带有羊群效应的生态-传染病模型动力学分析  

Dynamics Analysis of an Eco-epidemic Model with Herding Effect

作　　者：康爱花 薛亚奎[2] KANG Aihua;XUE Yakui(School of General Studies,Shanxi College of Technology,Shuozhou 036000,China;School of Mathematics,North University of China,Taiyuan 030051,China)

机构地区：[1]山西工学院通识教育学院,山西朔州036000 [2]中北大学数学学院,山西太原035051

出　　处：《信阳师范学院学报（自然科学版）》2024年第2期210-215,共6页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11971278);山西省青年基金项目(202103021223395);山西省高等学校科技创新项目(2021602)。

摘　　要：研究了一类带有羊群效应且疾病在被捕食者中传播的生态-传染病模型,其目的是探究此模型稳态变化以及分支出现的关键性参数。从理论上分析了模型各平衡点的存在性、局部渐近稳定性以及分支(跨临界分支、鞍节点分支、Hopf分支)发生的条件;利用数值模拟进一步验证理论结论的正确性。结果表明:疾病传染率、捕食者的死亡率以及捕食率等影响模型的稳定性。A kind of eco-epidemiological model considering herd behavior and disease transmission among predators was studied.Its main purpose was to explore conditions of steady-state change and key parameters of branch occurrence.The existence and local asymptotic stability of equilibrium points,the conditions for the occurrence of bifurcation(transcritical bifurcation,saddle node bifurcation,Hopf bifurcation)were discussed theoretically.Further,the numerical simulation were given to verify the correctness of the theoretical analyses.The results showed that the disease infection rate,the mortality rate of the predator and the predation rate could affect the stability of the model.

关 键 词：生态-传染病模型 羊群效应 稳定性 分支 

分 类 号：O175[理学—数学]