| 一类具有变免疫力的传染病模型的全局分析 |
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| 引用本文： | 叶星旸,;李学鹏. 一类具有变免疫力的传染病模型的全局分析[J]. 厦门水产学院学报, 2009, 0(1): 78-83 |
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| 作者姓名： | 叶星旸, 李学鹏 |
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| 作者单位： | [1]集美大学理学院,福建厦门361021; [2]福建师范大学数学与计算机科学学院,福建福州350007 |
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| 基金项目： | 福建省自然科学基金资助项目（2008J0199） |
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| 摘 要： | 借助微分方程定性与稳定性理论构造适当的Liapunov函数，对一类介于SIS和SIR间传播的具有变免疫力和常数输入的传染病模型进行讨论．对具种群规模制约的一般接触率，比较了种群在有无染病者输入时系统动力学行为的异同点，得到了地方病平衡点全局渐近稳定的充分条件．
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| 关 键 词： | 传染病模型 平衡点 全局渐近稳定 |
Global Analysis of Some Epidemic Models with Waning Immunity |
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| Affiliation: | YE Xing-yang, LI Xue-peng ( 1. School of Sciences, Jimei University, Xiamen 361021, 2. School of Mathematics and Computer Science, Fujian Normal University, China; Fuzhou 350007, China) |
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| Abstract: | Epidemic models with constant immigration of each class and waning immunity which corresponds to transitions from the SIS to the SIR frameworks are discussed by means of the qualitative and stability theory of differential equation and suitable Liapunov function. For the case with the population size dependent contact rate, the difference of the dynamic behavior between the existence and the absence of input of infectious individuals is shown, and the sufficient conditions of global asymptotical stability of the endemic equilibriums are obtained, respectively. |
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| Keywords: | epidemic models equilibrium global asymptotical stability |
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