一类含潜伏时滞的SIS传染病模型的定性研究  

Qualitative analysis of an SIS epidemic model with latent delay

作　　者：赵瑜[1] 原三领[2] 李盼[2] 

机构地区：[1]宁夏师范学院数学与计算机科学学院,宁夏756000 [2]上海理工大学理学院,上海200093

出　　处：《上海理工大学学报》2011年第5期480-484,共5页Journal of University of Shanghai For Science and Technology

基　　金：国家自然科学基金资助项目(10871129);上海市教委专项基金资助项目(09YZ208);宁夏自然科学基金资助项目(NZ102228)

摘　　要：利用构造Liapunov泛函的方法,研究了一类含有潜伏期时滞的SIS传染病模型.得到了地方病平衡点和无病平衡点局部及全局渐近稳定的充分条件;当时滞超过某一临界值时,地方病平衡点失去稳定性,通过Hopf分支在其附近跳出极限环.揭示了时滞对疾病传播的影响.An SIS epidemic model with a delay corresponding to the latent period was investigated. By means of constructing Liapunov functionals, some sufficient conditions for the local and global stability of the endemic equilibrium and the disease-free equilibrium were obtained, respectively. When the delay increases above some threshold, the endemic equilibrium loses its stability and Hopf bifurcation occurs,i, e. ,a family of periodic solutions bifurcates from the endemic equilibrium. The effect of the delay on the spread of disease was disclosed.

关 键 词：传染病模型 时滞 LIAPUNOV泛函 稳定性 HOPF分支 

分 类 号：O175.1[理学—数学]