Modeling COVID-19 with Discrete-Time Markov Chains

<p> Presentation given at the Southern Georgia Mathematics Conference.</p><p> <a href="https://cosm.georgiasouthern.edu/wp-content/uploads/SGMC-ABSTRACT-BOOKLET.pdf" target="_self"> Abstract Booklet </a></p><p> According to the WHO, globally, as of March 5, 2021, Coronavirus Disease 2019 (COVID-19) has infected over 115 million people, caused over 2.5 million deaths and widespread economic downturn. In this talk, we present our modeling, numerical simulation, and analysis of the stochastic dynamics of COVID-19 in a closed population that is considered the starting point of the outbreak of the disease. We present two COVID-19 epidemic models for the population, where at any given time an individual can be in any of the following categories: susceptible, exposed and mildly infectious, asymptomatic and infectious, symptomatic and infectious, symptomatic hospitalized and infectious, recovered with partial immunity, or deceased from disease related causes. Both models are discrete-time Markov chain (DTMC) models with multinomial transition probabilities. Using CDC data on daily infection rate for the state of Georgia, we attempt to fit the model to data using multiple linear regression and conduct sensitivity analysis on a selected stochastic model to determine the effects of varying disease parameters on the dynamics of the epidemic. The results from this work highlight the importance of applying statistical and stochastic methods to understand and control COVID-19 dynamics in a population.</p>