  We introduce a 2-layer network model for the study of the immunization
dynamics in epidemics. Spreading of an epidemic is modeled as an excitatory
process in a small-world network (body layer) while immunization by prevention
for the disease as a dynamic process in a scale-free network (head layer). It
is shown that prevention indeed turns periodic rages of an epidemic into small
fluctuation. The study also reveals that, in a certain situation, prevention
actually plays an adverse role and helps the disease survive. We argue that the
presence of two different characteristic time scales contributes to the
immunization dynamics observed.
