Ergodic stationary distribution and extinction of a stochastic eco-epidemiological model with disease in prey

We investigate a stochastic eco-epidemiological framework where disease transmission occurs within the prey population and interacts with the predators under environmental noise. By employing stochastic Lyapunov methods and Khasminskii’s theory, we establish persistence-extinction conditions and confirm the existence of an ergodic stationary distribution. Furthermore, we determine the threshold parameters that govern the long-term dynamics of the system. Theoretical results are supported through numerical simulations which illustrate how variations in key biological and noise parameters affect the coexistence and extinction of species. The study highlights the significant influence of stochastic perturbations on disease dynamics and provides useful insights into the stability of eco-epidemiological systems under random environmental effects. © 2025 Elsevier Ltd.