Global stability of an SIS epidemic model with feedback mechanism on networks

We study the global stability of endemic equilibrium of an SIS epidemic model with feedback mechanism on networks. The model was proposed by J. Zhang and J. Sun (Physica A 394:24–32, 2014), who obtained the local asymptotic stability of endemic equilibrium. Our main purpose is to show that if the feedback parameter is sufficiently large or if the basic reproductive number belongs to the interval $(1, 2]$ , then the endemic equilibrium is globally asymptotically stable. We also present numerical simulations to illustrate the theoretical results.