Global stability and attractivity of a network-based SIS epidemic model with nonmonotone incidence rate

In this paper, we study the global stability and attractivity of the endemic equilibrium for a network-based SIS epidemic model with nonmonotone incidence rate. The model was introduced in Li (2015). We prove that the endemic equilibrium is globally asymptotically stable if α (a parameter of this model) is sufficiently large, and is globally attractive if the transmission rate λ satisfies λλc∈(1,2], where λc is the epidemic threshold. Some numerical experiments are also presented to illustrate the theoretical results.