“…On the practical side, the study of this topic contributes to the understanding of behaviors of epidemics, while on the theoretical side, it provides a simple dynamical framework to demonstrate rich phase diagrams for analysis. Several mathematical models have been proposed to describe common infectious diseases, including two-state SIS model and threestate SIR model with S standing for susceptible, I for infected, and R for recovery in the epidemiological terminology [3,4]. A variety of methods have been developed to analyze the epidemic spreading processes, including generating function [5,6], pair-approximation [7], heterogeneous mean field theory [8][9][10], probability generating function [11,12], and branching process approximation [13,14].…”