| 具有脉冲接种和脉冲出生的SIR传染病模型 |
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| 引用本文： | 董志远.具有脉冲接种和脉冲出生的SIR传染病模型[J].山西师范大学学报,2009,23(4):34-37. |
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| 作者姓名： | 董志远 |
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| 作者单位： | 山西大同大学数学与计算机科学学院,山西大同037009 |
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| 摘 要： | 建立了脉冲接种和脉冲出生在同一时刻进行的SIR传染病模型,并研究了无病周期解的稳定性：利用频闪映射得到无病周期解,通过Floquet定理证明其局部稳定性从而得到基本再生数;利用脉冲微分不等式证明无病周期解的全局稳定性.
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| 关 键 词： | 脉冲接种 脉冲出生 无病周期解 稳定性 |
The SIR Epidemic Model with Birth Pulse and Pulse Vaccination |
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| DONG Zhi-yuan.The SIR Epidemic Model with Birth Pulse and Pulse Vaccination[J].Journal of Shanxi Teachers University,2009,23(4):34-37. |
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| Authors: | DONG Zhi-yuan |
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| Institution: | DONG Zhi-yuan (School of Mathematics and Computer Sciences, Shanxi Datong University, Datong 037009, Shanxi, China) |
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| Abstract: | In this paper, we propose an SIR epidemic model with pulse and pulse vaccination, which may carried on sunchronously. The dynamical behavior of the model is analyzed. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact periodic infection-free solution of the impulsive epidemic system, and using impulsive differential inequality, we prove that the periodic solution is globally asymptotically stable. |
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| Keywords: | pulse vaccination birth pulse infection-free periodic solution stability |
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