Date of Award

6-2022

Degree Type

Honors College Thesis

Academic Program

Mathematics BS

Department

Mathematics

First Advisor

Zhifu Xie, Ph.D.

Second Advisor

Bernd Schroeder, Ph.D.

Third Advisor

Sabine Heinhorst, Ph.D.

Advisor Department

Mathematics

Abstract

In this work, we develop a simple mathematical model to observe the spread of COVID-19 and vaccine administration in Mississippi. Based on the well-known Kermack-McKendrick Susceptible-Infected-Removed epidemiological model, the ASIRD−V model has eight ordinary differential equations that split infected populations and recovered populations into vaccinated and unvaccinated populations. After determining that the system is reliable for real-world applications, we investigate and determine the stability and equilibrium points of this system. The system is found to be disease-free when R0 < 1 and endemic when R0 > 1. We use MATLAB to numerically solve the system and optimize the model’s parameters over four short periods, two with the presence of vaccines and two without the presence of vaccines, using death data and vaccine data given by the Centers for Disease Control. By calculating the reproduction numbers of the time periods, we analyze the effects of certain policy changes as well as the reliability of this model in predicting the spread of the disease. While the health policies at the start of the pandemic are reliable short-term solutions to slow the spread, the presence of fully vaccinated individuals slows the spread in the long term.

Keywords: COVID-19, ASIRD-V model, Stability, Parameter optimization, Vaccinations, Reproduction number, Numerical simulation

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