具有时滞和脉冲接种的非线性发生率的流行病模型分析

数学物理学报 ›› 2012, Vol. 32 ›› Issue (4): 670-684.

具有时滞和脉冲接种的非线性发生率的流行病模型分析

蒋钰¹|梅立泉¹|宋新宇²|田卫军^1,3|丁雪梅¹

1.西安交通大学数学与统计学院西安 710049;
2.信阳师范学院数学系河南信阳 464000;
3.咸阳师范学院数学与信息科学学院陕西咸阳 712000

收稿日期:2010-04-26 修回日期:2011-12-30 出版日期:2012-08-25 发布日期:2012-08-25
基金资助:
国家自然科学基金(10971164)和中央高校基本科研业务费专项基金(xjj20100112)资助.

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

JIANG Yu¹, MEI Li-Quan¹, SONG Xin-Yu², TIAN Wei-Jun^1,3, DING Xue-Mei¹

1.School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049;
2.Department of Mathematics, Xinyang Normal University, Henan Xinyang 464000;
3.College of Mathematics and Information Science, Xianyang Normal University, Shanxi Xianyang 712000

Received:2010-04-26 Revised:2011-12-30 Online:2012-08-25 Published:2012-08-25
Supported by:
国家自然科学基金(10971164)和中央高校基本科研业务费专项基金(xjj20100112)资助.

摘要/Abstract

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.

关键词: 非线性发生率, 时滞, 预防接种, 隔离, 持续性

Abstract:

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 `infection-free' 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.

Key words: Nonlinear incidence rate, Time delay, Pulse vaccination, Quarantine, Permanence

中图分类号:

34D23

蒋钰, 梅立泉, 宋新宇, 田卫军, 丁雪梅. 具有时滞和脉冲接种的非线性发生率的流行病模型分析[J]. 数学物理学报, 2012, 32(4): 670-684.

JIANG Yu, MEI Li-Quan, SONG Xin-Yu, TIAN Wei-Jun, DING Xue-Mei. Analysis of an Impulsive Epidemic Model with Time Delays and Nonlinear Incidence Rate[J]. Acta mathematica scientia,Series A, 2012, 32(4): 670-684.

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