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HBV传染病模型的稳定性和持久性
  • ISSN号：1001-7011
  • 期刊名称：《黑龙江大学自然科学学报》
  • 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,大庆163319, [2]哈尔滨工业大学威海数学系,威海264209
  • 相关基金：基金项目：国家自然科学基金重点资助项目（11031002）
作者： 杨洪[1,2], 魏俊杰[2], 郭英[1]
关键词： 传染病模型, Logistic型增长, 稳定性, 持久性, epidemical model , Logistic growth , stability , permanence
中文摘要：

分析HBV传染病模型的稳定性和持久性，其中易感染者的增长方式是Logistic型，已感染者对易感染者的作用是非线性的，这样使得模型更具有生物学意义。研究解的正性和最终有界性，当基本再生数满足一定条件时，利用比较原理和Lyapunov—LaSalle不变集定理，证明无病平衡点的全局吸引性以及系统的持久性。

英文摘要：

Stability and permanence for HBV epidemical model, in which susceptible population growth is subject to Logistic growth and the effect of infected person for susceptible person is nonlinear, are analyzed. Thus the model has more biological significance. Firstly, we study the positivity and ultimate boundedness of the solution for epi- demical model. On the basis, when the basic reproductive number satisfies certain conditions, the global attractivity of the disease-free equilibrium is proven by comparison principle and Lyapunov-LaSalle＇s invariance principle. Finally, the permanence of the model is demonstrated.

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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
  • 《黑龙江大学自然科学学报》
  • 北大核心期刊（2011版）
  • 主管单位:黑龙江省教育厅
  • 主办单位:黑龙江大学
  • 主编：霍丽华
  • 地址：哈尔滨市学府路74号
  • 邮编：150080
  • 邮箱：hdxb@vip.sohu.com
  • 电话：0451-86608818
  • 国际标准刊号：ISSN：1001-7011
  • 国内统一刊号：ISSN：23-1181/N
  • 邮发代号:14-114
  • 获奖情况:
  • 国内外数据库收录:
  • 美国化学文摘（网络版）,美国数学评论（网络版）,德国数学文摘,日本日本科学技术振兴机构数据库,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）
  • 被引量:4204