Global analysis of an SIS model with an infective vector on complex networks

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• 作者：Yi Wang^a ;   ; ^{wangyi-mail@163.com} ; Zhen Jin^a ;   ; ^{jinzhn@263.net} ; Zimo Yang^b ;   ; ^{yangzimo415@gmail.com} ; Zi-Ke Zhang^b ;   ; ^{zhangzike@gmail.com} ; Tao Zhou^b ;   ; ^{zhutou@ustc.edu} ; Gui-Quan Sun^a ;   ; ^{gquansun@yahoo.com.cn}
• 关键词：Basic reproduction number ; Infective vector ; Complex networks ; Globally asymptotically stable
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2012
• 出版时间：April 2012
• 年：2012
• 卷：13
• 期：2
• 页码：543-557
• 全文大小：578 K

文摘

In this paper, 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 and study the effects of various immunization schemes. For the network model, we prove that if , the disease-free equilibrium is globally asymptotically stable, otherwise there exists an 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.