一类具有指数出生和标准发生率的SEIR传染病模型的稳定性分析  

Stability Analysis of a SEIR Epidemic Model with Exponential Birth and Standard Incidence Rate

作　　者：杨红彦 沈荣涛 曹雪靓 Yang Hong-yan;Shen Rong-tao;Cao Xue-jing(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou Gansu 730070)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《河西学院学报》2018年第2期22-28,共7页Journal of Hexi University

摘　　要：建立了一类具有指数出生和标准发生率的SEIR传染病模型,同时讨论了系统平衡点的存在性,分析求得了基本再生数R_0.当R_0<1时,通过构造适当的Liapunov函数,得到无病平衡点是全局渐近稳定的,疾病最终灭绝;当R_0>1时,无病平衡点不稳定,存在唯一的地方病平衡点是局部渐近稳定的,疾病最终形成地方病,然后进行了数值模拟,最后讨论了Hopf分岔的存在性.A SEIR epidemic model with exponential birth and standard incidence rate is established,and the existence of the equilibrium point of the system is discussed to get the threshold dataR0.WhenR0is smaller than one,it is found that the disease-free equilibrium E0is in globally asymptotic stability and the disease eventually dies out by constructing an appropriate Liapunov function.WhenR0 is greater than one,the disease-free equilibrium is not stable,the only equilibrium point is in locally asymptotic stability,the disease eventually evolves into endemic disease.Then numerical simulation is carried out and the existence of Hopf bifurcation is discussed.

关 键 词：传染病模型 平衡点 全局渐近稳定 局部渐近稳定 LIAPUNOV函数 HOPF分岔 

分 类 号：O175.1[理学—数学]