| 一类SIR模型的稳定性分析 |
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| 引用本文： | 张俊丽,任翠萍,董银丽.一类SIR模型的稳定性分析[J].宝鸡文理学院学报(自然科学版),2014(3):11-16. |
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| 作者姓名： | 张俊丽 任翠萍 董银丽 |
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| 作者单位： | 西安欧亚学院基础部,陕西西安710065 |
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| 基金项目： | 西安市2014年度社会科学规划基金项目（14EA02） |
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| 摘 要： | 目的通过研究一类SIR模型的稳定性,为疾病控制提供理论依据。方法利用特征值理论和Lyapunov泛函分析对所建立的模型进行理论分析。结果与结论当阙值R01时,无论时滞的大小,疾病都将不会流行并且最终会消失的;而当阈值R01时,无论时滞的大小,疾病在一定条件下可能会流行并且会发展成地方病。
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| 关 键 词： | SIR模型 稳定性 平衡点 阈值 |
The stability of a class of SIR models |
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| ZHANG Jun-li,REN Cui-ping,DONG Yin-li.The stability of a class of SIR models[J].Journal of Baoji College of Arts and Science(Natural Science Edition),2014(3):11-16. |
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| Authors: | ZHANG Jun-li REN Cui-ping DONG Yin-li |
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| Institution: | (Foundation Department, Xi＇an Eurasia University, Xi＇an 710065, Shaanxi, China) |
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| Abstract: | Objective--To provide the theoretical basis for disease control by studying the stabilityof a class of SIR models. Methods--The established model was discussed theoretically with the eigen-value theory and Lyapunov functional analysis. Results and Conclusion--If R0 〈1, the disease-freeequilibrium will be asymptotically stable in the large scale and diseases will dies out gradually. If R01〉1, the endemic equilibrium will be asymptotically stable, and diseases will be epidemic and finallycause endemic diseases. |
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| Keywords: | SIR model stability equilibrium threshold |
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