Some new aspects on COVID-19 transmission dynamics applicable to other epidemics: Insights from mathematical modeling and numerical simulations

In this study, a mathematical model is constructed, analyzed, and numerically simulated to investigate the effects of vaccination rates and efficacy on the incidence of COVID-19. The model subdivides the infectious class into symptomatic, asymptomatic, and hospitalized individuals, enabling us to explore questions inadequately addressed by prior models. First, the existence of a region where the model is epidemiologically feasible is established. Then a thorough qualitative analysis is carried out in order to characterize the long-term dynamics of the model solutions, and the model is calibrated using South Africa-reported data from the beginning of the epidemic until July 2022. In addition, different numerical scenarios with different transmission rates, non-pharmaceutical interventions (NPIs), and vaccination parameters were investigated. The model, analysis, and results of this study can be adapted to study the dynamics of other epidemics.