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一类具有常数输入率的有差异的两子群间的SIRS模型(英文) 被引量：1

An SIRS Model with Constant Immigration Rate Between Two Discrepant Subgroups
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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R0≤1时,系统仅存在无病平衡点,且它是全局渐近稳定的.当R0>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. An SIRS epidemiological model for a single species population with varying size and two discrepant subgroups is formulated and analyzed. If the basic reproduction rate R0≤1, only the disease-free equilibrium exists, which proves to be globally asymptotically stable. There exists a unique endemic equilibrium if R0〉1 and it is locally asymptotically stable whenever it exists. Sufficient conditions are obtained for global asymptotic stability of the endemic equilibrium via the method of Lyapunov functions.
作者 石超 刘贤宁 刘俊
机构地区 西南大学数学与统计学院
出处 《西南大学学报（自然科学版）》 CAS CSCD 北大核心 2010年第3期1-9,共9页 Journal of Southwest University(Natural Science Edition)
基金 教育部科学技术研究重点项目(109132) 教育部留学回国人员科研启动基金项目(教外司留[2008]890号).
关键词 SIRS模型 子种群 Krasnoselskill技巧 LYAPUNOV函数 全局渐近稳定性 SIRS model subgroup Krasnoselskii trick Lyapunov function global asymptotic stability
分类号 O175.1 [理学—基础数学]
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参考文献10

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共引文献9

同被引文献10

  • 1BRAUER F, DRIESSCHE P. Models for Transmission of Disease with Immigration of Infectives[J]. Math Biosei, 2001, 171(2): 143--154.
  • 2WANG Wen-di, MULONE G. Threshold of Disease Transmission in a Patch Environment [J]. J Math Anal Appl, 2003, 285(1): 321--335.
  • 3ARINO J, DRIESSCHE P. A Multi-city Epicemic Model [J]. Math Popul Stud, 2003, 10(3) : 175--193.
  • 4WANG Wen-di, ZHAO Xiao-qiang. An Epidemic Model in a Patchy Environment [J]. Math Biosei, 2004, 190(1) : 97--112.
  • 5CUI Jin-an, TAKEUCHI Y. Spreading Disease with Transport-related Infection [J]. J Theor Biol, 2006, 239(3): 376--390.
  • 6LIU Xian-ning, TAKEUCHI Y. Spread of Disease with Transport-related Infection and Entry Screening [J]. J Theor Bi- ol, 2006, 242(2): 517--528.
  • 7TAKEUCHI Y, LIU Xian-ning. Global Dynamics of SIS Models with Transport-related Infection [J]. J Math Anal Ap- pl, 2007, 329(2): 1460--1471.
  • 8LIU Jun-li, ZHOU Yi-cang. Global Stability of an SIRS Epidemic Model with Transport-related Infection [J]. Chaos, Solitons and Fractals, 2009, 40(1): 145--158.
  • 9WANGZhi-ping LIUXian-ning.DynamicsofaTri-trophicModelinPatchEnviroment.西南大学学报自然科学版,2007,:1-5.
  • 10刘俊,王稳地,石超.具有两种免疫来源的乙肝病毒模型的全局动力学(英文)[J].西南大学学报（自然科学版）,2010,32(1):5-10. 被引量：3

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西南大学学报（自然科学版）
2010年 第3期

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