Global Stability of an Eco-Epidemiological Model with Time Delay and Saturation Incidence

被引：4

作者：

Mao, Shuxue ^{[1
]}

Xu, Rui ^{[1
]}

Li, Zhe ^{[1
]}

Li, Yunfei ^{[1
]}

机构：

[1] Shijiazhuang Mech Engn Coll, Inst Appl Math, Shijiazhuang 050003, Peoples R China

来源：

DISCRETE DYNAMICS IN NATURE AND SOCIETY | 2011年 / 2011卷

基金：

中国国家自然科学基金;

关键词：

PREDATOR-PREY MODEL; HOPF-BIFURCATION; DISEASE; BEHAVIOR; SYSTEM;

D O I：

10.1155/2011/730783

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate a delayed eco-epidemiological model with disease in predator and saturation incidence. First, by comparison arguments, the permanence of the model is discussed. Then, we study the local stability of each equilibrium of the model by analyzing the corresponding characteristic equations and find that Hopf bifurcation occurs when the delay tau passes through a sequence of critical values. Next, by means of an iteration technique, sufficient conditions are derived for the global stability of the disease-free planar equilibrium and the positive equilibrium. Numerical examples are carried out to illustrate the analytical results.

引用

页数：22

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