Optimal control analysis of fractional order delayed SIQR model for COVID-19

Abstract

In this study, we propose an optimal control strategies for a fractional-order COVID-19 model with time delay. Existence and uniqueness of a solution to the fractional delay model are investigated. We compute the basic reproduction number and establish the local stability analysis of the model under the Caputo derivative. We develop a fractional order delayed optimal control problem based on vaccination and treatment as time-dependent control parameters. We derive the necessary and sufficient condition for optimal control. In MATLAB, the resulting fractional delay optimality system is numerically solved employing the forward–backward sweep method. Our findings suggest that combining fractional-order derivatives with time-delay in the model enhances dynamics while increasing model complexity.