| 一类具有时滞的流行病模型分析 |
| |
| 引用本文： | 魏会明,武津刚.一类具有时滞的流行病模型分析[J].数学的实践与认识,2007,37(24):83-88. |
| |
| 作者姓名： | 魏会明 武津刚 |
| |
| 作者单位： | 1. 西安交通大学,动力工程多相流国家重点实验室,陕西,西安,710049;信阳师范学院,数学与信息科学学院,河南,信阳,464000
2. 信阳师范学院,数学与信息科学学院,河南,信阳,464000 |
| |
| 摘 要： | 讨论了一类带有时滞的SE IS流行病模型,并讨论了阈值、平衡点和稳定性.模型是一个具有确定潜伏期的时滞微分方程模型,在这里我们得到了各类平衡点存在条件的阈值R0;当R0<1时,只有无病平衡点P0,且是全局渐近稳定的;当R0>1时,除无病平衡点外还存在唯一的地方病平衡点Pe,且该平衡点是绝对稳定的.
|
| 关 键 词： | 传染病模型 时滞 平衡点 稳定性 绝对稳定 阈值 |
| 修稿时间： | 2005年9月28日 |
Analysis of an Epidemic Model with Time Delay |
| |
| WEI Hui-ming,WU Jin-gang.Analysis of an Epidemic Model with Time Delay[J].Mathematics in Practice and Theory,2007,37(24):83-88. |
| |
| Authors: | WEI Hui-ming WU Jin-gang |
| |
| Abstract: | An SEIS epidemic model with time delay is discussed in this paper,the basic reproduction number R0 is obtained for the epidemic model.The equilibrium and stability are also discussed in this paper.The epidemic model is a differential equation with fixed time delay.The equilibria are decided by R0.Only the disease-free equilibrium arises when R0<1,and the disease-free equilibrium is globally asymptotic stability.The endemic equilibrium arises when R0>1,and the endemic equilibrium is absolutely stability.The results above are proved in this paper. |
| |
| Keywords: | epidemic model time delay equilibrium stability absolutely stable threshold |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
