed that many aspects of contact tracing are still not well understood, from the theoretical as well as from the practical point of view.In the present work, we focus on the tracing interval. The tracing interval is the time interval for which people are asked to give their contacts. The current practical guidelines mainly orient themselves at the infectious interval. In our research we vary this tracing interval and examine its effect on the spread of the disease in the onset. Thereto we setup a differential-difference equation model for the probability to be infectious at a certain age since infection when contact tracing is used. The probability to be infectious is then used to calculate the incidence depending on the tracing interval. Therewith we discuss the impact of contact tracing in dependence on the tracing interval.

MEPI-5 (Session: PS01)
Sheryl Grace Buenaventura Center for Applied Modeling, Data Analytics, and Bioinformatics for Decision-Support Systems in Health (AMDABIDS) - University of the Philippines Mindanao
"Understanding COVID-19 spread in the National Capital Region, Philippines using Genomic Sequences: A Phylodynamic Investigation"

To understand the disease dynamics in a particular location, incidence reports are used to estimate key epidemiological parameters such as transmission rates and reproductive numbers. However, incidence data often suffer from underreporting due to logistical concerns in disease surveillance, insufficient testing, etc. One way to address this concern is to use information from viruses' genomes to infer the past ecological dynamics of the disease. Here, we use publicly available SARS-CoV-2 genomic sequences data from the National Capital Region of the Philippines. We use the BEAST2 software to model its dynamics using a Birth-Death Susceptible-Infected-Recovered (BDSIR) model and infer its transmission history. Nineteen whole-genome sequences from NCR, sampled from 3 April to 18 July 2020, were used. We also model the spread of COVID-19 using incidence data through a deterministic ODE-based SIR model. The estimated transmission rate using the genomic sequences is 4.2x10-6 which is greater than the estimated transmission rate using the incidence reports at 2.0x10-8. The estimated basic reproduction number of the BDSIR (2.21) is also higher than that of the SIR (1.21). These results point out the need to cautiously use the reported incidences as basis in making policies in managing infectious diseases outbreak.

MEPI-6 (Session: PS01)
Tatiana Filonets National Taiwan University, Taipei, Taiwan
"Simulation of the first COVID-19 wave in Taiwan by using new epidemiological compartmental model"

As of March 10, 2021, there were 978 officially confirmed cases of COVID-19 in Taiwan, of which 862 were imported from outside of the country. Taiwan very quickly implemented non-pharmaceutical interventions, namely rapid case finding, hospital isolation, tracing and testing the contacts of infected individuals, central distribution of masks, and imposing home-quarantine on travelers from COVID-19 affected countries. In this work, we simulated the Taiwanese scenario of the first wave of COVID-19 January-March) in order to investigate the effectiveness of the public medical masks wearing and contact tracing to maintain the pandemic at a manageable level. For this purpose, we used a modified version of the SEIR model which takes into account asymptomatic cases, contact tracing, self-isolation, and masks wearing. In addition, we estimated the basic reproduction number and its dependence on the model parameters by using the next-generation matrix approach.Our results show that good realization of contact tracing program, the fast isolation, together with medical masks wearing by 90% of the population can help to control the local virus spreading. However, only high-quality implementation of these interventions can provide the basic reproduction number value below one.

MEPI-7 (Session: PS01)
Vizda Anam Basque Center for Applied Mathematics
"Modeling dengue immune responses mediated by antibodies: insight on the immunopathogenesis of severe disease"

Dengue fever is a viral mosquito-borne infection, a major international public health concern. With four antigenically related but distinct viruses (DENV-1 to DENV-4), the occurrence of the virus as four distinct serotypes results in many complications in disease response. Infection with one serotype results in lifelong protective immunity. Additionally, antibodies generated by exposure to any one type cross-react with other types, providing short duration cross protective immunity. Subsequent infection by a different dengue serotype increases the risk of developing severe disease with a high fatality rate. This disease augmentation phenomenon is called antibody-dependent enhancement (ADE).Here we present a minimalistic mathematical model developed to describe the dengue immunological response mediated by antibodies. Based on body cells and free virus interactions resulting infected cells activating antibody production, we explore the feature of ADE when pre-existing antibodies, analyzing: i) primary dengue infection, ii) secondary dengue infection with the same virus and iii) secondary dengue infection with a different dengue virus. Our mathematical results are qualitatively similar to the ones described in the empiric immunology literature and this framework will now be refined to be validated with the available laboratory data.

MEPI-8 (Session: PS01)
Hannah Lepper University of Edinburgh
"Integrating sewage and hospital-based surveillance data on antimicrobial resistance: resistance type affects community resistance patterns"

Using waste water to detect and quantify abundances of antibiotic resistance genes has the potential to improve our understanding of resistance in the community and study the relationship with resistance in hospitals. By investigating similarities and differences in patterns and drivers of resistance in hospital and sewage surveillance data, and how this differs between resistance types, we can gain insights in this relationship.Here we use a multivariate regression model to investigate correlations between sewage and hospital data, and the effects of antimicrobial usage on hospital and community resistance levels. A Poisson model for resistance gene abundance in waste water (Global Sewage Surveillance Project) and a binomial model for clinical isolate resistance testing (EARS-Net, ECDC) are combined through country-level covariance between the datasets.Our results show that fluoroquinolone resistance was positively associated with antimicrobial consumption (ESAC-Net, ECDC) in both the hospital and the community, whereas carbapenem resistance was not. After taking antimicrobial consumption into account, resistance to fluoroquinolones in hospitals and waste water was not correlated, but carbapenem resistance was. This indicates that emergence and transmission of different types of resistance have different drivers in hospitals and the community, and highlights the need for flexible approaches to surveillance and prevention.

MEPI-9 (Session: PS01)
Woldegebriel Assefa Woldegerima Postdoc Research fellow; University of Pretoria, South Africa
"Mathematical assessment of the impact of human-antibodies during the within-mosquito dynamics of Plasmodium falciparum parasites"

We develop and analyze a model for the within-mosquito dynamics of the Plasmodium falciparum malaria parasite. Our model takes into account the action and effect of blood resident human-antibodies, ingested by the mosquito during a blood meal from humans, in inhibiting gamete fertilization. The model also captures subsequent developmental processes that lead to the different forms of the parasite within the mosquito. Continuous functions are used to model the switching transition from oocyst to sporozoites as well as human antibody density variations within the mosquito gut are proposed and used. We quantify the average sporozoite load produced at the end of the within-mosquito malaria parasite's developmental stages. Our analysis shows that an increase in the efficiency of the ingested human antibodies in inhibiting fertilization within the mosquito's gut results in lowering the density of oocysts and hence sporozoites that are eventually produced by each mosquito vector. So, it is possible to control and limit oocysts development and hence sporozoites development within a mosquito by boosting the efficiency of antibodies as a pathway to the development of transmission-blocking vaccines which could potentially reduce oocysts prevalence among mosquitoes and hence reduce the transmission potential from mosquitoes to human.

MEPI-16 (Session: PS02)
Katherine Royce Harvard University
"Application of a novel mathematical model to identify intermediate hosts of SARS-CoV-2"

Intermediate host species provide a crucial link in the emergence of zoonotic infectiousdiseases, serving as a population where an emerging pathogen can mutate to becomehuman-transmissible. Identifying such species is thus a key component of predictingand possibly mitigating future epidemics. Despite this importance, intermediate hostspecies have not been investigated in much detail, and have generally only beenidentified by testing for the presence of pathogens in multiple candidate species. In thispaper, we present a mathematical model able to identify likely intermediate hostspecies for emerging zoonoses based on ecological data for the candidates andepidemiological data for the pathogen. Since coronaviruses frequently emerge throughintermediate host species and, at the time of writing, pose an urgent pandemic threat,we apply the model to the three emerging coronaviruses of the twenty-first century,accurately predicting palm civets as intermediate hosts for SARS-CoV-1 anddromedary camels as intermediate hosts for MERS. Further, we suggest mink,pangolins, and ferrets as intermediate host species for SARS-CoV-2. With the capacityto evaluate intermediate host likelihood among different species, researchers canfocus testing for possible infection sources and interventions more effectively.

MEPI-17 (Session: PS02)
Juan Pablo Restrepo Department of Mathematical Sciences, Universidad EAFIT
"Non-Homogeneous Poisson Process & Functional Data: A procedure for infectious diseases count data modeling"

In some epidemiological studies it is of interest to observe the behavior of the number of cases of a disease in a population, such as Dengue, Zika, Covid-19, among others; in order to predict the evolution of future cases. In this study, we propose to combine Non-Homogeneous Poisson Processes (NHPP) and Functional Data Analysis (FDA) methodologies for count-data prediction. We consider cumulative cases, subjected to time evolution and influence of explanatory variables. The proposed procedure allows to estimate the most representative cumulative-cases trajectory included its non-parametric confidence bands, as well as detect possible outlier trajectories, and predict future cumulative counting. An application with real infectious diseases data is also presented.

MEPI-18 (Session: PS02)
Joanna Sooknanan University of the West Indies Open Campus
"Harnessing social media in the modelling of pandemics – challenges and opportunities"

As COVID-19 spreads throughout the world without a straightforward treatment or widespread vaccine coverage in the near future, mathematical models of disease spread and of the potential impact of mitigation measures have been thrust into the limelight. With their popularity and ability to disseminate information relatively freely and rapidly, information from social media platforms offers a user-generated, spontaneous insight into users' minds that may capture beliefs, opinions, attitudes, intentions and behaviour towards outbreaks of infectious disease not obtainable elsewhere. The interactive, immersive nature of social media may reveal emergent behaviour that does not occur in engagement with traditional mass media or conventional surveys. In recognition of the dramatic shift to life online during the COVID-19 pandemic to mitigate disease spread and the increasing threat of further pandemics, we examine the challenges and opportunities inherent in the use of social media data in infectious disease modelling with particular focus on their inclusion in compartmental models.

MEPI-19 (Session: PS02)
Nao Yamamoto Arizona state university
"Quantifying Compliance with COVID-19 Mitigation Policies in the US"

The outbreak of COVID-19 disrupts the life of many people in the world. In response to this global pandemic, governments in the United States had implemented COVID-19 mitigation policies. However, those policies, which were designed to slow the spread of COVID-19, and its compliance, have varied across the states, which led to spatial and temporal heterogeneity in COVID-19 spread. This study aims to proposea spatio-temporal model for quantifying compliance with the US COVID-19 mitigation policies at a regional level. To achieve this goal, a partial differential equation is developed and validated with the COVID-19 data. The proposed model describes the combined effects of transboundary spread among state clusters and human mobilities on the transmission of COVID-19. The model may inform policymakers as they decide how to react to future outbreaks.

MEPI-20 (Session: PS02)
Orhun Davarci The University of Texas at Austin
"Integrating epidemiological data and mathematical models to forecast COVID-19 spread in the United States"

The rapid global outbreak of COVID-19 has raised interest in the computational forecast of the spread of infectious diseases, but the early projections in the current pandemic were limited in their ability to describe longer-term outcomes. This issue was partially due to the limited knowledge of the mechanisms of disease spread and development. Our study aims to integrate epidemiological time-series data into a mathematical model that can describe the fundamental mechanisms of COVID-19 spread, with the ultimate goal of utilizing model forecasts to determine early indicators of large outbreaks as well as assessing public health interventions to control their severity. We used publicly available data from the 10 most heavily impacted states in the US to calibrate a SEIRD-type model and obtain state-specific sets of epidemiological parameters. Our model was able to recapitulate the early observations of cumulative infections and deaths (CCC > 0.9, R2 > 0.9). We further explore the use of model parameters and forecasts as early indicators of subsequent large outbreaks. Finally, we argue that mechanistic models that describe infectious disease spread can help mitigate the human cost of pandemics by anticipating effective public health interventions and enabling the optimized allocation of key medical resources.

MEPI-21 (Session: PS02)
Tarun Mohan Texas Christian University
"Modeling the effect of multiple vaccines on the spread of SARS-CoV-2"

Several different vaccines have been introduced to combat the spread of SARS-CoV-2 infections. As the virus is capable of mutating to escape the protection given by the vaccine, using multiple vaccines is believed to help prevent the virus from mutating to escape all vaccines, helping to combat spread of the virus. We simulate the effect of using multiple vaccines on the virus using a mathematical model. With the model, we can better understand the effect of multiple types of vaccines in helping to control pandemics.

MEPI-22 (Session: PS02)
Julia Mautone Universidade de São Paulo
"Mathematical modeling of Influenza H1N1 over vaccine influence based on real data"

We build a mathematical model applied to influenza H1N1. The model structure consists of splitting the human population according to susceptible, infected by the disease, and recovered which includes the vaccinated population. We develop stability analysis and calculate equilibrium point and basic reproduction number. We analyze model parameters and their role over the representation of São Paulo's real data, provided by SINAN (a serious notifications system), which helps to estimate the disease transmission rate, as well as population mortality and birth rates, through the least-squares method. We take into account the numerical method accuracy related to the infected curve fitting and the real data from 2013. In an attempt to study the vaccination influence over the number of cases, and to identify risks and forecasting outbreaks, we carry out numerical simulations by varying the vaccination rate parameter. Spite of vaccination reaches a small group of the population each year (around 20% based on 2010-2018 data), we conclude it is a key parameter that plays a role over the possibility of reducing cases through the curve flattening. We encourage public policies as an effective measure, to provide significant stimulus and adherence to vaccination programs, and a decrease of infected cases number.

MEPI-23 (Session: PS02)
Gabriel McCarthy Texas Christian University
"Quantifying the effectiveness of quarantine measures"

Using a SEIR model we evaluate the COVID-19 pandemic in various states. We assume a changing infection rate to reflect the restrictions put into place to combat spread of the infection. Doing this allows us to mathematically represent the changes in behavior and restrictions in actions after the outbreak of COVID-19 and how they affected the spread of COVID-19. We test different formulations for the changing infection rate, from abrupt change to gradual decay of the infection rate to determine how best to model changes due to various mandates. This analysis helps us understand the effectiveness of different preventative measures found across the U.S so that the pandemic is stopped and dealt with effectively.

MEPI-24 (Session: PS02)
Quiyana Murphy Virginia Tech
"Modeling testing strategies to reduce SARS-COV-2 transmission"

As vaccines against SARS-CoV-2 are not yet available for everyone, it is important to implement non-pharmaceutical interventions to reduce SARS-CoV-2 transmission. Testing is a necessary factor in quantifying the number of infected individuals and reducing their interaction with the population (isolation). Additionally, identifying positive cases allows public health officials to track transmission via contact tracing and prevent additional infections with quarantine. To better inform testing strategies, we develop a deterministic ordinary differential equation mathematical model for given available resources in a community. Specifically, our model includes various characteristics to be attributed to the variability in testing strategies, including the sensitivity of testing, availability of testing, delay in testing results, and priority of testing. Three different tests with varying sensitivity, availability, and return time are incorporated: antibody tests, RT-PCR tests, and antigen tests. Three scenarios are considered to investigate the effects of priority testing on disease transmission: test only symptomatic individuals, equally spread available tests across all testable populations (surveillance), and prioritize tests for symptomatic individuals but use the remaining testing for surveillance. Our model can determine which allocation of testing type and strategy will most significantly decrease the infectious population (peak and duration) given locally available testing information.

MEPI-25 (Session: PS02)
Mohammad Mihrab Uddin Chowdhury Texas Tech University
"The Influence of Annual Birth Pulses on Disease Transmissibility in Amphibian Populations."

The dynamics of infectious disease in amphibians with multiple routes of transmissibility is a complex interconnected system. Depending on the population level and age stages (larvae, juveniles, and adults), infection spreads in a variety of ways. Due to seasonal reproductive behaviors, the population density of larvae rises at a certain time of year. We developed compartmental models using ordinary differential equations and difference equations to observe the effects of annual birth pulses on transmission dynamics of a fungal pathogen (Batrachochytrium salamandrivorans, Bsal) on a North American salamander population. Model simulations and analyses offer insights into control strategies aimed at reducing transmission and preventing epidemic outbreaks.

MEPI-27 (Session: PS02)
Erica Rutter University of California, Merced
"A Different COVID-19 Model: Characterizing the Spread of Misinformation of COVID-19 on Twitter"

Since the World Health Organization (WHO) declared COVID-19 a pandemic, mathematicians have mobilized to create models to predict the rise of COVID-19 through communities. In parallel to the spread of the virus, there has been an equally insidious spread of misinformation across various social media platforms. In this presentation, we will analyze the similarities and differences in transmission of various types of misinformation spread over Twitter in the past year. We build and analyze network graphs for the tweets (and retweets) of multiple types of misinformation (e.g, benign, conspiracy theory) and determine the characteristics that distinguish them. Can we predict the type of misinformation based on the way it spreads over twitter?

MEPI-28 (Session: PS02)
Harvir Singh Bhattal University of British Columbia
"Underreporting of SARS-CoV-2 Infections in British Columbia"

Our understanding on the epidemiology of COVID-19 is limited by the ability of health systems to ascertain SARS-CoV-2 infections. Due to asymptomatic infection and testing hesitancy in symptomatic individuals (which may vary throughout time and with age, disease severity, socioeconomic status, etc.), reported cases represent only a fraction of total infections. The gold standard to estimate the burden of disease in a population is seroprevalence surveys. However, such surveys are operationally expensive and provide only a snapshot on the ascertainment of cumulative infections. In the current poster, we introduce a method to estimate instantaneous infection ascertainment from the the instantaneous case-hospitalization fraction and the infection-hospitalization fraction (which itself is constrained from seroprevalence data). We applied these methods in an age-structured manner to estimate the instantaneous ascertainment of SARS-CoV-2 infections in the B.C. population, from the outset of the epidemic to date. This allowed us to back-calculate the true epidemic, from which we could more acutely identify epidemiological trends.

MEPI-29 (Session: PS02)
Caroline Franco Sao Paulo State University
"Modelling COVID-19 in Brazil: better fit to data obtained when including the percolation effect approximation"

The SARS-CoV-2 pandemic has had an unprecedented impact on multiple levels of society. Not only has the pandemic completely overwhelmed some health systems but it has also changed how scientific evidence is shared and increased the pace at which such evidence is published and consumed, by scientists, policymakers and the wider public. Through the COVID-19 Modelling (CoMo) Consortium and the Observatório COVID-19 BR, we created modelling frameworks that could help simulate the effect of different non-pharmaceutical interventions on mitigating the epidemic in numerous locations. Here, we describe how this framework was adapted to the Brazilian context and, more specifically, fitted to data from the city of Sao Paulo. We propose an approximation for the percolation effect observed in social networks connectivity, due to the adoption of social distancing measures, and we show that this leads to better fitting to data, indicating the importance of this effect in such a system.

MEPI-30 (Session: PS02)
Miller Ceron Universidad de Nariño
"A SEI model with nonlinear incidence rate: global stability analysis"

We propose a SEI epidemic model where the infected and the exposed are the spreaders of the disease. Besides, a general nonlinear incidence rate and death rate functions are considered to study the stability of the model. We prove that the endemic equilibrium is globally asymptotically stable when the basic reproduction number R0 is greater than unity and the disease free equilibrium is globally asymptotically stable when R0 is lower than unity.

MEPI-31 (Session: PS02)
Alexandra Catano-Lopez Departamento de Ciencias Matemáticas, Escuela de Ciencias, Universidad EAFIT
"A platform to simulate COVID-19 that allows inclusion of mathematical modeling into decision-making management"

The COVID-19 pandemic affected the entire world, forcing several institutions to designate a part of their resources to implement control strategies to reduce its incidence. Thus, mathematical modeling becomes an important tool to study the effects of control policies, as it communicates academic information to the public and decision-makers. Following these ideas, the group of mathematical epidemiology of EAFIT University in Colombia developed an online tool that shows the effect of modifying control strategies over different localities in Colombia. We developed this tool based on a novel discrete-time model with variations on parameters related to quarantine, identification, social distancing, migrations, vaccination, among others; besides visual tools that allow communication to the public. At the moment, we included in the platform over forty Colombian localities, in which we individualize the mathematical model estimating the corresponding parameters with real data provided from the Colombian national health institution. Every time we update the model with new data, the user can simulate and project different control scenarios over the affected population. In this work, we will present the structure of a platform that allows the non-expert users to simulate different control strategies; also, we could use it for monitoring other infectious diseases.

MEPI-49 (Session: PS02)
Samantha Bardwell University of British Columbia
"A Mathematical Model for Overdose in a Population of People Who Inject Drugs"

The presence of synthetic opioids (fentanyl and carfentanil) in heroin and other drugs has greatly increased the risk of fatal overdose among people who inject drugs (PWID) across Canada and elsewhere in the world. We sought to represent the dynamics of the population of PWID and various public health interventions using a mathematical framework that hybridizes an individual-based model with a compartmental analysis model. The goal of this study was to accurately formulate a simulated population of users whose risk is uniquely and dynamically determined. The model construction involved a significant literature review, and synthesis and analysis of data from collaborators implementing drug policy. We calibrated the model to represent the PWID population in downtown Toronto, but it can be adapted to examine effects of similar interventions in any location. The model results suggest that recruitment to the at-risk population is currently over-reported, and the present values should be re-evaluated. The model results also suggest that various factors, including age, previous overdoses, and history of incarceration, have a significant effect on the individual risk of fatal overdose. The information we obtain can be used to strategically target intervention strategies, and guide future research on the PWID population.

MEPI-2 (Session: PS03)
Martin Lopez-Garcia Department of Applied Mathematics, University of Leeds
"Exact approaches for the analysis of stochastic epidemic processes on small networks"

This research work is framed within the area of modelling hospital-acquired infections. I will introduce a number of existing compartmental-based approaches for modelling the spread of (typically antibiotic resistant) bacteria in hospital settings. Mathematical models with a relatively small number of compartments can be used for representing the spread of bacteria across patients and healthcare workers (HCWs), including relevant factors such as environmental contamination. However, more complex approaches (i.e., models with a large number of compartments, or network-based representations) are needed for example when introducing spatial considerations or HCW-patient contact network structures. When looking at network-based approaches, I will show some recent work on analysing exactly these epidemic dynamics on small networks. When considering an SIR epidemic process on a network, this analytic and computational approach amounts to the analysis of the corresponding continuous-time Markov chain (CTMC) with an explosive number of states, and makes special focus on algorithmic aspects and the organisation of the corresponding space of states S. Finally, I will present some recent results on the applicability of graph-automorphism lumping techniques in these systems.

MEPI-32 (Session: PS03)
Eva Stadler Kirby Institute, UNSW Sydney
"Who carries malaria parasites over the dry season?"

Transmission of Plasmodium parasites that cause malaria is often seasonal with very low transmission during the dry season and high transmission in the rainy season. Plasmodium falciparum parasites can survive the dry season within some humans. For malaria elimination efforts, it is crucial to learn more about this parasite reservoir in humans. We use a mathematical model incorporating random mosquito bites and slow acquisition of non-sterilizing general immunity to explore which factors influence whether someone carries parasites over the dry season. Based on model simulations, we hypothesize that parasite carriage over the dry season is exposure mediated. With increasing exposure, i.e., with higher age and Force Of Infection (FOI, the mean number of infectious mosquito bites per day), immunity increases. Higher levels of immunity lead to longer infections and a higher probability of carrying parasites over the dry season. We then test this hypothesis in data from a longitudinal study in Mali and find that carriers are significantly older, have a higher FOI, and develop clinical malaria later than non-carriers.

MEPI-33 (Session: PS03)
Helena Stage The University of Manchester
"Multi-Scale Superinfection Models in Evolutionary Epidemiology"

The study of evolutionary epidemiology is vital to understand and control the spread of anti-microbial resistance, but is inherently challenging because pathogen evolution is driven by forces acting at multiple scales: for example, HIV needs to escape the immune system within a host, but also needs to maintain the ability to be transmitted efficiently between hosts. Time-since-infection models are much more flexible than ODEs if we want to allow for realistic enough aspects of both within- and between-host scales, but capturing the feedback loops between such scales is a formidable challenge.We will discuss the main technical challenges in developing a general theory for time-since-infection models that allow for superinfection (e.g. multi-strain systems with partial cross-immunity), starting from the problem of characterising the system's steady states. We will distinguish between the cases when superinfection of the host facilitates the coexistence of two (or more) infections that interact synergistically by fuelling each other's spread (syndemic), and when these infections hinder each other. We show how in the former case multiple stable steady states are possible, while in the latter case the stable steady state is unique but possibly harder to compute. We discuss the consequent implications for public health control measures.

MEPI-34 (Session: PS03)
Augustine Okolie Technical University of Munich
"Phylogenetic Methods for Infectious Models"

Here, we adopt the maximum-likelihood framework based on a multi-type branching process (MTBP) for heterogeneous population where each host is assigned to a type (subpopulation). We extend this multi-type birth-death branching model to a tree-based SIR model which also incorporates contact tracing. On a rooted known phylogenetic tree where only the root node is infected and infectious, we investigate the probability density of a sampled tree given some epidemiological parameters. The maximum-likelihood parameter estimation of the basic model is combined with the results for contact tracing. We expect that the tracing events incorporate information about the heterogeneity in the contact structure, while the phylogenetic methods are better to estimate the timing of the infectious process. In that, we hope that the combined method will improve the estimations of the parameters of the epidemic process, as well as on the underlying contact structure.

MEPI-36 (Session: PS03)
Bhawna Malik
"Emergence of drug-resistant through behavioural interactions: Game theoretic approach"

Emergence of antibiotic drug resistance has raised great concerns for public health, especially in low and lower middle income country. Many studies indicate the emergence and high burden of drug residence is a complex dynamics influenced by several socioeconomic factors like poverty, health expenses, and self-medication. Self-medication through Over-the-counter (OTC) drug sales plays a major role in ever-increasing antibiotic consumption, and it is is more ubiquitous in more economically destitute society. To explore this, we developed a game-theoretic model of human choices in self-medication integrating economic growth in population, and disease transmission process. We show that combined impact of economy, infections and behaviour yield resistance as a self-reinforcing cycle in drug resistance. Our model illustrates that individuals' perceived risk plays an important role in disease dynamics. We show that increased and timely government aid can break this self-reinforcing cycle by reducing hospital treatment cost or other medical incentives, and thus, it can recover population from economic downfall due to continuous morbidity from antibiotic drug resistance.

MEPI-37 (Session: PS03)
Laxmi Shiv Nadar University, India
"Game theoretic approach to quantify the impact of ITNs under individuals choice on malaria transmission"

Insecticide Treated bed Nets (ITN) have proven to be highly effective control measure to reduce malaria transmission. It has been discussed earlier that ITNs with high efficacy may perform better in control malaria. But, even after massive distribution of ITN, malaria persists in most of the under developing countries, compromising the long term malaria elimination goals. However, many empirical studies pointed out that usage of ITN plays an important role in its effectiveness to control malaria. Individuals ITN usage are highly driven by ITN efficacy, mosquito density due to seasonal variation, replacement period, increment in daily productivity due to ITN misuse. To explore the complex interaction of ITN usage pattern and malaria prevalence, we develop a Game-Theoretic model of ITN usage and malaria transmission. Our results show the impact of parameters like imitation rate and ITN efficacy on human behaviour are critical. The analysis indicates that higher efficacy of ITN is not always optimal to control malaria effectively, which is an important information for malaria elimination strategies.

MEPI-38 (Session: PS03)
Mohamed Khalil Salem GSE Department (Mathematics), Faculty of Engineering, October University for modern sciences and Arts (MSA)
"Fractional order models of HIV: A Review"

HIV is one of most serious global challenges. About 38 million people are currently living with HIV. It cased AIDS which is a chronic life-threatening disease. In this work, an overview on mathematical models of human immunodeficiency virus (HIV) with memory are presented. Non integer order models (Fractional order models) are presented to study the impact of memory on the interaction between the CD4+ T and HIV.

MEPI-39 (Session: PS03)
Dylan Dronnier Ecole des Ponts
"Targeted Vaccination Strategies for Infinite-Dimensional Compartmental Models"

In classical homogeneous compartmental models, the critical proportion of the population needed to be immune to eradicate the disease is given by the formula: 1 - 1/R0, where R0 is the basic reproduction number. This so-called herd immunity threshold can be lower in heterogeneous models by targeting specific sub-groups of the population.In this talk, we formalize and study the problem of optimal allocation strategies for a (perfect) vaccine in infinite-dimensional compartmental models. The question may be viewed as a bi-objective minimization problem, where one tries to minimize simultaneously the cost of the vaccination, and a loss that may be either the effective reproduction number. We prove the existence of Pareto optimal strategies, describe the corresponding Pareto frontier, and study its convexity and stability properties. We also show that vaccinating according to the profile of the endemic state is a critical allocation, in the sense that, if the initial reproduction number is larger than 1, then this vaccination strategy yields an effective reproduction number equal to 1.In the second part of of the talk, we illustrate the theoretical framework developed previously with many examples.

MEPI-40 (Session: PS03)
Chaeyoung Lee Korea university
"Mathematical modeling for estimating the unidentified infected population of COVID-19"

The COVID-19 pandemic continues and causes major damage worldwide for more than a year. To prevent the spread of the infectious disease, it is significantly important to estimate the number of people who are infected but have not yet been confirmed because they can rapidly infect other people. Therefore, a mathematical model is proposed for predicting the unidentified infected population of COVID-19. This is the Susceptible-Unidentified infected-Confirmed (SUC) model, which is simple. Moreover, the proposed model is potentially useful in estimating the unidentified infected population to secure enough supplies for infection prevention, to prepare for testing and treatment of confirmed COVID-19 patients, and to monitor the impact of the new policies such as social distancing and school closures. Therefore, it is critical to estimate the unidentified infected population to control the spread of COVID-19.

MEPI-41 (Session: PS03)
Nicole Cusimano Basque Center for Applied Mathematics
"COVID-19 dynamics in the Basque Country: towards spatially dependent models"

More than one year after the discovery of the SARS-CoV-2 virus, the ongoing pandemic continues to affect the lives of people around the globe. Better understanding of the challenges posed by this virus are key to face the future with the right amount of caution, to guide current and future public health policies, and to inform the public to avoid the spreading of misinformation and fear. Mathematical models of infectious disease transmission have played (and will continue to play) an important role in this direction. In this talk, I will outline the development of the pandemic in the Basque Country, a compartmental modelling framework to describe the local reality (accounting for the basque government response in different stages of the pandemic), and discuss possible approaches to account for spatially refined information providing further insights into the local transmission dynamics.

MEPI-42 (Session: PS03)
Damián Knopoff Basque Center for Applied Mathematics
"A multiscale active particle model of epidemic spreading with heterogeneous interactions"

During this talk I will present a mathematical model of contagion and spread of a viral disease. The model is based on the kinetic theory for active particles and was developed using a multiscale framework accounting for the interaction of different spatial scales: from the small scale of viral particles and immune cells, to the larger scale of individuals and further up to the collective behavior of populations.The overall population is divided into compartments (susceptible, infectious, recovered and dead). Interactions between individual entities (hosts, viral particles, immune cells) are described at the micro-scale. A model of contagion through interactions is then proposed, depending on the interaction rate and a parameter describing the so-called social distance. Within infected hosts, viral particles and the immune system develop competitive interactions with transitions that may end up in a recovery or death. The dynamics of the system is then described by distribution functions at the meso-scale. The knowledge of these distribution functions allows to compute macroscopic variables (i.e. positive cases or deaths). Some case-studies are proposed in order to perform parameter sensitivity analyses and to understand responses of the system to different control measures aimed to reduce the impact of the disease.

MEPI-43 (Session: PS03)
Rey Audie S. Escosio Resilience Institute, University of the Philippines
"Modelling COVID-19 Dynamics with Different Community Quarantine Protocols in National Capital Region, Philippines"

The state of the pandemic in the Philippines surpasses 740,000 cumulative cases with very limited healthcare capacity as of March 30, 2021. Nearly half of this number comes from the National Capital Region of the Philippines. The response of the government is the implementation of the region-restricted Community Quarantines (CQ) labeled as Enhanced, Modified Enhanced, General, and Modified General. An SEIR mathematical model is developed to describe the transmission dynamics of the COVID-19 infection in the Philippines' capital region. The different tiers of CQs and non-pharmaceutical interventions are incorporated using population factors and a function affecting the susceptible and exposed compartments. The available data on cases and deaths are utilized for parameter estimation and uncertainty analyses of the model. Key model parameters that indicate the dynamics of the model are identified for different CQ periods. A more relaxed CQ level leads to more infections which can be attributed to the correspondent increase in the interacting population. The model could be developed for reliable use in short-term forecasting that may aid decision-making, such as in crafting and implementing CQs.

MEPI-44 (Session: PS03)
Iulia Martina Bulai University of Basilicata
"Influence of asymptomatic people on malaria transmission: a mathematical model for a low-transmission area case"

Malaria remains a primary parasitic disease in the tropical world, generating high morbidity and mortality in human populations. Recently, community surveys showed a high proportion of asymptomatic cases, which are characterized by a low parasitemia and a lack of malaria symptoms. Until now, the asymptomatic population is not treated for malaria and thus remains infective for a long time. In this paper, we introduce a four-dimensional mathematical model to study the influence of asymptomatic people on malaria transmission in low-transmission areas, specifically using data from Brazil. The equilibrium points of the system are calculated, and their stability is analyzed. Via numerical simulations, more in-depth analyzes of the space of some crucial parameters on the asymptomatic population are done, such as the per capita recovery rates of symptomatic and asymptomatic people, the ratio of the density of mosquitoes to that of humans, the mortality rate of mosquitoes and the probability of undergoing asymptomatic infection upon an infectious mosquito bite. Our results indicate that the disease-free equilibrium is inside the stability region if asymptomatic people are treated and/or the ratio of the density of mosquitoes to that of humans is decreased and/or the mortality rate of mosquitoes is increased.

MEPI-45 (Session: PS03)
Hyunwoo Cho Yonsei university
"Age-structured Pulmonary TB dynamics and cost-effectiveness analysis in Korea"

Objective: Tuberculosis(TB) is an infectious disease, causing more than 2000 deaths per year in Korea. Despite the effort of government, Korea still suffers from high mortality rate due to TB, ranking first among OECD countries. This study was aimed to evaluate the effect of close contact control strategies in different age groups and analyze cost-effectiveness of each control strategies.Method: An age-structured deterministic model was developed for the TB transmission in Korea. A SEIT (susceptible - exposed - infectious - treating) model was used with some additional compartments including 'high risk latent', 'low risk latent', and 'LTBI treated'. 15 different age groups were used to analyze different control strategies to different age group. Cost-effectiveness was analyzed using ICER through comparing incremental cost and incremental QALY by reducing number of TB patients.Result: The model suggested that close-contact control has the most effect in young age group(0-35). Expanding close-contact control will have mild effect on decreasing number of TB incidence every year, but decreasing the number of TB incidence by expanding close contact control does not guarantee cost-effectiveness in long term.

MEPI-46 (Session: PS03)
Andrew Bate University of York
"Biosecurity coalitions in small heterogenous networks"

Preventing disease outbreaks can have widespread benefits that are dependent on the actions of many farmers but can be undermined by the inaction of others. Consequently, understanding conditions where or how well farmers will work together is important to designing policies in preventing outbreaks. We use a coalition game theoretic approach, where farmers who have two decisions, whether to cooperate in a coalition and how much effort they put into preventing outbreaks. Additionally, each farmer considers three costs; a cost from an outbreak on their farm, a cost from an outbreak on a “neighbouring” farm (e.g. within range of movement restrictions), and the costs of outbreak prevention. For two heterogeneous farms, two similar farms are likely to cooperate, whereas farms with significantly different costs are unlikely to cooperate. For three identical farms, we consider two networks: all farms are “neighbours” (triangle network) or two farms are “neighbours” to be a third middle farm (line network). For triangle networks, full cooperation requires small on-farm costs, whereas for line networks, full cooperation can happen in situations where on-farm costs are larger than those from neighbouring farms. This all suggests that location and structure is important to whether farmers cooperate.

MEPI-47 (Session: PS04)
Lucia Wagner St. Olaf College
"Modeling Public Health Impact of E-Cigarettes on Adolescents and Adults"

Since the introduction of electronic cigarettes into the United States market in 2007, vaping usage has surged in both adult and adolescent populations. E-cigarettes are advertised as a safer alter-native to traditional cigarettes and as a method of smoking cessation, but the US government and health professionals are concerned that e-cigarettes attract young non-smokers. Here we develop and analyze a dynamical model of competition between traditional and electronic cigarettes for adult and adolescent users. With this model, we address three urgent questions: (1) how did the introduction of e-cigarettes influence the prevalence of smoking, (2) what is the predicted number of traditional smokers diverted to vaping after its inception, and (3) from a public health perspective, do e-cigarettes present a net benefit or harm to society?

MEPI-48 (Session: PS04)
Benjamin Adam Catching UCSF
"Examining face-mask usage as an effective strategy to control COVID-19 spread"

The COVID-19 global crisis is facilitated by high virus transmission rates and high percentages of asymptomatic and presymptomatic infected individuals. Containing the pandemic hinged on combinations of social distancing and face mask use. Here we examine the efficacy of these measures, using an agent-based modeling approach that evaluates face masks and social distancing in realistic confined spaces scenarios. We find face masks are more effective than social distancing. Importantly, combining face masks with even moderate social distancing provides optimal protection. The finding that widespread usage of face masks limits COVID-19 outbreaks can inform policies to reopening of social functions.

MEPI-51 (Session: PS04)
Majid Bani Yaghoub University of Missouri-Kansas City
"Characterizing spread of infection in cattle farms using wavefronts of a reaction-diffusion coinfection model"

The present work studies the transmission dynamics of Escherichia coli O157:H7 in a dairy farm using a coinfection Reaction-Diffusion Susceptible-Infected-Susceptible model. Analysis of the model includes existence and stability of equilibria, and calculation of the basic reproduction number. Furthermore, it is numerically shown that the model exhibits stationary and traveling wavefronts. Existence of a stationary wavefront implies that the likelihood of infection transmission is a function of host's location. This is in contrast with recent studies that use Turing patterns to determine the likelihood of infection. In addition, formation of a one-hump traveling wavefront characterizes establishment of an endemic equilibrium in the entire spatial domain.

MEPI-52 (Session: PS04)
Pedro Henrique Pinheiro Cintra Gleb Wataghin Institute of Physics, University of Campinas
"Evaluating the effect of non pharmaceutical interventions on COVID-19 infection dynamics through agent based models"

In order to provide both qualitative and quantitative results regarding the efficacy of non pharmaceutical interventions, we use an agent based model, considering typical epidemiological parameter distributions for COVID-19 in an age-stratified population in each case. We suppose individuals can assume the following states: susceptible, asymptomatic, infected, exposed, recovered and dead. They move and exchange contact inside a defined area. Introducing agglomeration sites and social distancing, we evaluate the effect of different non pharmaceutical interventions through simulation results of attack rate, death rate and epidemic curves created in each scenario. Lastly, we suppose the interventions are lifted at a given time and evaluate how the duration of interventions change the infection dynamics.

MEPI-53 (Session: PS04)
Alex Busalacchi San Diego State University
"Modeling transmission dynamics of black band disease on coral reefs: temperature dependent microbiomes"

Black band disease (BBD) is one of the most prevalent diseases causing significant destruction of coral reefs. Coral reefs acquire this deadly disease from bacteria in the microbiome community, the composition of which is highly affected by the environmental temperature. While previous studies have provided useful insights into various aspects of BBD, the temperature-dependent microbiome composition has not been considered in existing models. We develop a transmission dynamics model, incorporating the effects of temperature on the microbiome composition, and subsequently on BBD of coral reef. Based on our model, we calculate the basic reproduction number, providing an environmental threshold for the disease to exist in the coral reef community. Our results suggest that temperature has a significant impact on coral reef health, with higher environmental temperatures resulting in more coral infected with BBD in general. Our model and related results are useful in investigating potential strategies to protect reef ecosystems from stressors, including BBD.

MEPI-54 (Session: PS04)
Jingjing Xu University of Alberta
"A spatio-temporal model for the spread of chronic wasting disease"

Chronic wasting disease (CWD) is a prion-based transmissible spongiform encephalopathy in deer species (cervids) that results in 100% mortality. It poses a threat to cervid populations and the local ecological and economic communities that depend on them. Although empirical studies have shown that host social grouping, home range overlap, and male dispersal are essential in the disease spread, few mechanistic models explicitly consider those factors. We present a spatio-temporal, differential equation model in 2D space for CWD spread. This model includes direct and environmental transmission for an age-structured population where vital rates are influenced by CWD infection, and grouping, home range sizes, and habitat preferences change with the season. We show how the spreading speed of CWD and the basic reproduction number in 2D space respond to the seasonal changes in demographics, resource distribution, and epidemiological parameters. We will use this framework to assess demographic and spatial harvesting strategies in the future.

MEPI-55 (Session: PS04)
João Pedro Valeriano Miranda Institute for Theoretical Physics, State University of São Paulo, São Paulo, Brazil
"Memory effect in time-window epidemic curve forecasting using Approximate Bayesian Computation"

Fitting compartmental models to epidemiological data aiming to produce reasonable forecasts can become a very complex task, especially when the data assume a behavior difficult to be attained by models with constant parameters. A common alternative is to build models with time-dependent parameters, which does not necessarily simplify the fitting process, but can make the model more descriptive. In this work we propose to adopt a simple SEIRD model with constant parameters, but dividing the epidemiological data into different time-windows, in which it is assumed that the data can be piecewise fitted, as an alternative way of adopting time-dependent parameters. Using Approximate Bayesian Computation , posterior distributions of parameters obtained in previous windows are used as prior distributions of corresponding parameters in subsequent windows. We show that taking advantage of this information does improve the predictive capacity of the model, when compared to the strategy in which noninformative priors are adopted for each window. Finally, we assess the combination of time-windows with different lengths, seeking for more accurate forecasts.

MEPI-58 (Session: PS04)
Daniel Cardoso Pereira Jorge Instituto de Física Teórica - UNESP
"Estimating the effective reproduction number for heterogeneous models using incidence data"

The effective reproduction number, R(t), is a central point in the study of infectious diseases. It establishes in an explicit way the extent of an epidemic spread process in a population. The current estimation methods for the time evolution of R(t), using incidence data, rely on the generation interval distribution, g(tau), which is usually obtained from empirical data or already known distributions from the literature. However, there are systems, especially highly heterogeneous ones, in which there is a lack of data and an adequate methodology to obtain g(tau). In this work, we use mathematical models to bridge this gap. We present a general methodology for obtaining an explicit expression of the R(t) and g(tau) provided by an arbitrary compartmental model. Additionally, we present the appropriate expressions to evaluate those reproduction numbers using incidence data. To highlight the relevance of such methodology, we apply it to the spread of Covid-19 in municipalities of the state of Rio de janeiro, Brazil. Using two meta-population models, we estimate the reproduction numbers and the contributions of each municipality in the generation of cases in all others. Our results point out the importance of mathematical modelling to provide epidemiological meaning of the available data.

MEPI-59 (Session: PS05)
Khagendra Adhikari Tribhuvan University
" Modelling COVID-19 in Nepal: Effectiveness of Control Measures"

While most of the countries around the globe are combating with the pandemic of COVID-19, the level of its impact is quite variable among different countries. In particular, the data from Nepal, a developing country having open border provision with highly COVID-19 affected country India, have shown a biphasic pattern of epidemic, a controlled phase (until July 21, 2020) followed by an outgrown phase (after July 21, 2020). In this presentation, I will describe the biphasic epidemic pattern of Nepal via a mathematical model and analyze the effectiveness of the control strategies implemented in Nepal.

MEPI-60 (Session: PS05)
Ramesh Gautam Tribhuvan University
"Modeling Imported malaria in Nepal with control strategies"

The cross-border mobility of seasonal migrant workers between Nepal and India is a major challenge for the malaria elimination program of Nepal. Having the open border provision with highly endemic country of malaria India, most of the recorded malaria cases of Nepal are imported. Here, we proposed a malaria model including control strategies to protect the migrant workers from mosquito biting during their stay in India. Moreover, we will analyze the backward bifurcation and level of control strategies for the elimination of malaria in Nepal by 2026

MEPI-61 (Session: PS05)
Akhil Kumar Srivastav Vellore Institute of Technology
"Modeling and optimal control analysis of COVID-19: Case studies from Italy and Spain"

Coronavirus disease 2019 (COVID-19) is a viral disease which is declared asa pandemic by WHO. This disease is posing a global threat, and almost everycountry in the world is now affected by this disease. Currently, there is no vaccine for this disease, and because of this, containing COVID-19 is not an easytask. It is noticed that elderly people got severely affected by this disease spe-cially in Europe. In the present paper, we propose and analyze a mathematicalmodel for COVID-19 virus transmission by dividing whole population in oldand young groups. We find disease-free equilibrium and the basic reproductionnumber (R0). We estimate the parameter corresponding to rate of transmissionand rate of detection of COVID-19 using real data from Italy and Spain by leastsquare method. We also perform sensitivity analysis to identify the key parameters which influence the basic reproduction number and hence regulate thetransmission dynamics of COVID-19. Finally, we extend our proposed model tooptimal control problem to explore the best cost-effective and time-dependentcontrol strategies that can reduce the number of infectives in a specified intervalof time.

MEPI-62 (Session: PS05)
Laura Marcela Guzman Rincon University of Warwick
"Estimation of the Growth-Rate of the SARS-CoV-2 epidemic at a subpopulation level"

The rapid identification of potential SARS-CoV-2 outbreaks is key in the design of optimal intervention strategies and the control of its propagation. We propose a fast and accurate approach to estimate the growth rate of positive results of SARS-CoV-2 tests in a given subset of the population. This estimation has been used in the collected PCR tests in England, for different local authorities and age groups. We describe the mathematical structure of the model and how it also provides an estimation of the weekday effect in data collection.

MEPI-63 (Session: PS05)
"Modelling the COVID-19 epidemic using delayed-impulsive differential equations"

Presently the large focus of the world community is on controlling the spread of COVID-19 infection. As of 30 March 2021, the COVID -19 infection has already accounted 121 million people and 2.9 million deaths worldwide. Many vaccines are now been approved for the prevention of COVID-19. Particularly in India as per government data available on 30 March 2021 more than 60 million people have been vaccinated. Forecasting is important for the alleviation of potentially fatal impacts of infectious diseases. In a pandemic, pronouncements are given in short supply of data in uncertain conditions. Also, this is not possible to know when the next pandemic will occur; however, mathematical modeling has the potential to increase the efficacy when a pandemic occurs. We analyze the Susceptible-Exposed-Infected-Vaccinated-Recovered (SEIVR) epidemic mathematical model of COVID-19. Our model includes two important aspects of COVID-19 infection: delayed start and effect of impulsive vaccination. The model has been analyzed theoretically and numerically both. We found that the COVID-19 infection-free periodic solution is globally asymptotically stable. Numerical simulations further show that impulsive vaccination with the vaccine of high efficacy will have the potential to reduce the spread of COVID-19 infection.