EPIDEMIC MODELS FOR COMPLEX NETWORKS WITH DEMOGRAPHICS

In this paper, we propose and study network epidemic models with demographics for disease transmission. We obtain the formula of the basic reproduction number Ro of infection for an SIS model with births or recruitment and death rate. We prove that if R-0 <= 1, infection-free equilibrium of SIS model is globally asymptotically stable; if R-0 > 1, there exists a unique endemic equilibrium which is globally asymptotically stable. It is also found that demographics has great effect on basic reproduction number R-0. Furthermore, the degree distribution of population varies with time before it reaches the stationary state.