Summary: A directed epidemic propagation process is modeled by a deterministic cellular automaton with three local states (infected, immunized and susceptible). The model is characterized by the choice of the lifetimes of the infected and immunized states as external parameters and by the existence of a continuous control parameter determining the fraction of synchronized infection vectors. The various dynamical regimes observed in the fully synchronized state are described. In a region of parameter space where a statistically stationary disordered regime is observed, evidence is given of a phase transition between a localized damage and a spreading damage regime.