Mathematical Modeling, Analysis, and Simulation of the COVID-19 Epidemic

Abstract

The COVID-19 pandemic continues to present tremendous national challenges, as the number of cases in the United States rapidly increases. To understand this increase, many researchers have considered developing mathematical models that help to capture the dynamics of the spread of the disease. For COVID-19, the compartmental SEIR model and its variations have been widely employed. These models differ in the type of compartments included, nature of the transmission rates, seasonality, and several other factors. While the spread of COVID-19 is largely attributed to a wide range of human behaviors in the population, several of these traditional epidemiological SEIR models do not account for such behaviors. In this project, we consider a novel SEIR-based model that considers various behaviors including confinement, quarantine, and social distancing. We also explore having the transmission rate as a function of time. Furthermore, using the Next Generation Matrix method, we derive a basic reproduction number, which indicates the estimated number of new infectious cases per case. Numerical simulations for the various models we created was performed and a user-friendly graphical user interface was created. In the future, we plan to expand this project to incorporate control measures, such as face masks, age-based behaviors, transmission rates dependent on social behavior, and the CDC’s Five Pandemic Planning Scenarios. Ultimately, by accounting for behaviors in epidemiological models, we can investigate the COVID-19 pandemic more accurately and help educate the public about measures to mitigate it.