| 一类含时滞具有垂直传染的SIR传染病模型 |
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| 引用本文： | 孙树林,杨瑞.一类含时滞具有垂直传染的SIR传染病模型[J].吉林林学院学报,2011(5):497-504. |
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| 作者姓名： | 孙树林 杨瑞 |
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| 作者单位： | 山西师范大学数学与计算机科学学院,山西临汾041004 |
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| 摘 要： | 研究了一类含时滞具有垂直传染的SIR传染病模型,得到了系统的基本再生数R0,利用特征理论分析了系统的局部渐近稳定性,证明了R0〉1时系统是持久的;通过构造Lyapunov函数讨论了R0〉1时地方病平衡点的全局渐近稳定性,并且利用比较定理讨论了R0〈1时无病平衡点的全局渐近稳定性;最后利用MATLAB软件分析了时滞在SIR模型中的影响.
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| 关 键 词： | SIR传染病模型 时滞 全局渐近稳定 |
A Delayed SIR Model with Vertical Transmission |
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| Authors: | SUN Shu-lin YANG Rui |
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| Affiliation: | (School of Mathematics and Computer Science,Shanxi Normal University,Linfen 041004,China) |
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| Abstract: | A delayed SIR model with vertical transmission is researched and the basic regeneration number R0 of the system is obtained.By analyzing the characteristic theory,we discuss the local asymptotical stability of the system.The system is permanent if R0〉1.By Lyapunov functional method,if R0〉1,then the endemic equilibrium is globally asymptotical stability,and by comparison theorem,if R0〈1,then the disease-free equilibrium is globally asymptotical stability.Finally,the impact of delayed SIR model by MATLAB software is analyzed. |
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| Keywords: | SIR epidemic model delay globally asymptotical stability |
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