脉冲喷洒杀虫剂的植物病害模型的周期解

Periodic Solution of the Plants Diseases Model with Impulsive Spraying Insecticide

本文研究脉冲喷洒杀虫剂的植物病害模型.考虑在传染率随时间周期变化和森林树木总数保持不变的条件下,讨论具有垂直传播的一类具有单个种群的脉冲喷洒农药的SIRS模型,根据单值算子和Bohl-Brouaser不动点理论证明了无病周期解存在性,并且利用单值矩阵,Floquet理论得到其基本再生数并且给出了其无病周期解局部渐近稳定的条件.

Considering that the infection rate evolves periodically with time and the total numberof forest trees remain unchanged, we dicuss the SIRS model of impulsive spraying pesticide with vertical transmission and single species. Firstly, according to ＇the Monodromy operator and Bohl- Brouaser fixed point theory＇, we demonstrate the existence of a disease-free periodic solution of thesystem. Secondly, taking advantage of ＇Monodromy matrix and Floquet theory＇, we obtain a basic reproductive rate of the model. Lastly, we work out the conditions of locally asymptotic stability of disease-free periodic solution of the model.