| 一类具有双线性发生率的SEIR流行病传播数学模型 |
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| 引用本文： | 朱帅,马纯.一类具有双线性发生率的SEIR流行病传播数学模型[J].雁北师范学院学报,2007(4). |
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| 作者姓名： | 朱帅 马纯 |
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| 作者单位： | 山西大同大学工学院 中北大学数学系 山西大同 山西太原 |
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| 摘 要： | 利用Lasalle不变集原理探讨系统的渐近性态,研究了一类具有双线性发生率且染病期传染的SEIR流行病传播数学模型的动力学性质.得到了疾病绝灭与持续的阈值—基本再生数,证明了无病平衡点的全局渐近稳定性和地方病平衡点的全局渐近稳定性,揭示了潜伏期传染的影响.
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| 关 键 词： | 流行病 数学模型 动力学 基本再生数 局部渐近稳定性 全局渐近稳定性 |
A Kind of Bilinear SEIR Epidemic Spread Mathematic Model |
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| ZHU Shuai,Ma Chun.A Kind of Bilinear SEIR Epidemic Spread Mathematic Model[J].Journal of Yanbei Teachers College,2007(4). |
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| Authors: | ZHU Shuai Ma Chun |
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| Institution: | ZHU Shuai1,Ma Chun2 |
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| Abstract: | Dynamical behavior of a kind of SEIR model of epidemic spreads with the bilinear rate,which has infective force in infected period,is studied.The system's asymptotic property is discussed by Lasalle invariant set principle.The threshold,Basic Reproductive Number,which determines whether the disease is extinct or not is gotten.Global asymptotically stabilities of the disease-free equilibrium and the endemic equilibrium are proved.The influence of infectivity in latent period is exposed. |
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| Keywords: | epidemic mathematic model dynamics basic reproductive number local asymptotically stability global asymptotically stability |
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