Mathematical tools for understanding viral infections within-host and between-host

Monday, June 14 at 09:30am (PDT)
Monday, June 14 at 05:30pm (BST)
Tuesday, June 15 01:30am (KST)

SMB2021 SMB2021 Follow Monday (Tuesday) during the "MS01" time block.
Note: this minisymposia has multiple sessions. The second session is MS02-IMMU (click here).

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Hana Dobrovolny (Texas Christian University, United States), Gilberto Gonzalez-Parra (New Mexico Tech, United States)


The SARS-CoV-2 pandemic has made it clear that mathematical modeling plays an important role in rapidly advancing scientific knowledge in emergency situations. Population scale models have provided valuable information for public health authorities at the local and national levels, allowing them to assess the effect of different non-pharmaceutical interventions. At the within-host level, models of viral dynamics have helped to assess the possibility of re-purposing antivirals to treat the emerging epidemic. In order to be prepared for the next pandemic, we need to continue to refine mathematical tools for analyzing viral dynamics. This mini-symposium includes presentations on the development of mathematical modeling techniques for viral infections, covering both the within-host dynamics and population-level dynamics.

Guang Lin

(Purdue University, United States)
"Predicting the COVID-19 pandemic with uncertainties using data-driven models"
We have developed an integer-order COVID-19 epidemic model and a fractional-order COVID-19 epidemic model to reconstruct and forecast the transmission dynamics of COVID-19 in New York City. To quantify the uncertainties in the proposed data-driven epidemic model, we have investigated model sensitivity analysis, structural and practical identifiability analysis, model calibration, and uncertainty quantification. We have employed Bayesian model calibration and physics-informed machine learning algorithms to calibrate the model parameters. In the early stage of the outbreak in New York City, the reproduction number was around 4.3, which indicates this outbreak has high transmissibility. We observed that multi-pronged interventions, such as the stay-at-home order and social distancing, had positive effects on controlling the outbreak and slowing the virus's spread. In addition, we employed the proposed data-driven models to evaluate the effects of various strategies to deploy the Covid-19 vaccine to control the pandemic. We have also applied the formulation to infer the dynamics of COVID-19 in other cities/states, where the spread dynamic is different from New York City.

Ana Vivas-Barber

(Norfolk State University, United States)
"Using Seasonality and Variable Incubation Periods to Study the Impact of Including Domestic Animals on the Dynamics of Malaria Transmission"
We investigate the impact of including variable mosquito population and added variable long and short incubation periods on the transmission dynamics of Malaria in Korea. The SEIS model is based on malaria infected mosquitoes which bite humans or animals. This model studies plasmodium vivax malaria and has variables for animal population and mosquito attraction to animals. The basic reproduction number of the ODE model with seasonal mosquito population (exponential) is presented and analyzed. The existing time-independent Malaria population ODE model was extended to time-dependent model with the difference explored. Also, using bi-modal Malaria incubation, changes to the infectious population when constant incubation period is extended to varied in the ODE model. Endemic equilibrium and stability analysis for the model was conducted with conditions on variables to insure solvability and DFE.

Imelda Trejo Lorenzo

(Los Alamos National Laboratory, United States)
"A modified Susceptible-Infected-Recovered model for observed under-reported incidence data"
In this talk, I will present a mathematical model to quantify the fraction of unreported infected individuals during epidemic outbreaks. The model consists of three parts (1) a dynamical system base on the classical Susceptible-Infected-Recovered (SIR) epidemic model, (2) a stochastic model for the observed incidence and (3) a Bayesian approach to estimate the model parameters. We use the model to estimate the infection rate and fraction of under-reported individuals for the current Coronavirus 2019 outbreak in some American Countries. Our analysis reveals that consistently, about 50% of infected individuals were not observed in various South American outbreaks.

Naveen Vaidya

(San Diego State University, United States)
"Modeling the risk of SARS-CoV-2 transmission from fomites"
The novel coronavirus disease (COVID-19) constitutes one of the most devastating pandemics of the 21st century. While direct person-to-person transmission of SARS-CoV-2, the etiological agent of COVID-19, appears to be the primary route of transmission, the contraction of SARS-CoV-2 from fomites in the environment is also considered a potential contributor to the disease transmission. In this talk, I will present a mathematical model to predict the probability of detecting SARS-CoV-2 in the environmental reservoirs during the COVID-19 outbreak in a community. Furthermore, we extend our model to predict the potential contribution of fomite transmission to the generation of new COVID-19 cases. We validate our model using experimental data with a large number of swab samples collected from commonly touched surfaces across San Diego County. Our model, which is capable of describing transmission dynamics of COVID-19 within San Diego county, allows us to compute the risk for an individual to encounter virus in the environment. The results indicate that the persistence of virus in some environmental surfaces can lead to a significant number of COVID-19 cases in the community.

Hosted by SMB2021 Follow
Virtual conference of the Society for Mathematical Biology, 2021.