Fractional optimal control dynamics of coronavirus model with Mittag–Leffler law

Bonyah, Ebenezer; Sagoe, Ato Kwamena; Kumar, Devendra; Deniz, Sinan

Most countries around the world are battling to limit the spread of severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2). As the world strives to get an effective medication to control the disease, appropriate control measures for now remains one of the effective measures to reduce the spread of the disease. In this study, a fractional optimal control model is formulated in Atangana-Baleanu-Caputo derivative sense. The reproduction number and steady state of disease free of the Coronavirus model are examined and found to be globally stable. The existence and uniqueness of solution of the fractional Coronavirus model is established by using the Banach fixed point theorem approach. Three controls are considered in the model and Pontryagins Maximum Principle is used to establish the necessary conditions for optimal control solution. The numerical solution suggests that the best strategy is found to be the utilization of all three controls at the same time.