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

Wolbachia invasion to wild mosquito population in stochastic environment