| 具有年龄结构的离散流行病模型 |
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| 引用本文： | 张丽萍,王延松,谭立静.具有年龄结构的离散流行病模型[J].南京航空航天大学学报,2002,34(6):598-601. |
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| 作者姓名： | 张丽萍 王延松 谭立静 |
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| 作者单位： | 1. 南京航空航天大学理学院,南京,210016
2. 中兴通讯股份有限公司,南京,210000 |
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| 摘 要： | 离散的流行病模型能够更恰地描述某些流4行病的传播过程，本文针对恢复者不具有免疫力而被再次传染成为易感者的情况，提出了具有年龄结构的离散SIS（易感者Susceptible、染病者Infective、易感者Susceptible）模型，运用线性化方法，比较法及计算机模拟等方法对模型的动力学性态进行了较全面的研究，研究中引入基本再生数，其意义为在染病期内一个典型的染病者在完全易感的人群产生的新患者平均数，基本再生数决定平衡点的稳定性，文中主要得到了无病平衡点的全局稳定性，最后，对所研究的理论结果进行了计算机模拟。
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| 关 键 词： | 年龄结构 特征值 基本再生数 流行病 数学模型 传播规律 |
| 文章编号： | 1005-2615(2002)06-0598-04 |
| 修稿时间： | 2002年4月1日 |
Discrete Epidemic Model with Age Structure |
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| Zhang Liping.Discrete Epidemic Model with Age Structure[J].Journal of Nanjing University of Aeronautics & Astronautics,2002,34(6):598-601. |
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| Authors: | Zhang Liping |
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| Abstract: | Discrete models are suitable in studying the dynamics of some infectious diseases. The discrete age structured SIS model is formulated. The dynamical behavior of these models are studied by linearization method, the comparison principle and computer simulations. The basic reproductive number for the models is defined. It is the average number of the secondary infectious produced by a typical infective during the entire period of infectiousness. The basic reproductive number is used as the threshold to determine the existence and stability of the equilibrium. Some sufficient conditions for the global stability of disease free equilibrium are obtained. Finally, the spreading of infectious disease is numerically simulated. |
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| Keywords: | discrete SIS model age structure host characteristic value basic reproductive number |
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