BIFURCATION ANALYSIS OF A DISCRETE SIS MODEL WITH BILINEAR INCIDENCE DEPENDING ON NEW INFECTION

被引：15

作者：

Cao, Hui ^{[1
]}

Zhou, Yicang ^{[2
]}

Ma, Zhien ^{[2
]}

机构：

[1] Shaanxi Univ Sci & Technol, Dept Math, Xian 710021, Peoples R China

[2] Xi An Jiao Tong Univ, Dept Appl Math, Xian 710049, Peoples R China

来源：

MATHEMATICAL BIOSCIENCES AND ENGINEERING | 2013年 / 10卷 / 5-6期

关键词：

Discrete SIS model; bilinear incidence; flip bifurcation; saddle-Node bifurcation; Hopf bifurcation; BASIC REPRODUCTION NUMBER; EPIDEMIC MODEL; TRANSMISSION;

D O I：

10.3934/mbe.2013.10.1399

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

A discrete SIS epidemic model with the bilinear incidence depending on the new infection is formulated and studied. The condition for the global stability of the disease free equilibrium is obtained. The existence of the endemic equilibrium and its stability are investigated. More attention is paid to the existence of the saddle-node bifurcation, the flip bifurcation, and the Hopf bifurcation. Sufficient conditions for those bifurcations have been obtained. Numerical simulations are conducted to demonstrate our theoretical results and the complexity of the model.

引用

页码：1399 / 1417

页数：19

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