Computationally efficient optimal control analysis for the mathematical model of Coronavirus pandemic

Corona virus disease which has caused frustration in the human community remains the concern of the globe as every government struggles to defeat the pandemic. In this manuscript, we have extensively studied a new deterministic SEQIHR model of deadly Corona virus pandemic governed by nonlinear ordinary differential equations to provide deep insight into the dynamics of the disease. The purpose is to perform a complete mathematical analysis and the design of an optimal control strategy for the developed deterministic model by utilizing the preventive measures of quarantine and hospitalization. Some comprehensive mathematical techniques are employed to demonstrate the positivity and boundedness of solutions. Two main equilibrium points of the pandemic model are stated. To handle the future dynamical behavior of the pandemic, the threshold parameter value is computed using the next-generation method. The local and global asymptotic stability conditions of both the equilibria are obtained successfully. A numerical analysis to observe the effectiveness of quarantine and hospitalization strategies is performed and illustrated by graphs. We implemented the well known Non-Standard Finite Difference (NSFD) method to find the numerical solution of model. Numerical simulations are conducted to support our analytic results. The developed model is subjected to sensitivity analysis and the most sensitive parameters are identified. The bifurcation nature of the developed model is examined. An optimal control problem is introduced for the proposed model to determine the best controls for the implemented hospitalization and quarantine strategies. With the attention of reducing the number of exposed and infected persons, an optimum control problem and its derived associated optimality conditions of Pontryagin type are explored. An important feature of this study is to employ NSFD method backward in time for the first time to solve optimal control problem instead of other standard methods. The extremals are obtained numerically. Moreover, we have shown the effectiveness of optimal controls on the human community to view more features of the state variables in the proposed model.