一类带传染病的捕食与被捕食模型的动力学分析  

Asymptotic Behavior of a Predator-Prey System with Disease in the Prey

作　　者：饶佳威 宋兴传 田艳玲 RAO Jiawei;SONG Xingchuan;TIAN Yanling(School of Mathematical Science,South China Normal University,Guangzhou 510631,China)

机构地区：[1]华南师范大学数学科学学院,广东广州510631

出　　处：《应用数学》2024年第3期805-824,共20页Mathematica Applicata

基　　金：广东省自然科学基金面上项目(2020A1515010445)。

摘　　要：本文研究一种带人为捕获率的食饵患病的捕食与被捕食模型.首先,通过将平衡点进行成对分析,得到各平衡点局部稳定性结论和一些阈值;其次,通过构造Liapunov函数得到捕食者无病平衡点、共存无病平衡点、食饵地方病平衡点和共存地方病平衡点的全局稳定性;最后,通过数值模拟验证了理论分析的结果,并讨论了疾病、捕食者以及对食饵的人为捕获率对系统的共同作用.In this paper,we study a predator-prey model with prey harvesting and infected disease for the prey.Firstly,by analyzing the equilibrium points in pairs,the local stability results and some threshold values are obtained.Secondly,by constructing the Liapunov functions,we obtain the global stability results of disease-free equilibrium without predator,coexisting disease-free equilibrium,preyendemic equilibrium and coexisting endemic equilibrium.Finally,some numerical simulations are given to illustrate our theoretical results,and the joint effects of diseases,predators,and human capture rates of prey on the system are discussed.

关 键 词：捕食-被捕食者模型 食饵患病 稳定性 人为捕获率 

分 类 号：O175.13[理学—数学] O193[理学—基础数学] O29