FINITE-TIME STABILITY OF WOLBACHIA-DRIVEN MOSQUITOES BASED ON STOCHASTIC DIFFERENTIAL EQUATIONS WITH TIME-VARYING DELAY

Abstract

It is well known that various environmental factors, such as temperature, rainfall and humidity, strongly influence the development and reproduction of mosquito populations and thus the transmission dynamics of mosquito-borne diseases. In this paper, a stochastic noise is introduced to describe the effects of environmental changes on mosquito population dynamics. Considering the waiting period of wild mosquitoes from mating to emergence, the finite-time stability of wild mosquitoes by releasing Wolbachia-infected mosquitoes was studied using a stochastic differential equation with time-varying delay. Finite-time stability describes the phenomenon that the bound of the state does not exceed a specified threshold at a fixed time interval. Sufficient conditions for the finite-time stability are obtained by employing the Lyapunov function and stochastic comparison theorem. Numerical simulations are also provided to illustrate our theoretical results.