一类自适应网络上的传染病模型研究

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。

Research of an epidemic model on adaptive networks

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.