| 一类具有饱和传染率、免疫接种和垂直传染的SIR传染病模型的全局稳定性分析 |
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| 引用本文： | 朱春娟.一类具有饱和传染率、免疫接种和垂直传染的SIR传染病模型的全局稳定性分析[J].井冈山大学学报（自然科学版）,2015(4):13-16. |
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| 作者姓名： | 朱春娟 |
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| 作者单位： | 韶关学院数学与统计学院, 广东, 韶关 512005 |
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| 基金项目： | 韶关市科技计划项目(2014CX/K231) |
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| 摘 要： | 针对一类具有饱和传染率、免疫接种和垂直传染的SIR传染病模型,确定了疾病的基本再生数。得出结论:当疾病的基本再生数小于1时,无病平衡点是全局渐近稳定的,当疾病基本再生数大于1时,地方病平衡点是全局渐近稳定的。
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| 关 键 词： | SIR传染病模型 饱和传染率 免疫接种 垂直传染 稳定性 |
| 收稿时间： | 4/8/2015 12:00:00 AM |
| 修稿时间： | 2015/5/24 0:00:00 |
GLOBAL STABILITY OF A SIR EPIDEMIC MODEL WITH SATURATING INFECT RATE,VACCINATION AND VERTICAL TRANSMISSION |
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| ZHU Chun-juan.GLOBAL STABILITY OF A SIR EPIDEMIC MODEL WITH SATURATING INFECT RATE,VACCINATION AND VERTICAL TRANSMISSION[J].Journal of Jinggangshan University(Natural Sciences Edition),2015(4):13-16. |
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| Authors: | ZHU Chun-juan |
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| Institution: | College of Mathematics and Statistics, Shaoguan University, Shaoguan, Guangdong 512005, China |
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| Abstract: | In this paper, the SIR epidemic model with saturating infect rate, vaccination and vertical transmission is studied; the basic reproduction number R0 for the existence of infectivedisease was established. If R0 <1, the disease-free equilibrium is global asymptotically stable. If R0 >1, a unique endemic equilibrium exists and is globally stable in the interior of the feasible region.We discuss the biological significance at the end. |
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| Keywords: | SIR epidemic model saturating infect rate vaccination vertical transmission equilibrium global stability |
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