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一类自适应网络上的传染病模型研究
引用本文:陈璐,张晓光. 一类自适应网络上的传染病模型研究[J]. 山东大学学报(理学版), 2019, 54(9): 76-82. DOI: 10.6040/j.issn.1671-9352.0.2018.729
作者姓名:陈璐  张晓光
作者单位:1.山西大学数学科学学院, 山西 太原 030006;2.山西大学复杂系统研究所, 山西 太原 030006
基金项目:国家自然科学基金资助项目(11601294,61803242,11801340);山西省青年基金资助项目(201801D221001,201801D221011,201601D021012)
摘    要:利用多项分布下的三元组逼近公式,对自适应网络中的SIS矩封闭传染病模型进行封闭,研究多项分布下自适应行为对传染病传播的影响,通过定性与稳定性理论,得到了模型的基本再生数R0,分析了平衡点的稳定性.得到断边重连自适应行为对传染病传播具有多重作用:当相对传染率足够小时,模型发生标准的前向分支,R0<1时疾病趋于灭绝;反之,从数学理论上严格证明了重连可导致后向分支和鞍结点分支等复杂动力学行为的发生,因此R0<1不足以控制传染病的传播。

关 键 词:自适应网络  传染病模型  稳定性  后向分支  鞍结点分支  

Research of an epidemic model on adaptive networks
CHEN Lu,ZHANG Xiao-guang. Research of an epidemic model on adaptive networks[J]. Journal of Shandong University, 2019, 54(9): 76-82. DOI: 10.6040/j.issn.1671-9352.0.2018.729
Authors:CHEN Lu  ZHANG Xiao-guang
Affiliation:1. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, China;2. Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China
Abstract:By using the triple approximation formula under multinomial distributions, the SIS moment closure infectious disease model in the adaptive network is closed, the effects of adaptive behavior on the spread of infectious diseases under multinomial distributions is studied. Through the theory of qualitative and stability, the basic reproduction number R0 of the model is obtained and the stability of the equilibrium points are analyzed. Adaptive behavior of rewiring has multiple effects on infectious disease transmission are obtained: When the relative infection rate is small enough, the model has a standard forward bifurcation and when R0<1, the disease tends to be extinct; on the contrary, mathematically, it is rigorously proved that the rewiring can lead to the occurrence of complex dynamic behaviors such as the backward bifurcation and saddle-node bifurcation, ect. Therefore R0<1 is not enough to control the spread of infectious diseases.
Keywords:adaptive network  epidemic model  stability  backward bifurcation  saddle-node bifurcation  
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