MC7 -- Modified SIR model to study COVID-19 infections in Spartanburg county

In this project, we applied a simple mathematical description known as an SIR model to study COVID-19 infections in Spartanburg County. It is a common epidemiological model that can compute and predict the number of cases over time in a closed population. Basic SIR models divide total populations into three categories: susceptible, S, infected, I, and removed, R. This results in a system of three differential equations, one for each population group, S, I, and R respectively. There are many variations and applications of this model available in literature. In this study, we modified basic SIR model to ‘SECIR’ model to study COVID-19 infections. We added two additional population groups; first, the exposed but not yet infected people, and second is the cautious group of the population. This group is made up of people who take precautions, follow social distancing, stay home and work from home. The cautious group in the population contributes positively to reduce the number of infections by following recommendations. Our SECIR model consists of five groups: susceptible, exposed, cautious, infected, and removed. This modified model resulted in five coupled nonlinear ordinary differential equations which we solved using highly accurate Runge-Kutta numerical method in MATLAB. The results of the model show that as we increase the initial value of the cautious group, the number of infections decrease, and the peak infections can be achieved sooner in the outbreak. We further investigated the effects of time constrained immunity on the dynamics of infections as well as the effect of vaccinations