A Simple Model of Recurrent Epidemics

A cellular automaton conceived as a simple model of disease spreading is investigated. We show that the steady-state of the model is described by a spatial organization of the infections individuals on fronts and undamped temporal oscillations in the number of infections individuals. This behaviour is observed both for a deterministic and stochastic input of susceptible individuals, hence showing that recurrent epidemic behaviour can be persistent without any external forcing. The simplicity of the model suggests that such spatio-temporal behaviour can be obtained from nothing, but a direct transmission mechanism between nearest neighbors provided some mechanism for the introduction of new susceptible individuals, e.g., loss of immunity is present.