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

Primary: 58F15, 58F17; Secondary: 53C35.

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Epidemic models for complex networks with demographics

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

In this paper, we propose and study network epidemic models withdemographics for disease transmission. We obtain the formula of thebasic reproduction number $R_{0}$ of infection for an SIS model withbirths or recruitment and death rate. We prove that if $R_{0}\leq1$,infection-free equilibrium of SIS model is globally asymptoticallystable; if $R_{0}>1$, there exists a unique endemic equilibrium whichis globally asymptotically stable. It is also found thatdemographics has great effect on basic reproduction number $R_{0}$.Furthermore, the degree distribution of population varies with timebefore it reaches the stationary state.
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