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| 两类易感者具垂直传染和预防接种的SIRS传染病模型 | |
| 引用本文： | 付景超,井元伟,张中华,张嗣瀛. 两类易感者具垂直传染和预防接种的SIRS传染病模型[J]. 系统科学与数学, 2009, 29(4): 502-511 |
| 作者姓名： | 付景超 井元伟 张中华 张嗣瀛 |
| 作者单位： | 1. 东北电力大学理学院,吉林,132012;东北大学信息科学与工程学院,沈阳,110004 2. 井元伟,东北大学信息科学与工程学院,沈阳,110004 3. 张中华,东北电力大学理学院,吉林,132012 4. 张嗣瀛,东北电力大学理学院,吉林,132012;东北大学信息科学与工程学院,沈阳,110004 |
| 摘 要： | 讨论了具有连续预防接种和脉冲预防接种且具有垂直传染的双线性SIRS传染病模型,分别给出了SIRS传染病模型基本再生数.利用Liapunov函数方法和LaSalle不变原理证明了连续预防接种下无病平衡点和正平衡点的全局稳定性;利用脉冲微分方程的Floquet 乘子理论和比较定理,证明了无病周期解的存在性和全局稳定性. |
| 关 键 词： | 传染病模型 连续接种 脉冲接种 周期解 稳定性 |
The Two SIRS Epidemical Models with Vertical Infection and Vaccination in the Easily Infected Groups |
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| FU Jingchao,JING Yuanwei,ZHANG Zhonghua,ZHANG Siying. The Two SIRS Epidemical Models with Vertical Infection and Vaccination in the Easily Infected Groups[J]. Journal of Systems Science and Mathematical Sciences, 2009, 29(4): 502-511 | |
| Authors: | FU Jingchao JING Yuanwei ZHANG Zhonghua ZHANG Siying |
| Affiliation: | (1)College of Sciences, Northeastern Dianli University, Jilin 132012;(2)The School of Information Science and Engineering, Northeastern University, Shenyang 110004; (3)College of Sciences, Northeastern Dianli University, Jilin 132012; (4)College of Sciences, Northeastern Dianli University, Jilin} 132012. |
| Abstract: | The SIRS epidemical models with continuous and impulsive vaccinations are discussed. The reproduction numbers corresponding to those two models are given. A complete global analysis is given to the continuous vaccination models by using a Liapunov function and a Lasalle invariable theory. In the SIRS epidemical models with impulsive vaccinations, the existence and global stability of the disease-free periodic solution is proved by using a Floquet multiplication theory and a comparative theorem. |
| Keywords: | Epidemical models continuous vaccination impulsive vaccination periodic solution global stability. |
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