Global stability of two SIS epidemic mean-field models on complex networks: Lyapunov functional approach

The global stability of the endemic equilibrium is of particular interest in characterizing the behaviours of epidemic models on complex networks. Due to the specific structures of SIS models, rigorous proof of the global property for systems has been challenging. In this paper, we propose a general method to calculate the basic reproduction number R0 of some mean-field epidemic models on complex networks by the renewal process. This method can be generalized to estimate the basic reproduction number R0 of edge-based compartmental model and pairwise model on complex networks. Furthermore, we show an overall results for the globally asymptotical stability of the endemic equilibrium compared with constructing monotone sequences in existing literatures.