Dynamic analysis of a diffusive eco-epidemiological system with fear effect and prey refuge

In the evolutionary development of species, the prey can produce the fear effect in the face of predation behaviors. This fear effect may affect the own reproduction growth of the prey. In order to reduce the risk of predation, the prey has the instinct to protect themselves. At the same time, the population is easy vulnerable by disease in the ecosystem. Driven by these biological facts, we propose an eco-epidemiological system with two-predator-one-prey that considers fear effect and prey refuge. At the same time, we consider the impact of spatial diffusion on the stability of the system. We discuss the conditions for the existence of all equilibrium points with biological meanings in non-spatial system. We also obtain local stability conditions for all equilibrium points. We show that the deterministic system is bistable. Kolmogorov analysis is used to analyze the appearance of limit cycles and chaos in the non-spatial system. We consider k as a bifurcation parameter and study the existence of Hopf bifurcation. In the spacial diffusion system, we deduce the local stability conditions of the diffusion system and obtain the occurrence conditions of Turing instability. Numerical simulations are given to explain the phenomena beyond the scope of analytical methods and better understand the complex predator-prey interactions.