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Zbl 1238.92042
Wang, Yi; Jin, Zhen; Yang, Zimo; Zhang, Zi-Ke; Zhou, Tao; Sun, Gui-Quan
Global analysis of an SIS model with an infective vector on complex networks. (English)
[J] Nonlinear Anal., Real World Appl. 13, No. 2, 543-557 (2012). ISSN 1468-1218

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 2000:: *92D30 Epidemiology
91D30 Social networks
05C82
93C95 Appl. of control theory

Keywords: basic reproduction number; global asymptotic stability

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