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.https://doi.org/10.1007/s10441-019-09373-9.
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
https://math.snu.edu.in/people/researchers/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)
Amit Sharma
JC DAV COLLEGE DASUYA
"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.