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Epidemic models for complex networks with demographics

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


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