Vaccination Model and Optimal Control Analysis of Novel Corona Virus Transmission Dynamics

In this paper, the mathematical model of the coronavirus pandemic with vaccination is formulated and analyzed to show the impact of severe acute respiratory syndrome coronavirus 2 pathogens in the environmental reservoir. In the model analysis, the vaccination-induced reproduction number which helps us in establishing the local and global stability of COVID-19-free and endemic equilibrium points was derived. The local stability of the COVID-19-free equilibrium is established via the Jacobian matrix and Routh-Hurwitz criteria. In contrast, the global stability of the endemic equilibrium is proved by using an appropriate Lyapunov function. Sensitivity indices are also discussed. The proposed model is extended into the optimal control problem by incorporating three control variables: preventive, medical care, and surface disinfection. Then, the necessary conditions for the optimal control of the disease were analyzed by applying Pontryagin minimum principle. Finally, the numerical simulations indicated that a combination of medical care and surface disinfection strategies is effective in controlling the disease epidemic.