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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 ›› 2024, Vol. 41 ›› Issue (6): 1179-1188.doi: 10.3969/j.issn.1005-3085.2024.06.014

• • 上一篇    

一个具有饱和发生率的生态–流行病模型

王玲书,  李梦嫄,  王  艳   

  1. 河北经贸大学微分方程及应用研究中心，石家庄 050061
  • 收稿日期:2022-03-11 接受日期:2022-12-25 出版日期:2024-12-15 发布日期:2024-12-15
  • 基金资助:
    河北经贸大学科学基金 (2021ZD07).

An Eco-epidemiological Model with Saturation Incidence

WANG Lingshu,   LI Mengyuan,   WANG Yan    

  1. Center for Differential Equations and their Applications, Hebei University of Economics and Business, Shijiazhuang 050061
  • Received:2022-03-11 Accepted:2022-12-25 Online:2024-12-15 Published:2024-12-15
  • Supported by:
    The Scientific Research Foundation of Hebei University of Economics and Business (2021ZD07).

摘要：

对一个具有饱和发生率的生态-流行病模型进行了研究，考虑了捕食者种群疾病的潜伏期所引起的时滞对模型稳定性的影响。运用时滞微分方程的特征值理论，研究了模型可行平衡点的局部稳定性，得到了共存平衡点处出现Hopf分支的充分条件。通过构造适当的Lyapunov泛函并应用LaSalle不变性原理，得到了可行平衡点全局渐近稳定性的充分条件，从而验证了疾病消灭及流行而最终形成地方病的充分条件。

关键词: 生态–流行病模型, 饱和发生率, 稳定性

Abstract:

In this paper, the stability of an eco-epidemiological predator-prey model with saturation incidence. Using the theory of time-delay differential equations, the local stability of feasible equilibria is studied, and sufficient conditions for the occurrence of Hope branches at coexisting equilib are obtained. By constructing appropriate Lyapunov functional and applying the LaSalle invariance principle, the global asymptotic stability of feasible equilibria is discussed, and sufficient conditions are obtained for the elimination and spread of diseases to ultimately form endemic diseases.

Key words: eco-epidemiological model, saturation incidence, stability

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