一类植物疾病模型的动力学分析  

Dynamic analysis of a class of plant disease model

作　　者：贺静敏 白朵 王爱丽 HE Jing-min;BAI Duo;WANG Ai-li(School of Mathematics and Information Science,Baoji University of Arts and Sciences,Baoji 721013,Shaanxi,China)

机构地区：[1]宝鸡文理学院数学与信息科学学院,陕西宝鸡721013

出　　处：《宝鸡文理学院学报（自然科学版）》2024年第1期1-5,18,共6页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：国家自然科学基金项目(11801013);陕西省突发公共卫生应急专项项目(20JG002)。

摘　　要：目的讨论具有饱和效应的控制措施对植物疾病传播过程的影响。方法建立了一类以移除感染植株和补种健康植株为控制措施的植物疾病模型,采用饱和函数刻画移除感染植株的数量。结果模型的无病平衡态和地方病平衡态均不稳定,不存在极限环。模型存在无穷远奇点,且不稳定。结论模型的解最终趋于连接3个奇点的异宿轨。Purposes—To investigate the impact of control measures with saturation effect on the spread of plant disease.Methods—A class of plant disease model with the control measures of rogueing infected plants and replanting healthy plants is built in this paper.The saturation function is used to characterize the number of infected plants.Results—The disease-free equilibrium and the endemic equilibrium are unstable.The limit cycle for the model doesn't exist.The model not only exists the singularities at infinity but also is unstable.Conclusions—Any solution of the model tends to the heteroclinic orbit which connects three singularities.

关 键 词：植物疾病 饱和效应 平衡态 Poincaré变换 无穷远奇点 

分 类 号：O175.7[理学—数学]