| 具有连续预防接种和垂直传染的SIR流行病模型的稳定性分析 |
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| 引用本文： | 李春艳,李冬梅,尹晓.具有连续预防接种和垂直传染的SIR流行病模型的稳定性分析[J].黑龙江大学自然科学学报,2009,26(6). |
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| 作者姓名： | 李春艳 李冬梅 尹晓 |
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| 作者单位： | 哈尔滨理工大学,应用科学学院,哈尔滨,150080 |
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| 基金项目： | 黑龙江省自然科学基金资助项目，黑龙江省教育厅资助项目 |
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| 摘 要： | 研究一类具有垂直传染和双线性发生率的连续预防接种的SIR模型,得到决定疾病持续生存的阈值.当阈值小于1时,仅存在无病平衡点;当闽值大于1时,除存在无病平衡点外,还存在唯一的地方病平衡点.利用Hurwitz判据得到了地方病平衡点的局部渐近稳定性.利用Lasalle不变原理和Liapunov函数得到了无病平衡点和地方病平衡点全局渐近稳定.
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| 关 键 词： | 流行病 地方病平衡点 阈值 全局稳定性 |
The stability analysis of the SIR epidemic models with vertical infection and continuous vaccination |
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| LI Chun-yan,LI Dong-mei,YIN Xiao.The stability analysis of the SIR epidemic models with vertical infection and continuous vaccination[J].Journal of Natural Science of Heilongjiang University,2009,26(6). |
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| Authors: | LI Chun-yan LI Dong-mei YIN Xiao |
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| Abstract: | An SIR epidemic model with vertical infection,continuous vertical and bilinear incidence rates,is considered.The threshold which determines the existence of the infective disease is found.When it is smaller than 1,there only exists disease free equilibrium;when it is bigger than 1,the endemic equilibrium and the disease free equilibrium exist.By Hurwitz criterion,the locally asymptotical stability of the disease free equilibrium is proved.By Lasalle invariant theorem and Liapunov function,the global asymptotical stability of disease free equilibrium and the endemic equilibrium is proved. |
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| Keywords: | epidemic endemic equilibrium threshold global stability |
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