ABS 029: Mathematical modeling and analysis of the SARS-CoV-2 pandemic

Srihan Pothapragada ¹

¹ University of Maryland: College Park

Van Wickle (2025) Volume 1, ABS 029

Introduction: A pneumonia-like illness emerged late in 2019, coined COVID-19 (caused by SARS-CoV-2), causing a devastating pandemic that spread to almost every country on earth (causing over 700 million confirmed cases and 7 million deaths worldwide). Mathematical modeling and analysis have historically been used to gain insight and understanding on the transmission dynamics and control of infectious diseases in human (and other non-human) populations. In this talk, I will discuss a mathematical modeling approach, based on using a model that stratifies the total population into several mutually-exclusive compartments based on disease status, for studying the trajectory and burden of the SARS-CoV-2 pandemic, and assessing some intervention and mitigation strategies.

Methods: We developed a deterministic compartmental S.I.R model to explore the dynamics of the SARS-CoV-2 pandemic. The total population at time t, denoted by N(t), was divided into three mutually-exclusive compartments based on disease status, namely susceptible (S), infected (I), and recovered (R), so that N(t)=S(t)+I(t)+R(t). The resulting model, which consists of a deterministic system of three nonlinear differential equations, is rigorously analyzed to gain insight into its dynamical features. In particular, it was shown that its disease-free equilibrium is shown to be asymptotically stable whenever its associated reproduction is less than one, and unstable if it exceeds one.

Results: The dynamics of the disease is governed by the value of an epidemiological threshold, known as the basic reproduction number (R₀). The disease dies out if R₀ is less than one, and persists in the community if its value exceeds one. Hence, this study shows that bringing (and maintaining) R₀ to a value less than one is necessary and sufficient for controlling and mitigating the spread of the COVID-19 pandemic in a population.

Discussion: Through the analysis of the S.I.R model, this study demonstrates that reducing the basic reproduction number (R₀) below one is sufficient and necessary to prevent disease transmission. These findings confirm the importance of timely and sustained public health interventions that lower R₀. The model provides a general framework for evaluating mitigation strategies and guiding policy decisions in managing current and future pandemics.