| 一类离散SIS传染病模型的稳定性 |
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| 引用本文： | 郭志明,彭华勤. 一类离散SIS传染病模型的稳定性[J]. 广州大学学报(自然科学版), 2012, 11(4): 5-8 |
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| 作者姓名： | 郭志明 彭华勤 |
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| 作者单位： | 广州大学数学与信息科学学院,广东广州,510006 |
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| 基金项目： | 基金项目:国家自然科学基金重点项目 |
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| 摘 要： | 建立了一类新的离散SIS传染病模型，该模型中人口总数依赖于出生函数而随时间变化．针对不同的出生函数，得到了该模型的基本再生数R，证明了当R≤1时疾病最终消失，无疾病平衡点是全局稳定的．当R0〉1时疾病能够继续存在，成为一种地方性疾病，并且该平衡点是稳定的．
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| 关 键 词： | 离散传染病模型 基本再生数 稳定性 |
The stability of discrete SIS epidemic models |
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| GUO Zhi-ming,PENG Hua-qin. The stability of discrete SIS epidemic models[J]. Journal og Guangzhou University:Natural Science Edition, 2012, 11(4): 5-8 |
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| Authors: | GUO Zhi-ming PENG Hua-qin |
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| Affiliation: | g(School of Mathematics and Information Sciences,Guangzhou University,Guangzhou 510006,China) |
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| Abstract: | In this paper,a new discrete SIS model is established.In this model,whole population varies with time according to birth functions.For different birth functions,basic reproduction numbers are found.It is proved that when the basic reproduction number R≤1,the epidemic disease dies out eventually and disease-free equilibrium is globally asymptotically stable;while R>1 implies that the epidemic disease cannot to be eliminated,it will become endemic disease.Furthermore,the endemic equilibrium is stable. |
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| Keywords: | discrete epidemic model basic reproduction number stability |
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