食饵染病且具有非线性功能反应函数的传染病模型的稳性分析

Stability analysis of an infectious disease model with disease and nonlinear functional response function

文章研究一类食饵染病且具有非线性功能反应函数S~α(α>1)的传染病模型,讨论系统平衡点的存在性,借助特征根法,Routh-Hurwitz判别法,Lyapunov-LaSalle不变集法给出平衡点稳性的条件,得出无病平衡点的全局稳性和地方病平衡点的不稳性。

This paper studies a class of predator-prey epidemic and infectious disease model with nonlinear response function, the conditions of existence of the equilibrium point in the system, by means of eigenvalue method, Routh-Hurwitz discriminant analysis, Lyapunov-LaSalle invariant set method,conditions of stability of equilibriumwas was given,the global stability of the disease-free equilibrium and the endemic equilibrium point instability was established.