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Global analysis of an SIS model with an infective vector on complex networks. (English) Zbl 1238.92042

Summary: A modified SIS model with an infective vector on complex networks is proposed and analyzed, which incorporates some infectious diseases that are not only transmitted by a vector, but also spread by direct contacts between human beings. We treat direct human contacts as a social network and assume spatially homogeneous mixing between vector and human populations. By mathematical analysis we obtain the basic reproduction number \(R_{0}\) and study the effects of various immunization schemes. For the network model we prove that if \(R_{0}<1\), the disease-free equilibrium is globally asymptotically stable, otherwise there exists a unique endemic equilibrium such that it is globally attractive. Our theoretical results are confirmed by numerical simulations and suggest a promising way for the control of infectious diseases.

MSC:

92D30 Epidemiology
91D30 Social networks; opinion dynamics
05C82 Small world graphs, complex networks (graph-theoretic aspects)
93C95 Application models in control theory
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