文章建立了一类具有杀虫剂函数作用的SI随机模型. 通过构造比较系统, 利用随机微分方程的比较定理等方法, 证明了系统全局正解的存在性, 均值有界性和害虫灭绝随机周期解的全局吸引性, 确定了易感害虫非平均持续生存和染病害虫灭绝的充分条件, 进而研究了系统的一些动力学行为.

In this paper, an SI stochatic model with effect of pesticides function is proposed. By constructing comparison systems and using comparison theorem of differential equation, the existence and uniqueness of the positive global solution, the boundedness of expectation and the global attractivity for pest extinction stochastic periodic solution are all proved. The sufficient condition of non-persistence in the mean and extinction are established. Furthermore, we investigate some dynamic behavior of the system.