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具有Beddington-DeAngelis发生率和免疫损害项的带时滞的病毒感染模型的稳定性分析
  • 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：北京科技大学数理学院,北京100083
  • 相关基金：国家自然科学基金资助项目（61174209）;北京科技大学冶金工程研究院基础研究基金资助项目（YJ2012-001）
作者： 程贝贝, 胡志兴, 廖福成
关键词： 稳定性, HOPF分支, LYAPUNOV泛函, Beddington-DeAngelis发生率, 时滞, stability, Hopf bifurcation, Lyapunov functional , Beddington-DeAngelis incidence rate , de-lay
中文摘要：

研究一类具有Beddington-De Angelis发生率和免疫损害项的带时滞的病毒感染模型的动力学性质。通过分析相应的特征方程,分别证明无病平衡点和染病无免疫平衡点E1的局部渐近稳定性以及在正平衡点处Hopf分支的存在性;利用适当的Lyapunov泛函和La Salle不变原理,证明无病平衡点及染病无免疫平衡点的全局渐近稳定性;数值模拟验证了以上结论。

英文摘要：

Dynamic properties of a delayed viral infection model with Beddington-DeAngelis incidence rate and immune impairment are investigated. By analyzing corresponding characteristic equations, the lo- cal stabilities of the uninfected equilibrium, the infected equilibrium without immunity and the existence of Hopf bifurcation at the infected equilibrium with immunity are established, respectively. Then, apply- ing suitable Lyapunov functional and the LaSalle＇ s invariance principle, the global stabilities of the unin- fected equilibrium and the infected equilibrium without immunity are proved. Finally, numerical simula-tions are carried out to support the main results.

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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