  We investigate epidemic models with spatial structure based on the cellular
automata method. The construction of the cellular automata is from the study by
Weimar and Boon about the reaction-diffusion equations [Phys. Rev. E 49, 1749
(1994)]. Our results show that the spatial epidemic models exhibit the
spontaneous formation of irregular spiral waves at large scales within the
domain of chaos. Moreover, the irregular spiral waves grow stably. The system
also shows a spatial period-2 structure at one dimension outside the domain of
chaos. It is interesting that the spatial period-2 structure will break and
transform into a spatial synchronous configuration in the domain of chaos. Our
results confirm that populations embed and disperse more stably in space than
they do in nonspatial counterparts.
