四川大学学报（自然科学版）2018，Vol.55Issue(3)：445-451,7.DOI:10.3969/j.issn.0490-6756.2018.03.005
带非线性发生率的离散SIR模型的动力学行为
Dynamics behavior of discrete SIR model with a nonlinear incidence rate
摘要
Abstract
In this paper we investigate the dynamics behavior of the discrete-time SIR epidemic model with a nonlinear incidence rate λSp I .Firstly ,we determine the topological type of the endemic fixed point ,including the existence and stability of the fixed point .Furthermore ,we analyze the bifurcation situations ,and discuss the flip bifurcation on the center manifold and the Neimark-Sacker bifurcation of this SIR system by center manifold theorem and normal form theory . T heir bifurcation directions are given respectively .Finally ,some biological explanations of our mathematical results are presented .关键词
SIR传染病模型/中心流行/flip分岔/Neimark-Sacker分岔Key words
SIR epidemic model/Center manifold/Flip bifurcation/Neimark-Sacker bifurcation分类
数理科学引用本文复制引用
朱春梅,李燕..带非线性发生率的离散SIR模型的动力学行为[J].四川大学学报（自然科学版）,2018,55(3):445-451,7.基金项目
国家自然科学基金(11471228) （11471228）
