Periodic solutions in an epidemic model with diffusion and delay

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A spatial diffusion SI model with delay and Neumann boundary conditions are investigated. We derive the conditions of the existence of Hopf bifurcation in one dimension space. Moreover, we analyze the properties of bifurcating period solutions by using the normal form theory and the center manifold theorem of partial functional differential (PFDs) equations. By numerical simulations, we found that spatiotemporal periodic solutions can occur in the epidemic model with spatial diffusion, which verifies our theoretical results. The obtained results show that interaction of delay and diffusion may induce outbreak of infectious diseases.