Dynamical behaviours of a delayed diffusive eco-epidemiological model with fear effect

This paper concerned with a delayed diffusive eco-epidemiological model with fear effect. First, we discuss the existence and boundedness of the solution of the system. Then we give some conditions for the existence and stability of the nonnegative equilibria, and Turing instability. Furthermore, we choose the delay as bifurcation parameter to study Hopf bifurcation. Finally, we present some numerical simulations to verify our theoretical results. By mathematical and numerical analyses, we find that the fear can prevent the occurrence of limit cycle oscillation and increase the stability of the system, and the diffusion can induce the spatial pattern in the system. •We propose a delayed diffusive eco-epidemiological model with fear effect.•We have studied Hopf bifurcation and Turing bifurcation of the model.•We have discussed the global stability of the equilibria.•The results show that system can generate a wide variety of spatial patterns.