Date of Award

Spring 5-2-2024

Document Type

Honors Project

Degree Name

Bachelor of Science

Department

Mathematics

Department Chair or Program Director

Esunge, Julius

First Advisor

Lee, Leo

Second Advisor

Sumner, Suzanne

Third Advisor

Hydorn, Debra

Major or Concentration

Mathematics

Abstract

Mathematical models in epidemiology describe how diseases affect and spread within a population. By understanding the trends of a disease, more effective public health policies can be made. In this paper, the Susceptible-Infected-Recovered-Susceptible (SIRS) Model was examined analytically and numerically to compare with the data for Coronavirus Disease 2019 (COVID-19). Since the SIRS model is a complex model, analytical techniques were used to solve simplified versions of the SIRS model in order to understand general trends that occur. Then by Euler's Method, the Runge-Kutta Method, and the Predictor-Corrector Method, computational approximations were obtained to solve and plot the SIRS model. Finally, with the Predictor-Corrector Method, the SIRS model was compared to COVID-19 data for 2021 in the United States. Using two different databases between the model and real data complicated the fit of the SIRS model on COVID-19. Nevertheless, the SIRS model could still potentially fit as the reinfection of COVID-19 has been a prevalent issue today.

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