Global stability of a fractional order SIR epidemic model with double epidemic hypothesis and nonlinear incidence rate

Abstract

In this paper, we consider a fractional order SIR epidemic model with double epidemic hypothesis and specific functional response, where the fractional derivative is defined in the Caputo sense. The nonnegativity and boundedness of solutions in this system are proved. The basic reproduction number is obtained. Qualitative results show that the model has four equilibria: one disease-free equilibrium and three endemic equilibrium points. Local and global stability analysis of the equilibria are established.