Fractional Optimal Control Model of SARS-CoV-2 (COVID-19) Disease in Ghana

TL;DR

This paper develops a fractional-order COVID-19 model for Ghana using Atangana Baleanu Caputo derivatives, analyzing optimal control strategies like social exclusion and vaccination to effectively curb the disease.

Contribution

It introduces a novel fractional mathematical model for COVID-19 in Ghana and evaluates optimal control strategies using real data, enhancing understanding of intervention impacts.

Findings

Fractional operator significantly impacts disease compartments.

Incidence rate increases when v>0.6.

Social exclusion and vaccination are highly effective controls.

Abstract

Research focus on optimal control problems brought on by fractional differential equations has been extensively applied in practice. However, because they are still open-ended and challenging, a number of problems with fractional mathematical modeling and problems with optimal control require additional study. Using fractional-order derivatives defined in the Atangana Baleanu Caputo sense, we alter the integer-order model that has been proposed in the literature. We prove the solution's existence, uniqueness, equilibrium points, fundamental reproduction number, and local stability of the equilibrium points. The operator's numerical approach was put into practice to obtain a numerical simulation to back up the analytical conclusions. Fractional optimum controls were incorporated into the model to identify the most efficient intervention strategies for controlling the disease. Utilizing actual data from Ghana for the months of March 2020 to March 2021, the model is validated. The simulation's results show that the fractional operator significantly affected each compartment and that the incidence rate of the population rose when v>0.6. The examination of the most effective control technique discovered that social exclusion and vaccination were both very effective methods for halting the development of the illness.