具有非线性传染率的传染病模型分析  

Analyses of a SIS epidemic model with nonlinear incidence rate

作　　者：李群宏[1] 宋自根[1] 朱亮[1] 

机构地区：[1]广西大学数学与信息科学学院,广西南宁530004

出　　处：《云南大学学报（自然科学版）》2008年第5期437-442,447,共7页Journal of Yunnan University(Natural Sciences Edition)

基　　金：广西壮族自治区自然科学基金资助项目(0640002);广西研究生教育创新项目资助(2006105930701M16)

摘　　要：建立了一类具有非线性传染率函数的SIS型传染病模型,考虑因病死亡、人口的输入和输出、出生率与自然死亡率等因素,分析了系统无病平衡点和地方病平衡点的存在性及其局部稳定性,得到了系统可能存在的周期运动,并利用全局分支方法研究了模型的BT分支,找到了系统所具有的鞍结点分支曲线、Hopf分支曲线和同宿轨分支曲线,再现了退化平衡点附近的轨线变化规律.A new SIS epidemic model with nonlinear incidence rate was proposed. Upon the consideration of vertical transmission, output and input of population, recruitment and natural mortality, the existence and stability of the disease-free equilibrium and the endemic equilibrium for the model were qualitatively analyzed and the limit cycles were also discussed. At last, the Bogdanov-Takens bifurcation was analyzed by carrying out a global qualitative method and the curves of saddle-node bifurcation, Hopf bifurcation and homoclinic bifurcation were obtained at the degenerate equilibrium.

关 键 词：传染病模型 非线性传染率 稳定性 分支 同宿轨 

分 类 号：O179[理学—数学]