Pattern dynamics of a spatial epidemic model with time delay

• We presented an epidemic model with delay.
• Emergence of spatial pattern is obtained.
• Rich dynamics is shown by analysis and numerical results.
• Observed data confirms our theoretical results.

The nonlinear incidence rate can explain the complicated infectious process of disease. And time delay describing the latent period widely exists in the process of disease contagion. In this paper, a spatiotemporal epidemic model with nonlinear incidence rate is investigated. In particular, we considered that the time delay is relatively small. In this case, the characteristic equation are derived, we obtain two mechanisms of instability of the positive constant stationary state, that is, One is the diffusion induced instability, and the other one is delay induced instability. Moreover, the results of numerical simulation validate our theoretical analyses. The obtained results may well catch some major features for epidemic models.