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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2019, Vol. 36 ›› Issue (4): 406-418.doi: 10.3969/j.issn.1005-3085.2019.04.004

• • 上一篇    下一篇

一类具有阶段结构和饱和发生率的生态流行病模型的稳定性

王玲书,  张雅南,  苏  欢   

  1. 河北经贸大学数学与统计学学院，石家庄  050061
  • 收稿日期:2017-05-09 接受日期:2017-10-10 出版日期:2019-08-15 发布日期:2019-10-15
  • 基金资助:
    国家自然科学基金(11371368)；河北省教育厅科学技术研究项目(ZD2018052)；河北经贸大学基金(2015KYQ01).

Stability of an Eco-epidemiological Model with Stage Structure and Saturation Incidence

WANG Ling-shu,  ZHANG Ya-nan,  SU Huan   

  1. School of Mathematics and Statistics, Hebei University of Economics & Business, Shijiazhuang 050061
  • Received:2017-05-09 Accepted:2017-10-10 Online:2019-08-15 Published:2019-10-15
  • Supported by:
    The National Natural Science Foundation of China (11371368); the Scientific Research Foundation of Hebei Education Department (ZD2018052); the Foundation of Hebei University of Economics & Business (2015KYQ01).

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摘要： 本文研究一类食饵具有阶段结构且捕食者染病的具有饱和发生率的捕食者-食饵模型的稳定性及其Hopf分支，讨论了由疾病的潜伏期引起的时滞对种群动力学性态的影响．通过分析特征方程，运用Hurwitz判定定理，讨论了该模型边界平衡点和正平衡点的局部稳定性，并得到了Hopf分支存在的充分条件；通过构造适当的Lyapunov泛函，运用LaSall不变集原理，讨论了该模型边界平衡点和正平衡点的全局稳定性，从而得到了疾病流行而最终形成地方病及消灭的充分条件．

关键词: 生态流行病模型, 饱和发生率, 时滞, 阶段结构, Hopf分支, 稳定性

Abstract: In this paper, an eco-epidemiological predator-prey model with saturation incidence and stage structure for the prey is investigated. A time delay describing the latent period of the disease in this model is discussed. By analyzing the characteristic equations, the local stability of the boundary equilibria and the positive equilibrium is established, respectively. Moreover, it is proved that the system undergoes a Hopf bifurcation at the positive equilibrium. By using Lyapunov functions and the LaSalle's invariance principle, the global stability of the boundary equilibria and the positive equilibrium is addressed, respectively. Therefore, the sufficient conditions are given for the disease extinction and permanence of the model.

Key words: eco-epidemiological model, saturation incidence, time delay, stage-structure, Hopf bifurcation, stability

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