### Mathematical Biosciences and Engineering

2014, Issue 6: 1295-1317. doi: 10.3934/mbe.2014.11.1295

# Epidemic models for complex networks with demographics

• Received: 01 March 2014 Accepted: 29 June 2018 Published: 01 September 2014
• MSC : Primary: 58F15, 58F17; Secondary: 53C35.

• 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.

Citation: Zhen Jin, Guiquan Sun, Huaiping Zhu. Epidemic models for complex networks with demographics[J]. Mathematical Biosciences and Engineering, 2014, 11(6): 1295-1317. doi: 10.3934/mbe.2014.11.1295

### Related Papers:

• 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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