一类植物传染病模型的动力学分析

Dynamics analysis of a class of plant epidemic model

研究了一类植物传染病模型,计算了模型的基本再生数.当基本再生数小于1时,模型仅有唯一的无病平衡点,利用Routh-Hurwitz判据和Liapunov函数方法,讨论了无病平衡点的全局渐近稳定性.当基本再生数大于1时,无病平衡点不稳定,模型还存在唯一的地方病平衡点,借助复合矩阵证明了地方病平衡点的全局渐近稳定性.

A class of plant disease model was studied,and the basic reproduction number was obtained. When the basic reproduction number was less than or equal to one,there was only the disease free equilibrium. The global stability of the disease-free equilibrium was obtained by the Routh-Hurwitz criteria and Liapunov function methods. When the basic reproduction number is greater than one,the disease free equilibrium was unstable,and there also existed an endemic equilibrium. The global stability of the endemic equilibrium was proved by the compound matrix.