Modelling and analysis of a fractional-order epidemic model incorporating genetic algorithm-based optimization

Infectious diseases have always been a threat to the smooth running of our daily activities. To regulate the disease's devastating outcome, we have performed a qualitative study of infectious disease using an SIR model. While formulating the model, we have taken into account the saturated incidence function with three controls, namely, treatment control, vaccination control, and media awareness. To make the model more robust, we have updated the model using Caputo fractional-order differential equation. We have determined the existence and uniqueness of the solution along with all possible equilibrium points. We have also obtained the basic reproduction number and the criteria of asymptotic local and global stability, taking the basic reproduction number as the threshold parameter. Finally, to control the disease, we have performed the optimization using a metaheuristic search and optimization technique, genetic algorithm (GA).