An epidemiological stochastic predator prey model with prey refuge and harvesting

Abstract Predator-prey interactions are fundamental to understanding ecosystem stability and biodiversity. In this study, we propose and analyze a stochastic predator-prey model that incorporates two critical ecological factors: prey refuge and harvesting. The model also integrates disease transmission within the predator population, adding an important layer of realism. Using rigorous mathematical techniques, we demonstrate the existence and uniqueness of a global positive solution, thereby confirming the model's biological feasibility. We further derive sufficient conditions for two key ecological scenarios: stochastic permanence, which ensures the sustained co-existence of prey and predators over time, and extinction, where one or both populations decline to zero. The interplay between prey refuge and harvesting is thoroughly examined to understand their combined impact on population dynamics. All theoretical results are validated by detailed numerical simulations, highlighting the applicability of the model to real-world ecological systems. From simulation results, we realized that with adequate level of prey refuge and harvesting of predators, the susceptible predator and prey co-exist with extensive oscillations while the infected predator population was moving towards extinction. In addition, we have investigated the effect of disease transmission on system dynamics. Our results show that, as the transmission rate of disease increases, the susceptible predator is approaching extinctions, and, on the other hand, when it declines, the susceptible predators show robust oscillations while the infected is approaching extinction. In both cases, the prey population demonstrates robust stability due to the prey refuge. Our findings show that the management of harvesting and prey refuge can be effective ecological tactics for disease control and species protection under stochastic environmental effects.