A Study of Stochastic Ecological Model with Prey Harvesting as a Tool of Disease Control

Abstract

This study explores the hierarchical dynamics of a predator model in which the population of prey is comprised of two classes: susceptible and infected (SI) prey including the non-selective prey harvesting. The system’s points of equilibrium are found. The model’s stability properties were tested by both locally and globally. Next, we have implemented the stochastic perturbations and indicated that the deterministic model of stochastic perturbations is robust. The stochastic perturbations effects on the dynamics were discussed via simulations. The deterministic method results in a stochastic system with an effect of atmospheric random noise were presented. That is, we have explored the SI prey–predator model’s stability incorporating prey harvesting by introducing stochastic perturbations that were not previously studied. Finally, some numerical examples and diagrams help our complex dynamics of our model using time series diagrams and phase portraits which supports our theoretical results. Parallel to this, we presented the time series diagram and phase portraits for the stochastic perturbation system.