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Epidemic dynamics on semi-directed complex networks. (English) Zbl 1283.92056
Summary: An SIS model for epidemic spreading on semi-directed networks is established, which can be used to examine and compare the impact of undirected and directed contacts on disease spread. The model is analyzed for the case of uncorrelated semi-directed networks, and the basic reproduction number \(R_0\) is obtained analytically. We verify that the \(R_0\) contains the outbreak threshold on undirected networks and directed networks as special cases. It is proved that if \(R_0<1\) then the disease-free equilibrium is globally asymptotically stable, otherwise the disease-free equilibrium is unstable and the unique endemic equilibrium exists, which is globally asymptotically stable. Finally numerical simulations for these analytical results are given.

MSC:
92C60 Medical epidemiology
92C42 Systems biology, networks
92D30 Epidemiology
92-08 Computational methods for problems pertaining to biology
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