## Global asymptotic stability and a property of the SIS model on bipartite networks.(English)Zbl 1238.34110

Summary: We study an SIS model on bipartite networks, in which the network structure and a connectivity-dependent infection scheme are considered. Applying the theory of the multigroup model, we prove the existence and the asymptotic stability of the endemic equilibrium. And then we examine the ratio between the densities of infected female and male individuals on the bipartite networks. In particular, we find that when the scale exponent $$(\gamma _{F})$$ of females is equal to and that of males $$(\gamma _{M})$$, the ratio is only determined by the scale exponents and the proportion between the infection rates of females and males $$(\lambda _{F}/\lambda _{M})$$. We also present a result for the ratio by numerical simulations when $$\gamma _{F}\neq \gamma _{M}$$.

### MSC:

 34D23 Global stability of solutions to ordinary differential equations 92D30 Epidemiology
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### References:

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