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 R 0 $R_{0}$ for the model and prove that the disease-free equilibrium is globally attractive and that the disease dies out when R 0 1 $R_{0}>1$ . 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