一类具有HollingⅡ型功能反应及庇护效应的捕食-食饵生态流行病模型的动力学分析  

Dynamic Analysis of a Predator-Prey Ecological Epidemic Model with Holling Ⅱ Functional Response and Shelter Effect

作　　者：王立阳 罗颜涛 余庆 WANG Liyang;LUO Yantao;YU Qing(School of Mathematics and Systems Science,Xinjiang University,Urumqi 830017,China;Southwest Computer Co.,Ltd.,Chongqing 400060,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830017 [2]西南计算机有限责任公司,重庆400060

出　　处：《昆明理工大学学报（自然科学版）》2024年第6期213-222,共10页Journal of Kunming University of Science and Technology(Natural Science)

基　　金：国家自然科学基金项目(12201540);新疆维吾尔自治区自然科学基金项目(2022D01C64);新疆高校科研项目(XJEDU2021Y001).

摘　　要：为研究食饵庇护效应和捕捞如何综合影响生态系统的动态行为,提出一类具有捕捞项、食饵庇护效应以及HollingⅡ功能反应函数的捕食-食饵生态流行病模型.在可行域上得到模型解的正性和一致有界性,并给出模型的基本阈值动力学,随后借助Hurwitz判据,Dulac准则以及Lyapunov函数分别讨论系统各平衡点的局部渐近稳定性和全局稳定性.结果表明捕捞是影响食饵种群疾病灭绝的重要因素,同时对捕食者种群数量的增长也有一定的影响.To investigate the combined effects of prey refuge and fishing on the dynamic behavior of ecosystems,a predator-prey eco-epidemiological model with fishing terms,prey refuge effect,and Holling II functional response function is proposed.The positivity and uniform boundedness of the model's solution on the feasible domain are obtained,and the basic threshold dynamics of the model are presented.Subsequently,the local asymptotic stability and global stability of each equilibrium point of the system are discussed using Hurwitz criterion,Dulac criterion,and Lyapunov function,respectively.The results indicate that fishing is a crucial factor affecting the extinction of diseases in prey populations,and it also has a certain impact on the growth of predator populations.

关 键 词：生态流行病模型 稳定性 HollingⅡ反应函数 捕捞 庇护效应 

分 类 号：Q141[生物学—生态学] O175[生物学—普通生物学]