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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 05C82 Small world graphs, complex networks (graph theory) 93C95 Applications of control theory