Optimal control analysis of a COVID-19 model

In this paper, an optimal control model for the transmission dynamics of COVID-19 is investigated. We established important model properties like nonnegativity and boundedness of solutions, and also the region of invariance. Further, an expression for the basic reproduction number is computed and its sensitivity w.r.t model parameters is carried out to identify the most sensitive parameter. Based on sensitivity analysis, optimal control strategies were presented to reduce the disease burden and related costs. It is demonstrated that optimal control does exist and is unique. The characterization of optimal trajectories is analytically studied via Pontryagin's Minimum Principle. Moreover, various simulations were performed to support analytical results. The simulation results showed that the proposed controls significantly influence the disease burden compared to the absence of control cases. Further, it reveals that the applied control strategies are effective throughout the intervention period in reducing COVID-19 diseases in the community. Besides, the simulation results of the optimal control suggested that concurrently applying all controlling strategies outperform in mitigating the spread of COVID-19 compared to any other preventive measures.