Wolbachia invasion to wild mosquito population in stochastic environment

Abstract

Releasing Wolbachia-infected mosquitoes to invade the 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, the well-posedness, positivity, and Markov-Feller property of the 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 the persistence and extinction of Wolbachia-infected and uninfected mosquito populations. Our results indicate that even for a low initial Wolbachia infection frequency, a successful Wolbachia invasion into the wild mosquito population can be driven by stochastic environmental fluctuations. Finally, some numerical experiments are carried out to support our theoretical results.