A stochastic mosquito population suppression model based on incomplete cytoplasmic incompatibility and time switching

In this paper, we establish and study a stochastic mosquito population suppression model incorporating the release of Wolbachia-infected males and time switching, where stochastic noises are given by independent standard Brownian motions. By combining the actual mosquito control strategy in Guangzhou, we assume that the waiting release period T between two consecutive releases of Wolbachia-infected males is less than the sexually active lifespan $\bar{T}$ of them. The existence and uniqueness of global positive solutions and stochastically ultimate boundedness for the stochastic model are obtained. Some sufficient conditions for the extinction and the existence of stochastic non-trivial periodic solutions are established. Furthermore, we assume that the release function is a general periodic function and some stochastic dynamical behaviors are obtained. Numerical examples are presented to illustrate the theoretical results.