Dynamical analysis of a stochastic eco-epidemiological model with infected prey driven by Lévy jumps

In the context of frequent animal disease outbreaks, studying disease dynamics from the perspective of environmental perturbations offers one important scientific approach for disease control. This work investigates a stochastic eco-epidemiological model based on a predator–prey ecosystem, in which disease spreads exclusively among prey population. The ecological dynamics are modeled through species interactions, in which the predator regulates the infected prey population. Environmental perturbations are characterized by white noise and Lévy jumps. The research firstly analyzes the stability of the deterministic system. Then, to ensure that the stochastic model possesses ecological significance, we establish the existence and uniqueness of the global positive solution for it. Furthermore, under the condition that the noise intensities are not excessively large, this work identifies the critical threshold R1s determining the infected prey extinction and the stationary distribution existence. This threshold analysis not only serves as theoretical foundation for disease control, but also contributes to understanding the long-term behavior of the epidemic. Finally, we validate our results through numerical simulations and further analyze the impact of environmental perturbations by numerical simulation techniques.