Epidemic models for complex networks with demographics

Zhen Jin; Guiquan Sun; Huaiping Zhu

doi:10.3934/mbe.2014.11.1295

Article Contents

2014, Volume 11, Issue 6: 1295-1317. Doi: 10.3934/mbe.2014.11.1295

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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

Received: February 28, 2014

Revised: May 31, 2014

Published: August 2014

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Abstract

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.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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