Complex dynamics of a fractional-order epidemic model with saturated media effect

Abstract

A four-compartmental fractional-order epidemic model has been investigated to understand the transmission mechanism of infectious diseases with the population’s memory effect. The existence and uniqueness criterion of the model solution of the proposed fractional-order model is verified. Utilizing the next-generation matrix method, a threshold quantity called, the basic reproduction number () is obtained. The model possesses two equilibrium points, infection-free and endemic. The asymptotic stability (local and global) of the proposed system at the equilibrium points has been analyzed thoroughly. It is observed that the total number of infections during the disease is influenced by the fractional-order of the model which represents the population’s memory. A transcritical bifurcation is exhibited around the infection-free equilibrium point when the basic reproduction number crosses unity. Additionally, a fractional-order optimal control problem has been studied by considering two disease interventions: media awareness and treatment. The policy containing infectious disease spread has been determined based on a cost-effectiveness analysis. Sensitivity indices are computed to determine which parameters significantly impact and hence may used in controlling the disease. Some numerical simulations have been performed to verify analytical results by using MATLAB2022a.