Spreadable probabilistic cellular automata models: An application in epidemiology

Many important physical processes reveal spreadable phenomena which describe the expansion with time of a given spatial property. The general spreadability concept have been studied using models based on partial differential equations (PDE's). These spreadable dynamics are generally non linear and then difficult to simulate particularly in 2 dimensions. A cellular automata approach have been used as an alternative modelling tool to model and simulate spreadable systems in the deterministic case. We propose in this paper a probabilistic cellular automaton model that exhibits the growth with time of a spatial property. The obtained local dynamics are directly implemented and the numerical results are performed to illustrate spreadable phenomena. An example to epidemic propagation is given to illustrate the considered phenomena.