一类斑块环境下口蹄疫传染病模型的动力学分析

Dynamical Analysis of a Foot-and-Mouth Disease Epidemic Model in Patchy Environment

摘要: 针对口蹄疫病毒在斑块环境中的传播现象，建立了一个斑块口蹄疫传染病模型。分别就单斑块和两个斑块中病毒动力学行为展开研究。通过下一代矩阵理论，定义了模型的基本再生数，分析了单斑块模型无病平衡点及地方病平衡点的存在性和局部稳定性；通过构造合适的李雅普诺夫函数证明了单斑块模型平衡点的全局渐进稳定性。在两个对称的斑块环境中，通过李亚普诺夫函数法进一步确定了多斑块模型无病平衡点和地方病平衡点的全局渐进稳定性。

Abstract: A patchy foot-and-mouth disease epidemic model was established to study the transmission dynamics of the virus in patch environment. The viral transmission behaviors were investigated in both single-patch and two-patch systems. Using the next-generation matrix theory, the basic reproduction number of the model was defined, and the existence as well as local stability of the disease-free equilibrium and endemic equilibrium in the single-patch model were analyzed. By constructing an appropriate Lyapunov function, the global asymptotic stability of the equilibria in the single-patch model was demonstrated. In a symmetric two-patch environment, the global asymptotic stability of the disease-free equilibrium and endemic equilibrium in the multi-patch model was further confirmed through the Lyapunov function method.