Stochastic Predator-Prey Model with Disease in Prey and Hybrid Impulses for Integrated Pest Management

Abstract

The stochastic effect is sometimes crucial in the case of integrated pest management due to fluctuating exotic environmental and climate conditions, and it also affects the resources required for pest extinction. Hence, we extend the classical predator-prey model into an impulsive control system by incorporating disease in the prey along with a stochastic element, which helps in controlling optimal pesticide level more accurately in most economic means for pest eradication. Further in analysis, it is obtained that the solution of the proposed model is positively bounded and globally attractive. The long-term behavior of the model is examined, and the condition for pest eradication is driven. The analysis shows that pest control becomes more complex due to the high amplitude of impulsive period and higher intensities of external interference. Finally, we perform some numerical simulations to support our analytical findings and their interpretation.