Modeling and analyzing COVID-19 infections in South Africa

In this paper, we present a mathematical model that incorporates seasonal variations in COVID-19 transmission within South Africa. By fitting the model to real-world data, we estimate its parameters and demonstrate its enhanced accuracy in describing the local infection dynamics. We analyze the basic reproduction number and establish threshold dynamics through theoretical analysis, alongside investigating its numerical relationship with specific parameters. Furthermore, we conduct an optimal control analysis to evaluate the impact of intervention strategies, including quarantine, vaccination and medical treatment, on COVID-19 spread. Our findings emphasize the effectiveness of combining all three interventions in reducing the number of exposed and infected individuals. We identify that implementing these interventions when the infected population is at its lowest yields optimal results.