| 具有隔离仓室流行病传播数学模型的全局稳定性 |
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| 引用本文： | 徐文雄,张太雷.具有隔离仓室流行病传播数学模型的全局稳定性[J].西安交通大学学报,2005,39(2):210-213. |
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| 作者姓名： | 徐文雄 张太雷 |
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| 作者单位： | 西安交通大学理学院,710049,西安 |
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| 摘 要： | 研究了一类具有隔离仓室的非线性高维自治微分系统SEIQR流行病传播数学模型,得到疾病绝灭与否的阈值———基本再生数R0,证明了无病平衡点和地方病平衡点的存在性及全局渐近稳定性,进而推得结论:适当地增大隔离强度,将有益于有效地控制疾病的蔓延.这就从理论上揭示了隔离对疾病控制的积极作用.
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| 关 键 词： | 流行病 数学模型 阈值 基本再生数 非线性 高维自治微分系统 全局稳定性 轨道渐近稳定 |
| 文章编号： | 0253-987X(2005)02-0210-04 |
| 修稿时间： | 2004年6月10日 |
Global Stability for the Model with Quarantine in Epidemiology |
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| Xu Wenxiong,Zhang Tailei.Global Stability for the Model with Quarantine in Epidemiology[J].Journal of Xi'an Jiaotong University,2005,39(2):210-213. |
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| Authors: | Xu Wenxiong Zhang Tailei |
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| Abstract: | A kind of non-linear high dimensional autonomous system, SEIQR epidemiology model containing quarantine is studied. The threshold, basic reproductive number, which determines whether a disease is extinct or not is obtained. The existence and global stabilities of the disease-free equilibrium and the endemic equilibrium are proved. The conclusions indicate that a proper increasing of segregation intension benefits the efficient restraining disease spread. It is theoretically showed that the segregation has an active effect on disease controlling. |
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| Keywords: | epidemic mathematical model threshold basic reproductive number nonlinearity high dimensional differential system global stability orbital asymptotical stability |
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