Optimal Control Analysis of the Dynamics of COVID-19 with Application to Ethiopian Data

Abstract

In this paper, we proposed an optimal control of the COVID-19 transmission dynamics. First, we investigated system features such as solution boundedness, positivity, disease-free and endemic equilibrium, and the local and global stability of equilibrium points. Besides, a disease-free equilibrium point is globally asymptotically stable if the basic reproduction number is less than one, and an endemic equilibrium point exists otherwise. Secondly, we have shown the sensitivity analysis of the basic reproduction number. Also the model is then fitted using COVID-19 infected reported in Ethiopia from February 1,2023 to March 2,2023. The values of model parameters are then estimated from the data reported using the least square method together with the the MATLAB software. Moreover, the optimal corruption minimization strategies are determined using three controls strategies, namely prevention, vaccination and treatment. The existence of the optimal controls and characterization is established using Pontryagin’s Maximum Principle. Finally, based on analysis of optimality system, the combination of the prevention and treatment of infected is the most optimal and least cost strategy to minimize the burden of the disease.