# American Institute of Mathematical Sciences

2014, 11(6): 1295-1317. doi: 10.3934/mbe.2014.11.1295

## Epidemic models for complex networks with demographics

 1 Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030051, China 2 LAMPS and CDM, Department of Mathematics and Statistics, York University, Toronto, ON, M3J1P3, Canada

Received  March 2014 Revised  June 2014 Published  September 2014

In this paper, we propose and study network epidemic models with demographics for disease transmission. We obtain the formula of the basic reproduction number $R_{0}$ of infection for an SIS model with births or recruitment and death rate. We prove that if $R_{0}\leq1$, 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.
Citation: Zhen Jin, Guiquan Sun, Huaiping Zhu. Epidemic models for complex networks with demographics. Mathematical Biosciences & Engineering, 2014, 11 (6) : 1295-1317. doi: 10.3934/mbe.2014.11.1295
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