Spatial models are widely used in epidemiology to investigate persistence and extinction of disease as well as their spatial patterns. One of the most important issues in studying epidemic models is the role of infection on the persistence and extinction of the disease. In this paper, we investigate a spatial susceptible-infected-recovered-infected model using cellular automata. We show that, in the regime where disease disappears in the susceptible-infected-recovered-susceptible model, spiral and target waves will emerge in the two-dimensional space due to the reinfection. The obtained results may point out that reinfection has great influence on the epidemic spreading, which enriches the findings of spatiotemporal dynamics in epidemic models.
Keywords: Cellular automata; Epidemiology; Persistence; Reinfection.