Mathematical modelling of COVID-19 transmission with optimal control and cost-effectiveness analysis

The present global health threat is the novel coronavirus disease (COVID-19), caused by a new strain of the SARS-CoV-2 coronavirus. In this study, have employed optimal control theory, aided by Pontryagin’s Maximum Principle, to explore optimal control measures. Specifically, we have investigated time-dependent intervention strategies, including the proper use of personal protective measures and vaccination. Bifurcation analysis was conducted and results shows that the model system exhibit a forward bifurcation. The optimal control system have been numerically simulated using the fourth-order Runge–Kutta methods. The results show that the implementation of the combination of the two interventions was more significant and effective in minimizing the spread of the COVID-19 than the implementation of a single control measure. These findings underscore the significance of multifaceted intervention approaches over singular control measures. Notably, the combined implementation of interventions emerges as markedly more effective in containing COVID-19 transmission. Moreover, our study identifies personal protective measures as a particularly cost-effective intervention, offering substantial relief from the burden of the pandemic within the population. We anticipate that our research will inform evidence-based approaches to pandemic control and aid in the ongoing global efforts to safeguard public health.