Wolbachia invasion to wild mosquito population in stochastic environment

TL;DR

This paper develops a stochastic model for Wolbachia-infected mosquito invasion, providing conditions for persistence or extinction, and shows environmental fluctuations can facilitate invasion even at low initial infection levels.

Contribution

The study introduces a stochastic mosquito population model with Wolbachia invasion, deriving sharp threshold conditions for long-term outcomes and highlighting the role of environmental variability.

Findings

Environmental fluctuations promote Wolbachia invasion.

Threshold conditions determine persistence or extinction.

Numerical simulations support theoretical results.

Abstract

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.