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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 for the model and prove that the disease-free equilibrium is globally attractive and that the disease dies out when R 0 < 1, while the disease is uniformly persistent when 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.

A novel [Formula: see text] epidemic spreading model with distributed delay on complex heterogeneous network is presented. The formula of the basic reproductive number is presented to the model. It is proven that the disease dies out if the basic reproductive number is less than unity, while if the basic reproductive number is more than unity, the disease is uniformly persistent. The results enrich the previous results.

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