| 一类具有常数输入率的有差异的两子群间的SIRS模型 |
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| 引用本文： | 石超,刘贤宁,刘俊.一类具有常数输入率的有差异的两子群间的SIRS模型[J].西南大学学报,2010,32(3). |
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| 作者姓名： | 石超 刘贤宁 刘俊 |
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| 作者单位： | 西南大学数学与统计学院,重庆,400715 |
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| 基金项目： | 教育部科学技术研究重点项目，教育部留学回国人员科研启动基金 |
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| 摘 要： | 建立并分析了一类总人口变动的包含具有差异性两子群的单种群的SIRS传染病模型.当基本再生率R_0≤1时,系统仅存在无病平衡点,且它是全局渐近稳定的.当R_0 >1时,存在唯一的地方病平衡点,并且它存在即局部渐近稳定.通过Lyapunov函数法建立了地方病平衡点全局渐近稳定的充分条件.Abstract：An SIRS epidemiological model for a single species population with varying size and two discrepant sub-groups is formulated and analyzed.If the basic reproduction rate R_0≤ 1, only the disease-free equilibrium exists, which proves to be globally asymptotically stable.There exists a unique endemic equilibrium if R_0 > 1 and it is local-ly asymptotically stable whenever it exists.Sufficient conditions are obtained for global asymptotic stability of the endemic equilibrium via the method of Lyapunov functions.
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| 关 键 词： | SIRS模型 子种群 Krasnoselskill技巧 Lyapunov函数 全局渐近稳定性 |
An SIRS Model with Constant Immigration Rate Between Two Discrepant Subgroups |
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| SHI Chao,LIU Xian-ning,LIU Jun.An SIRS Model with Constant Immigration Rate Between Two Discrepant Subgroups[J].Journal of Southwest Agricultural University,2010,32(3). |
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| Authors: | SHI Chao LIU Xian-ning LIU Jun |
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