  Releasing sterile Wolbachia-infected mosquitoes to invade wild mosquito
population is a method of mosquito control. In this paper, a stochastic
mosquito population model with Wolbachia invasion perturbed by environmental
fluctuation is studied. Firstly, well-posedness, positivity and Markov-Feller
property of solution for this model are proved. Then a group of sharp
threshold-type conditions is provided to characterize the long-term behavior of
the model, which pinpoints the almost necessary and sufficient conditions for
persistence and extinction of Wolbachia-infected and uninfected mosquito
populations. Especially, our results indicates that even the initial Wolbachia
infection frequency is low, the Wolbachia invasion into wild mosquito
population can be promoted by stochastic environmental fluctuations. Finally,
some numerical experiments are carried out to support our theoretical results.
