A mathematical model for analyzing the transmission and control of COVID-19 pandemic with efficient interventions

The COVID-19 pandemic caused by SARS-CoV-2 continues to pose a significant global threat. Mathematical modeling offers a valuable tool for understanding transmission dynamics and designing control strategies. The recent emergence of new variants of the disease and the incidents of infections on people who had been previously recovered from the disease has necessitated the need to study the control of the transmission of the disease in the face of re-infection. Thus, this study presents a novel compartmental model for the COVID-19 epidemic that incorporates the possibility of re-infection. The model captures the transition of individuals through susceptible, quarantined, exposed, infected, treated, and recovered compartments. Various mathematical analysis of the model were presented to provide the reading audience with vital information on the disease dynamics. Afterwards, we employed optimal control theory to identify interventions that minimize the infected population while considering the associated costs. By applying Pontryagin's Maximum Principle, we determine the optimal control strategies for these interventions. This framework allows us to evaluate the effectiveness of various control measures, such as minimal contact, early therapeutic treatment of infected individual, quarantine and vaccination, in mitigating the epidemic while accounting for the possibility of re-infection. Our findings can inform public health decision-making as they provide insights into the most effective strategies for controlling the transmission of COVID-19 in the presence of re-infection.