Dynamics Modeling and Analysis of SIS Epidemic Spreading in Cluster Networks

In this paper, we propose and study an SIS epidemic model with clustering characteristics based on networks. Using the method of the existence of positive equilibrium point, we obtain the formula of the basic reproduction number R0. Furthermore, by constructing Lyapunov function, we also prove that the disease-free equilibrium of the model is globally asymptotically stable when R0<1. When R0>1, there is only one positive equilibrium point which is globally asymptotically stable. It is also shown that the infection proportion and the basic reproduction number R0 increases as the clustering coefficient increases when the average degree of networks is fixed.