  A deterministic cellular automaton rule defined on the Moore neighbourhood is
studied as a model of epidemic propagation. The directed nature of the
interaction between cells allows one to introduce the dependence on a disorder
parameter that determines the fraction of ``in-phase'' cells. Phase-disorder is
shown to produce peculiar changes in the dynamical and statistical properties
of the different evolution regimes obtained by varying the infection and the
immunization periods. In particular, the finite-velocity spreading of
perturbations, characterizing chaotic evolution, can be prevented by
localization effects induced by phase-disorder, that may also yield spatial
isotropy of the infection propagation as a statistical effect. Analogously, the
structure of phase-synchronous ordered patterns is rapidly lost as soon as
phase-disorder is increased, yielding a defect-mediated turbulent regime.
