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潜伏期具传染力SEIS模型正平衡点的全局稳定性
  • ISSN号：1000-0984
  • 期刊名称：《数学的实践与认识》
  • 时间：0
  • 分类：O175.13[理学—数学;理学—基础数学]
  • 作者机构：[1]第二炮兵工程大学理学院,陕西西安710025, [2]西安交通大学数学与统计学院,陕西西安710049
  • 相关基金：国家自然科学基金重点项目（10531030）
作者： 张辉[1], 徐文雄[2], 冯锋[3]
关键词： 非线性发生率, 全局渐近稳定, LIAPUNOV函数, 周期轨道稳定性, nonlinear incidence rate, globally asymptotically stable, liapunov function, orbital stability of periodic orbit
中文摘要：

研究了一类具有一般形式非线性发生率g（S）h（I）的SEIR传染病模型.利用Liapunov函数方法,证明了当R_0≤1时,无病平衡点P_0在G内全局渐近稳定,疾病最终消失.利用周期轨道稳定性和Poincare-Bendixson性质理论,证明了当R_0〉1时,地方病平衡点P~＊在G的内部全局渐近稳定,疾病流行形成地方病.

英文摘要：

A SEIR epidemic model with general nonlinear incidence rate g（S）h（I） is studied. By using Liapunov function method, it is proved that the disease-free equilibrium P0 is globally asymptotically stable in G if R0 ≤ 1 and the disease always dies out eventually. By using orbital stability of periodic orbits and Poincare-Bendixson property theory, it is proved that the endemic equilibrium P＊ is globally asymptotically stable in the interior of G if R0≥ 1, and the disease spreads to the endemic.

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期刊信息
  • 《数学的实践与认识》
  • 中国科技核心期刊
  • 主管单位:中国科学院
  • 主办单位:中国科学院数学与系统科学研究院
  • 主编：林群
  • 地址：北京大学数学科学学院
  • 邮编：100871
  • 邮箱：bjmath@math.pku.edu.cn
  • 电话：010-62759981
  • 国际标准刊号：ISSN：1000-0984
  • 国内统一刊号：ISSN：11-2018/O1
  • 邮发代号:2-809
  • 获奖情况:
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:22973