一类具扩散的SIR传染病模型的稳定性分析

摘要

研究一类具有空间扩散的SIR传染病模型，通过讨论线性化方程的特征值得到该模型的染病平衡点是局部稳定的，并利用Lyapunov函数得到该平衡点全局渐近稳定的一个充分条件。%　　An SIR epidemic model with spatial diffusion is investigated. Local stability of the endemic equilibri⁃um of the epidemic model is presented by analyzing eigenvalues corresponding to linearization equation. A suffi⁃cient condition is obtained for the global asymptotic stability of the endemic equilibrium by Lyapunov function method.