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一类具有种群Logistic增长及非线性发生率的时滞SIS传染病模型的稳定性与Hopf分支
陈争1,马昌凤2
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摘要:
分析一类具有种群Logistic增长及非线性发生率的时滞SIS传染病模型的正平衡点局部稳定性,应用规范型理论和中心流形定理给出该模型关于Hopf分支周期解的稳定性及分支方向的计算公式.最后使用Matlab软件对所得结果进行数值模拟验证.
关键词:  SIS传染病模型  非线性发生率  稳定性  Hopf分支
DOI:
投稿时间:2010-05-10修订日期:2010-07-09
基金项目:国家自然科学基金,福建省自然科学基金
Stability and Hopf Bifurcation of a Delayed SIS Model with Species Logistic Growth and a Nonlinear Incidence Rate
Abstract:
A delayed SIS Model with Species Logistic growth and a non-linear incidence rate is studied.First,the local stability of the positive equilibrium is investigated.Then,based on center manifold and normal form,the formulas for the determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are obtained.Finally,some numerical simulations are carried out by matlab program.
Key words:  SIS epidemic model  incidence rate  stability  Hopf bifurcation

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