一类植物疾病模型的动力学分析

Dynamic analysis of a class of plant disease model

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.