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一类具有垂直传播的SEIRS捕食传染病模型的全局分析
  • ISSN号：1001-9626
  • 期刊名称：《生物数学学报》
  • 时间：0
  • 分类：O175.1[理学—数学;理学—基础数学]
  • 作者机构：[1]第四军医大学生物医学工程系,陕西西安710032, [2]陕西师范大学数学与信息科学学院,陕西西安710062, [3]空军工程大学理学院应用数学物理系,陕西西安710051
  • 相关基金：基金项目：国家自然科学基金（10671209）项目资助;陕西省自然科学基金（SJ08-ZT13）项目资助
作者： 刘烁[1], 马丽娜[2], 李建全[3]
关键词： 垂直传播, 潜伏期, 捕食系统, 传染病模型, 平衡点, 稳定性, Vertical transmission, Latent period, Predator-prey system, Epidemic model, Equilibrium, stability
中文摘要：

通过假设捕食系统中疾病只在食饵种群中传播，被传染的易感者经过一段潜伏期后才具有传染性，潜伏者与染病者均具有垂直传播能力，染病者恢复后对该病不具有终身免疫力。建立了一类具有垂直传播的SEIRS捕食传染病模型，运用极限系统理论，分两种情形讨论了系统平衡点的存在性及局部稳定性，利用Lyapunov函数和二次复合矩阵等方法，得到了平衡点全局渐近稳定的条件．

英文摘要：

By assuming that disease only exists in the prey species,a susceptible individual infected by infective becomes infectious individual after a latent period, the infectives and the latent individuals have the ability of vertical transmission,and the infectives can be cured but the recovered have temporary immunity, an SEIRS predator-prey epidemic model with vertical transmission is investigated. Through the limiting system theory, the existence and the local stability of the equilibria for two cases are discussed. By constructing the liapunov function and using the second additive compound matrix, the sufficient and necessary conditions of the global stability of the boundary equilibria and the sufficient condition of the global stability of the co- existing equilibrium are obtained.

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期刊信息
  • 《生物数学学报》
  • 北大核心期刊（2008版）
  • 主管单位:中国数学会
  • 主办单位:中国数学会生物数学学会
  • 主编：陈兰荪
  • 地址：辽宁省鞍山师范学院158号
  • 邮编：114007
  • 邮箱：smbjbm@tom.com
  • 电话：0412-2960893
  • 国际标准刊号：ISSN：1001-9626
  • 国内统一刊号：ISSN：34-1071/O1
  • 邮发代号:
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  • 国内外数据库收录:
  • 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,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）
  • 被引量:5686