A SIR Model Assumption for the Spread of COVID-19 with the Effects of Vaccination

Abstract

This study is to propose a Susceptible-Infected-Recovered (SIR) model to describe the spread of COVID-19 pandemic with the effects of vaccination. Vaccination becomes one of the crucial roles in lessening the impact of this virus on the society. To investigate this impact, it is worth making a comparison between the models without and with vaccination effort in studying the models. In this study, the analytical solutions are derived with the aid of stability analysis. The solutions consist of both numerical and graphical approaches using Maple and Matlab softwares. The steady-states, associated eigenvalues and reproduction number of  and  are calculated to determine the stability and the conditions of the existence of disease-free equilibrium and endemic equilibrium. Using these results, it is concluded that the effect of vaccination is significant in mitigating this virus from spreading unboundedly.