Eco-epidemiological predator–prey dynamics under harvesting and environmental noise
摘要
Understanding the complex interaction of the epidemiological process in the lake ecosystem is crucial for managing biodiversity and disease outbreaks. Within this study, we develop a deterministic and stochastic model to investigate the dynamics of the deterministic system and the contribution of environmental white noise. The growth of prey fish species in the ecosystem is influenced by infection and regulated by harvesting. We establish stability criteria for the deterministic system at various steady points and analyze the Hopf bifurcation, a transition from a steady state to periodic oscillations. In this study, for the stochastic system, we develop the conditions necessary for a globally unique positive solution and its boundedness. We also identify criteria for species extinction and permanence concerning long-term behavior. In addition, we explore the existence of a stationary distribution subject to specific conditions. We implement the numerical simulations that contrast the deterministic and stochastic systems to illustrate our analytical findings.