| 具有Logistic出生率和饱和接触率SIR模型的全局分析 |
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| 引用本文： | 胡新利.具有Logistic出生率和饱和接触率SIR模型的全局分析[J].纺织高校基础科学学报,2011,24(2):209-211. |
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| 作者姓名： | 胡新利 |
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| 作者单位： | 西安交通大学数学系,陕西 西安 710049;西安工程大学理学院,陕西 西安 710048 |
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| 基金项目： | 陕西省教育厅科研项目(2010JK559); 西安工程大学基础研究基金项目(09XG09) |
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| 摘 要： | 研究了一类具有Logistic出生率和饱和接触率的SIR模型,得到了疾病绝灭的阈值Ro.通过比较原理和Dulac函数证明了:当R0≤1时无病平衡点全局渐近稳定；当R0＞1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： | 比较原理 Dulac函数:全局稳定性:传染病模型 |
Global analysis of SIR epidemic model with the Logistic birth rate and the saturated contact rate |
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| HU Xin-li.Global analysis of SIR epidemic model with the Logistic birth rate and the saturated contact rate[J].Basic Sciences Journal of Textile Universities,2011,24(2):209-211. |
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| Authors: | HU Xin-li |
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| Affiliation: | HU Xin-li1,2(1.Department of Mathematics,Xi'an jiaotong University,Xi'an 710049,China,2.School of Science,Xi'an Polytechnic University,Xi'an 710048,China) |
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| Abstract: | The SIR epidemic model with the Logistic birth rate and the saturated contact rate is investigated.The basic reproduction number R0 is identified.By using comparison principle and Dulac function,it is showed that if R0≤1,the disease-free equilibrium is globally stable;if R0>1,a unique endemic equilibrium is globally stable. |
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| Keywords: | comparison principle Dulac function globally stable epidemic model |
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