Finite-time stability of a stochastic reaction-diffusion model with impulsive control and incomplete CI for mosquito suppression

This paper investigates the finite-time stability of a mosquito suppression model incorporating incomplete CI, impulsive control, stochastic noise and spatial diffusion. Due to the multi-generational lag of CI, Wolbachia -based suppression alone cannot drive mosquito density below critical thresholds within a finite time, impulsive spraying is therefore introduced as a complementary mechanism. To capture environmental stochasticity and mosquito dispersal, the model is formulated as a stochastic reaction-diffusion system with impulsive control. For this system, we prove the existence and uniqueness of global positive solutions and establish explicit sufficient conditions for finite-time stability in both the delay-free and delaed cases. These conditions are related to CI incompleteness, noise intensity, diffusion coefficients and impulsive strength. Numerical simulations validate the theoretical findings and demonstrate that both impulsive interventions and white noise can effectively promote finite-time population suppression.