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一个有快慢进展的TB模型的全局稳定性分析 被引量：4

Global Stability of a TB Model with Fast and Slow Progression
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摘要 建立了一个有快慢进展、接种和治疗的TB模型,定义了模型的基本再生数R0,通过构造Lyapunov函数来研究解的渐近性态.证明了当R01时,无病平衡点是全局渐近稳定的;也证明了当R0>1时,惟一的地方病平衡点是全局渐近稳定的. A TB transmission model with fast and slow progression, vaccination, and therapy is formulated. The basic reproduction number R0 is defined. The asymptotic behaviors of solutions are studied by constructing Lyapunov functions. It is proved that the disease-free equilibrium is globally asymptotically stable when R0 ≤1, and the unique endemic equilibrium is globally asymptotically stable when R0 〉 1.
作者 刘璐菊 王春娟
机构地区 西安交通大学理学院 西安交通大学医学院
出处 《数学的实践与认识》 CSCD 北大核心 2007年第21期63-69,共7页 Mathematics in Practice and Theory
基金 国家自然科学基金(10531030)
关键词 TB模型 快慢进展 接种 全局渐近稳定的 LYAPUNOV函数 TB model fast and slow progression vaccination globally asymptotically stable lyapunov function
分类号 O175 [理学—基础数学]
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参考文献8

  • 1Bloom B R. Tuberculosis: Pathogensis, Protection, and Control[M]. ASM Press, Washington, D. C, 1994.
  • 2Blower S M, Mclean A R, Porco T C. The intrinsic transmission dynamics of tuberculosis epidemics[J]. Nat Med, 1995,1(8):815-821.
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  • 6P van den Driessche, Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission[J]. Math Bioscl, 2002,180(1-2): 29-48.
  • 7Lasalle J P. The Stability of Dynamical Systems[M]. SIAM, Philadelphia, 1976.
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同被引文献18

  • 1Liu L, Zhou Y, Wu J. Global dynamics in a TB model incorporating case detection and two treatment stages [ J ]. Rocky Mountain Journal of Mathematics, 2008, 38 ( 5 ) : 1541-1559.
  • 2Liu L. Global stability in a tuberculosis model incorporating two latent periods [ J ]. International Journal of Biomathematics, 2009, 2 (3) : 357-362.
  • 3Smith H L. Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems [ M ]. Providence, Rhode Island: American Mathematical Sociely, 1995 : 81-82.
  • 4Yang Y, Li J, Ma Z, et al. Global stability of two models with incomplete treatment for tuberculosis [ J ]. Chaos, Solitons & Fractals, 2010, 43 (1 -12) : 79 -85.
  • 5佚名.暮光之城的剧情简介[EB/OL].2009-03-01[2011-05-26].http://movie.douban.corn/subject/2268359/.
  • 6佚名.暮光之城[EB/OL].2009-11-20[2011-05-16].http://data.movie.xunlei.eom/movie/40790.
  • 7佚名.暮光之城[EB/OL].2008-11-10[2011-05-10].http://www.youku.coin/show-page/id-ZCCl188049624l1de83b1.html.
  • 8Van Den Driessche P, Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission[J]. Math. Biosci., 2002, 180(1 -2) : 29 -48.
  • 9Guo H. Global dynamics of a mathematical model of tuber-culosis [ J ]. Canadian Appl. Math. Quart. , 2005, 13 (4) : 313 -323.
  • 10La Salle J P. The Stability of Dynamical Systems [ M ]. SIAM : Philadelphia, 1976.

引证文献4

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数学的实践与认识
2007年 第21期

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