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带有非线性传染率的传染病模型
  • ISSN号：1000-4424
  • 期刊名称：《高校应用数学学报：A辑》
  • 时间：0
  • 分类：O175.12[理学—数学;理学—基础数学]
  • 作者机构：[1]运城学院应用数学系,山西运城044000, [2]空军工程大学应用数学物理系,陕西西安710051
  • 相关基金：国家自然科学基金（10471040,10671209）;山西省自然科学基金（2005Z010）;山西省重点学科基金;空军工程大学理学院科研基金
作者： 辛京奇[1], 王文娟[1], 张凤琴[1], 王伟[2]
关键词： 传染病模型, 平衡点, 稳定性, 持续性, epidemic model, equilibrium, stability, persistence
中文摘要：

对一类带有非线性传染率NSEIS传染病模型，找到了其基本再生数．借助动力系统极限理论，得到当基本再生数小于1时，无病平衡点是全局渐近稳定的，且疾病最终灭绝．当基本再生数大于1时，无病平衡点是不稳定的，而唯一的地方病平衡点是局部渐近稳定的．应用Fonda定理，得到当基本再生数大于1时疾病一致持续存在．

英文摘要：

For an SEIS epidemic model with nonlinear incidence rate, the basic reproduction number is found. By means of the limit theory of dynamical systems, it has been obtained that the disease-free equilibrium is globally asymptotically stable and the disease dies out eventually when the basic reproduction number is less than 1, and that the disease-free equilibrium is unstable and the unique endemic equilibrium is locally asymptotically stable when the basic reproduction number is greater than 1. By Fonda＇s theorem, it has been obtained that the disease is uniformly persistent.

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期刊信息
  • 《高校应用数学学报：A辑》
  • 北大核心期刊（2011版）
  • 主管单位:国家教育部
  • 主办单位:浙江大学 中国工业与应用数学学会
  • 主编：林正炎 李大潜
  • 地址：杭州市玉泉浙江大学数学系
  • 邮编：310027
  • 邮箱：amjcu@zjy.edu.cn
  • 电话：0571-87951602
  • 国际标准刊号：ISSN：1000-4424
  • 国内统一刊号：ISSN：33-1110/O
  • 邮发代号:
  • 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:3669