Analysis of an SIRS epidemic model with time delay on heterogeneous network

Abstract

We discuss a novel epidemic SIRS model with time delay on a scale-free network in this paper. We give an equation of the basic reproductive number R0 for the model and prove that the disease-free equilibrium is globally attractive and that the disease dies out when R0< 1 , while the disease is uniformly persistent when R0> 1. In addition, by using a suitable Lyapunov function, we establish a set of sufficient conditions on the global attractiveness of the endemic equilibrium of the system.