期刊文献+

一类带有周期参数的SIS传染病模型 被引量:1

A Kind of SIS Epidemic Model with Periodic Parameters
下载PDF
导出
摘要 通过对经典的SIS传染病模引入周期性变化的疾病传播参数,建立了一类具有周期性变化参数的SIS传染病模型。借助微分方程比较定理和稳定性理论,对其进行定性分析,得到了决定疾病灭绝与否以及模型动力学形态的阈值。在该阈值之下,模型的无病周期解是全局渐近稳定的,这意味着疾病最终灭绝;在该阈值之上,模型的无病周期解是不稳定的,同时模型还存在全局渐近稳定的地方病周期解,这意味着疾病将持续存在于种群之中,并且染病者的数量呈周期性变化。 The spread of some communicable diseases often has a certain periodicity. By incorporating the periodic parameters of disease transmission into the classical SIS epidemic model, an SIS epidemic model with periodic parameters is established. By means of the comparison theorem and the stability theory of ordinary differential equations, the threshold determining whether the disease dies out or not and determining the dynamical behaviors of the model is obtained via qualitative analysis. When the threshold is negative, the disease - free periodic solution of the model is globally asymptotic stable, which implies that the disease dies out eventually. When the threshold is positive, the disease - free periodic solution of the model is unstable, and the model still has a unique endemic periodic solution that is globally stable. This implies that the disease persists in the population, and that the number of the infected individuals will change with a certain periodicity.
作者 杨友社
出处 《空军工程大学学报(自然科学版)》 CSCD 北大核心 2011年第4期82-86,共5页 Journal of Air Force Engineering University(Natural Science Edition)
基金 国家自然科学基金资助项目(11071256)
关键词 传染病模型 周期解 全局渐近稳定性 阈值 epidemic model periodic solution globally asymptotic stability threshold
  • 相关文献

参考文献10

  • 1Ma Z, Li J. Dynamical modeling and analysis of epidemics [ M ]. New York:World scientific ,2009.
  • 2Hethcote H W. The mathematics of infectious diseases [ J ]. SIAM reviews,2000, 42:599 - 653.
  • 3Brauer F, Castillochavez C. Mathematical model in population biology and epidemiology[ M ]. New York:Springer,2011.
  • 4Li J, Ma Z. Stability analysis for SIS epidemic models with vaccination and constant population size[ J]. Discrete and continuous dynamical systems : series B, 2004 (4) : 637 - 644.
  • 5Thieme Horst R. Uniform persistence and permanence for non -autonomous semiflows in population biology[ J]. Mathematical biosciences ,2000,166 : 173 - 201.
  • 6Gerd Herzog, Ray Redheffer. Nonautonomous SEIRS and thron models for epidemiology and cell biology [ J ]. Nonlinear analy- sis: real world applications ,2004,5:33 -44.
  • 7Li M Y, Graef J R, Wang L, et al. Global dynamics of a SEIR models with varying total population size [ J ]. Mathematical biosci- ences,1999,160:191 -213.
  • 8Piyawong W, Twiaell E H, Gumel A B. An unconditionally convergent finite - difference scheme for the SIR model [ J ]. Applied mathematics and computation,2003,146:611 - 625.
  • 9Dietz K, Schenzle D. Mathematical models for infections disease statistics [ C ]//A celebration of statistics the ISI centenary volume. Berlin :Springer, 1985 : 103 - 108.
  • 10Martcheva M. A nonautonomous multistrain SIS epidemic models[ J]. Journal of biological dynamics,2009,3:235 -250.

同被引文献38

引证文献1

二级引证文献3

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部