The eco-epidemiology, combining interacting species with epidemiology, can describe some complex phenomena in real ecosystem. Most diseases contain the latent stage in the process of disease transmission. In this paper, a spatial eco-epidemiological model with delay and disease in the predator is studied. By mathematical analysis, the characteristic equations are derived, then we give the conditions of diffusion-driven equilibrium instability and delay-driven equilibrium instability, and find the ranges of existence of Turing patterns in parameter space. Moreover, numerical results indicate that a parameter variation has influences on time and spatially averaged densities of pattern reaching stationary states when other parameters are fixed. The obtained results may explain some mechanisms of phenomena existing in real ecosystem.
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