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一类具有垂直传播的捕食传染病模型的全局分析
  • ISSN号：1000-4424
  • 期刊名称：《高校应用数学学报：A辑》
  • 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：国家自然科学基金（10671209）;陕西省自然科学基金（SJ08-ZT13）
作者： 刘烁[1], 马丽娜[2], 李建全[3], 李文潮[1]
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捕食者种群中传播，被传染的易感者经过一段潜伏期后才具有传染性，染病者康复后对该病具有永久免疫力，建立了一类具有垂直传播的捕食系统的传染病模型（SEIR），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Ljapunov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 the infected individuals become infectious after a latent period and those recovered have permanent immunity, an SEIR epidemic model with vertical transmission in predator-prey system is established. According to the limiting system theory, the existence and the stability of the equilibria for two cases are discussed. By using the Liapunov function and the second additive compound matrix, the conditions of the stability of the equilibria are obtained.

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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