具非线性传染力和饱和发生率的植物病虫害模型稳定性分析

Stability Analysis of Plants Pests Models with Nonlinear Infectious Force and Saturation Terms

研究了SEIR植物病虫害模型,对原有的SEIR模型做出了一些改进.原有的SEIR模型中的非线性项只考虑了易感植物与染病植物的相互作用而产生一个潜伏虫害植物,但实际上易感植物与潜伏期类植物也会有个相互作用从而使易感植物转化为潜伏期植物,对非线性项进行改进后得到一个新的SEIR模型,研究这个模型的稳定性.然后给改进的模型的非线性项再添加一个饱和感染率,主要考虑到由于染病个体的增多会引起人们的自我防患意识从而有一个对患病的抑制作用,因此需要再在非线性项上再加一个饱和项.

The SEIR model is studied, and some improvements to the original SEIR model are made. Stability analysis of plant diseases and insect pests models with nonlinear infectious force and saturation terms. But in fact, susceptible plants and latent plants also interact with each other, thus transforming susceptible plants into latent plants. After improving the nonlinear term, a new SEIR model is obtained. Study the stability of the model. Then add a saturation term to the nonlinear term of the improved model. Because considering the increase of infected individuals will cause people’s awareness of self prevention and thus have an inhibitory effect on disease. Therefore, we need to add a saturation term to the nonlinear term.