一类时滞虫媒传染病模型的稳定性分析

Stability Analysis of a Vector-borne Disease Model with Time Delay

  • 摘要: 建立和研究了一类具有非线性发生率和时滞的虫媒传染病模型,以雅克比矩阵和谱半径为工具得到了基本再生数R0的表达式.证明了当R0<1时,系统存在唯一的无病平衡点,且是全局渐近稳定的,此时疾病消失;当R0>1时,存在唯一的地方病平衡点,并分析了该平衡点渐近稳定的条件.

     

    Abstract: A vector-borne disease transmission model with nonlinear incidence rate and time delay was established and studied. The expression of basic reproduction number R0 was derived by using Jacobian matrix and spectral radius as tools. If R0<1, then the model had an unique globally asymptotically stable disease-free equilibrium, and the disease would fade away. If R0>1, then the model had an unique endemic equilibrium, and the conditions for the asymptotic stability of the equilibrium were analyzed.

     

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