具有时滞和脉冲接种的非线性发生率的流行病模型分析  

Analysis of an Impulsive Epidemic Model with Time Delays and Nonlinear Incidence Rate

作　　者：蒋钰[1] 梅立泉[1] 宋新宇[2] 田卫军[1,3] 丁雪梅[1] 

机构地区：[1]西安交通大学数学与统计学院,西安710049 [2]河南信阳师范学院数学系,河南信阳464000 [3]陕西咸阳师范学院数学与信息科学学院,陕西咸阳712000

出　　处：《数学物理学报（A辑）》2012年第4期670-684,共15页Acta Mathematica Scientia

基　　金：国家自然科学基金(10971164);中央高校基本科研业务费专项基金(xjj20100112)资助

摘　　要：主要目的是介绍一类采用隔离措施的具有时滞和脉冲接种的非线性发生率的流行病模型,总人口数是变化的.作者研究了无病周期解的全局吸引性,地方病周期解的存在性和持久性.该文得到该流行病模型持久性的充分条件.数值模拟显示了时滞和脉冲接种对系统的动力行为所产生的影响.结果显示:如果疾病的接种比率比较小或康复类群体具有免疫力的时间较短将会导致无病周期解的全局吸引性丧失而形成永久性的地方病.该文的主要特色是把三个时滞,非线性发生率,脉冲接种和隔离措施同时引进到SEIQRS流行病模型中.The aim of this study is to introduce an impulsive SEIQRS epidemic model with time delays,quarantine measure and nonlinear incidence rate.The total population size is varied.The global attractivity of an ’infection-free’ periodic solution,the existence,and the permanence of an endemic periodic solution are investigated.We obtain a sufficient condition for the permanence of the epidemic model with pulse vaccination.We show that time delay, pulse vaccination can bring different effects on the dynamic behavior of the model by numerical analysis.Our results also show a smaller pulse vaccination rate or a shorter latent period of the disease or a shorter immunity period of the recovered could cause global attractive ’infectionfree’ periodic solution to lose and epidemic disease to be permanent.The main feature of this study is to introduce three time delays,nonlinear incidence rates and impulses into the SEIQRS epidemic model and give pulse vaccination strategies.

关 键 词：非线性发生率 时滞 预防接种 隔离 持续性 

分 类 号：O175.1[理学—数学]