A cellular automata model that describes as limit cases of his parameters the spread of contagious diseases modeled by systems of ordinary or partial differential equations is developed. Periodic features of the behavior of human settlement are considered. The model is built taking into account the range of motion of the elements of population. For small (large) values of this range, the behaviors described by partial (ordinary) differential equation models are reproduced. Emphasis is done in the study of those scenarios in which the above mentioned equations fail to describe. Some interesting behaviors in these cases are reported.