Dynamics of a stochastic predator–prey model with disease in predators and Ornstein–Uhlenbeck process

Invasive species can inflict significant harm on biodiversity and disrupt ecosystem stability. Introducing pathogens to combat invasive species is recognized as an effective method for preserving biodiversity. Against this backdrop, we examine a predator–prey model involving diseased predators, taking into account the impact of environmental noise, and then propose a stochastic predator–prey model where predators carry diseases. In this model, we assume that the intrinsic growth rate of the prey and the disease transmission rate of the predator follow an Ornstein–Uhlenbeck process. Our contributions in this study can be summarized as follows: First, we establish the existence and uniqueness of the global solution for the stochastic predator–prey model, along with an analysis of moment estimation for the global solution. Second, we provide sufficient conditions for the existence of stationary distribution and population extinction within the stochastic predator–prey model. Furthermore, we derive the precise expression of the probability density function near the quasi-positive equilibrium [Formula: see text] of the stochastic predator–prey model. Lastly, we validate our analytical findings through numerical simulations.