Optimal Control Strategies of COVID-19 Dynamics Model

Abstract

In this paper, we proposed the optimal control for the dynamics of COVID-19 with cost effectiveness strategies. First, we showed that model solution is positive, and bounded in a fixed domain. Besides, we used next-generation matrix to compute the basic reproduction number. If the basic reproduction number is less than one, then the disease-free equilibrium point is both locally and globally stable, respectively, via the help of Jacobian matrix and Lyapunov function, otherwise the endemic equilibrium occurs. The sensitivity analysis was determined with regard to all basic parameters. Then the model is fitted with COVID-19 infected cases reported from October 1, 2022 to October 30, 2022 in Ethiopia. The values of model parameters are then estimated from the data reported using the least-square method. Furthermore, using Pontryagin maximum principle, the model is extended to optimal control incorporating three control namely: personal protective, vaccination, and treatment of infected humans. Finally, based upon the numerical simulation of optimal controls and cost effectiveness analysis, the most optimal and less costly strategy to minimize the disease is combination of vaccination and treatment of infected.