Abstract
This paper deals with the mathematical modelling of the red palm weevil (RPW), Rhynchophorus ferrugineus (Olivier) (Coleoptera: Curculionidae), in date palms using chemical control by utilizing injection and sex pheromone traps. A deterministic and stochastic model for RPW is proposed and analyzed. The existence of a positive global solution for the stochastic RPW model is investigated, and the conditions for the extinction of RPWs from the stochastic system are obtained. The adequate criteria for the presence of a unique ergodic stationary distribution for the RPW system are established by creating suitable Lyapunov functions. The impact of chemical injection and pheromone traps on RPW is demonstrated. The importance of environmental noise on RPW is highlighted and simulated using the Milstein method.