A Pontryagin's maximum principle and optimal control model with cost-effectiveness analysis of the COVID-19 epidemic

The COVID-19 pandemic has ravaged almost every part of the world, causing severe loss of life and economic damage to the world economy. This study proposes a mathematical model of SARS-COV-2 by considering the high-risk population. We establish the local and global stability of the model based on a threshold. The local and global sensitivity analysis is conducted to predict the epidemiological parameters responsible for driving the infection. Using the Pontryagin maximum principle and optimal control theory, we included four time-dependent controls to assess the impact of five different strategies on our model. Results from numerical simulation of the model with controls show that the number of infections decreased. Finally, the cost-effectiveness analysis shows the most effective strategy with the lowest intervention cost.