| 具有饱和接触率和垂直感染的SIR模型全局分析 |
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| 引用本文： | 胡新利,孙法国,王彩霞. 具有饱和接触率和垂直感染的SIR模型全局分析[J]. 纺织高校基础科学学报, 2010, 23(1): 120-122 |
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| 作者姓名： | 胡新利 孙法国 王彩霞 |
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| 作者单位： | 西安工程大学理学院,陕西,西安,710048 |
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| 基金项目： | 西安工程大学校管课题，西安工程大学基础研究基金 |
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| 摘 要： | 研究了一类具有饱和接触率和垂直感染的SIR模型,得到了疾病绝灭的阈值R0.通过构造V函数和Dulac函数,证明了当R0≤1时,无病平衡点全局渐近稳定;当R01时,存在惟一地方病平衡点,且全局渐近稳定.
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| 关 键 词： | Dulac函数 全局稳定性 传染病模型 |
Global analysis of SIR epidemic model with the saturated contact rate and vertical transmission |
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| HU Xin-li,SUN Fa-guo,WANG Cai-xia. Global analysis of SIR epidemic model with the saturated contact rate and vertical transmission[J]. Basic Sciences Journal of Textile Universities, 2010, 23(1): 120-122 |
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| Authors: | HU Xin-li SUN Fa-guo WANG Cai-xia |
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| Affiliation: | ( School of Science,Xi＇an Polytechnic University ,Xi＇an 710048, China) |
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| Abstract: | A SIR epidemic model with the saturated contact rate and vertical transmission is considered. The basic reproduction number R0 disease-free equilibrium is is identified. By using V function and Dulac function, it is showed that if R0 ≤ 1, the globally stable;if R0 〉 1 ,a unique endemic equilibrium is globally stable. |
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| Keywords: | dulac function globally stable epidemic model |
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