一类具有多种传播途径的SIRW传染病模型的全局稳定分析

Global Analysis of the Waterborne Diseases Model with Multiple Transmission Ways

本文针对一类具有多种传播途径的SIRW传染病动力学模型进行全局稳定分析.通过两种方法来进行证明,方法一利用二次复合矩阵和极限系统理论相结合的方法;方法二利用Volterra-Lyapunov稳定矩阵与Lyapunov方程相结合的方法.两种方法均能证明当R_0>1时,地方病平衡点是全局稳定的.

In this paper,we use two approaches to prove the global stability for the endemic equilibrium of the waterborne diseases model with multiple transmission ways.First we use the second additive compound matrix and the limiting system theory;Next we incorporate the Volterra-Lyapunov stable matrices theory into the classical Lyapunov functions.Both of the two methods can prove that the unique positive endemic equilibrium of system(1-4) is globally asymptotically stable when R_0 > 1.