Cost‐Effective Optimal Control Studies of Corona Virus Transmission

ABSTRACT This paper analyzes the endemic spreading of COVID‐19 among co‐circulating respiratory infections by constructing a compartmental mathematical model of human and environment interactions. The mathematical structure describes the coupled interaction between the human population and the polluted viral environmental compartment. The existence, uniqueness, positivity, and boundedness of solutions are analyzed to confirm the well‐posedness of the mathematical formulation from the viewpoint of mathematical analysis and biological relevance. This paper embraces locally asymptotically stable disease‐free steady state under the condition of and unstable under the condition of . On the other hand, conditions of disease persistence steady state for both local as well as global asymptotical stability are incorporated under the conditions that spectral radius of next‐generation number yields greater than unity. Specifically, the local sensitivity computational analysis is implemented targeting the core parameters determining the communicating ability of the disease. Finally, the optimal control approach is introduced through the intervention of preventive actions, treatment of sick people, and environment decontamination. Computational results are implemented using MATLAB and cost‐effectiveness analysis of different action plans are carried out to explore the effectiveness of concerted action plans combining prevention, treatment, and environmental cleaning.