捕食者患病且具有分布时滞感染率的捕食–食饵模型
A Predator-Prey Model with Infected Predator and Distributional Time-Delay Infection Rates
DOI: 10.12677/AAM.2023.1211477, PDF,    科研立项经费支持
作者: 徐钰滢, 卢 旸*：东北石油大学数学与统计学院应用数学系，黑龙江 大庆
关键词: 捕食–食饵模型；捕食者患病；分布时滞；全局渐近稳定性；一致持久性；Predator-Prey Model； Infected Predator； Distributed Delay； Global Asymptotic Stability； Uniform Persistence
摘要: 本文研究了捕食者患病且具有分布时滞感染率的捕食–食饵模型。文中假设疾病仅在捕食者种群中流行，易感捕食者和患病捕食者皆以食饵为唯一的食物来源。文中运用单调动力系统理论和构造Lyapunov泛函相结合的方法得到了模型中所有边界平衡点的全局稳定性，同时运用一致持久生存理论得到了患病捕食者一致持久生存的充分条件。最后，文末数值模拟的部分不仅验证了定性理论分析结果的正确性，而且就同一模型针对感染率大小不同以及疾病潜伏期长短不同的情形分别进行了敏感度分析。
Abstract: In this paper, we investigate a predator-prey model in which predators are infected and have dis-tributed time-lagged infection rates. It is assumed that the disease is endemic only in the predator population and that both susceptible and infected predator’s use prey as their only food source. The global stability of all boundary equilibrium points in the model is obtained using a combination of monotone dynamical systems theory and the construction of Lyapunov generalized functions, and a sufficient condition for the consistent persistence of the infected predator is obtained using the theory of consistent persistence. Finally, the numerical simulation section at the end of the paper not only verifies the correctness of the qualitative theoretical results, but also analyzes the sensitiv-ity of the same model to different infection rates and disease incubation periods.
文章引用：徐钰滢, 卢旸. 捕食者患病且具有分布时滞感染率的捕食–食饵模型[J]. 应用数学进展, 2023, 12(11): 4834-4853. https://doi.org/10.12677/AAM.2023.1211477

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