空间离散传染病扩散模型研究

Analysis of spatial discretized diffusive endemic model

采用二阶中心差商方法得到传染病扩散模型的空间离散形式,并应用电路系统中的解耦合方法,得到该模型在两个空间齐次平衡态处线性化系统的特征方程,研究了两个平衡态的局部稳定性问题。结果表明:两个平衡态均不会出现Hopf分支;通过构造Lyapunov函数和应用Lasalle不变性原理,研究了两个平衡态的全局稳定性问题,并通过MATLAB数值模拟,给出理论分析的直观解释。

This article considers a spatial discretized diffusive epidemic model,which is derived by using the secend order centered difference approximations and appling the decoupling method in circuit systems.The characteristic equations of the linearized system at the two spatial homogeneous steady states are derived respectively.Then the local stability of the two steady states and the nonexistence of Hopf bifurcation are researched.The global stability of the two steady states are studied by constructing Lyapunov functions and applying Lasalle invariance principle.Simulations are given to demonstrate the theoretical results by means of the package of MATLAB.