Fractional COVID-19 Modeling and Analysis on Successive Optimal Control Policies

Abstract

A fractional-order coronavirus disease of 2019 (COVID-19) model is constructed of five compartments in the Caputo-Fabrizio sense. The main aim of the paper is to study the effects of successive optimal control policies in different susceptible classes; a susceptible unaware class where awareness control is observed, a susceptible aware class where vaccine control is observed, and a susceptible vaccinated class where optimal vaccination control is observed. These control policies are considered awareness and actions toward vaccination and non-pharmaceuticals to control infection. Equilibrium points are calculated, which subsequently leads to the computation of the basic reproduction ratio. The existence and uniqueness properties of the model are established. The optimal control problem is constructed and subsequently analyzed. Numerical simulations are carried out and the significance of the fractional-order from the biological point of view is established. The results showed that applying various control functions will lead to a decrease in the infected population, and it is evident that introducing the three control measures together causes a drastic decrease in the infected population.

Keywords

• mathematical model
• fractional-order
• Caputo-Fabrizio
• optimal control
• existence and uniqueness
• basic reproduction ratio