带有分布时滞的离散SIRS传染病模型的稳定性分析  

Stability Analysis of a Disscretized SIRS Epidemic Model with Time Delay

作　　者：李冬梅[1] 张颖[1] 牛犇[1] 

机构地区：[1]哈尔滨理工大学应用科学学院应用数学系,黑龙江哈尔滨150080

出　　处：《生物数学学报》2013年第2期247-259,共13页Journal of Biomathematics

基　　金：黑龙江省自然科学基金资助项目(A200502);黑龙江省教育厅资助项目(12521099)

摘　　要：考虑了非线性发病率对SIRS模型的影响,建立了一类带有分布时滞的离散SIRS传染病模型,确定了疾病流行的阈值,利用不等式性质研究了模型的持久性,利用lyapunov函数方法得到无病平衡点和地方病平衡点稳定性的充分条件.A discrete SIRS model with distributed time delay is established by consider- ing the effect of nonlinear incidence rates. The basic reproduction number is obtained and the persistence of the model is discussed. By using Lyapunov functional, we give a group of sufficent conditions to ensure the global stability of the disease-free equilibrium and the endemic equilib- rium, respectively.

关 键 词：分布时滞 离散模型 阈值 持久性 稳定性 

分 类 号：O175.2[理学—数学]