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一类带有非线性接触率的SIR传染病模型的稳定性
  • ISSN号：1000-4424
  • 期刊名称：《高校应用数学学报：A辑》
  • 时间：0
  • 分类：O175.13[理学—数学;理学—基础数学]
  • 作者机构：[1]黑龙江八一农垦大学理学院,黑龙江大庆163319, [2]哈尔滨工业大学 威海 理学院,山东威海264209
  • 相关基金：国家自然科学基金（11031002）,黑龙江省教育厅科学技术项目
作者： 杨洪[1], 魏俊杰[2]
关键词： 传染病模型, 非线性接触率, 稳定性, epidemical model, nonlinear incidence rate, stability
中文摘要：

分析传染病模型的稳定性，并考虑到已感染者对易感染者的作用是非线性的。文中首先研究了传染病模型解的正性和最终有界性。在此基础上，当基本再生数满足一定条件时，构造一个满足条件的Lyapunov函数，证明了无病平衡点的全局稳定性。

英文摘要：

The stability of epidemical model is analyzed with consideration of the non-linear effect of infected person on susceptible person. Firstly, the positivity and ultimate boundedness of the solution for epidemical model are studied. On the basis, when the basic reproductive number satisfies certain conditions, it is proved that the disease-free equilibrium is global asymptotically stable by Lyapunov function.

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时滞微分方程与离散系统的定性理论及其相关问题
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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