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一类带时滞的SIR传染病模型的稳定性与Hopf分岔分析
  • ISSN号：1008-9020
  • 期刊名称：《甘肃高师学报》
  • 时间：0
  • 分类：O175[理学—数学;理学—基础数学]
  • 作者机构：[1]天津大学理学院,天津300072
  • 相关基金：国家自然科学基金（10771159 11071185）
作者： 高彩琳[1]
关键词： 稳定性, 时滞, 预防接种免疫力, HOPF分岔, stability, time-delay, vaccinal immunity, Hopf bifurcation
中文摘要：

研究了一类带有时滞且具有预防接种免疫力的SIR传染病模型.借助特征值理论分析了无病平衡点和地方病平衡点的稳定性,同时以时滞为分岔参数,得出Hopf分岔的条件,进一步应用规范型和中心流形定理得出了关于Hopf分岔周期解的稳定性和分岔方向的计算公式.

英文摘要：

A SIR epidemiological model with vaccinal immunity and delay system is studied.The eigenvalue method is applied to analyze the the stability of disease free equilibrium point and endemic equilibrium point.Also,the bifurcation condition can be drawn if time-delay is the parameter-bifurcation.Further more,explicit algorithm for determining the direction of the Hopf bifurcation and stability of the bifurcating periodic solution is derived by normal form theorem and center manifold argument.

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期刊信息
  • 《甘肃高师学报》
  • 主管单位:甘肃省教育厅
  • 主办单位:兰州城市学院
  • 主编：莫超
  • 地址：甘肃兰州安宁区街坊路11号
  • 邮编：730070
  • 邮箱：gsgsxb28@sohu.com
  • 电话：0931-7601128
  • 国际标准刊号：ISSN：1008-9020
  • 国内统一刊号：ISSN：62-1139/G4
  • 邮发代号:
  • 获奖情况:
  • 国内外数据库收录:
  • 被引量:4107