  We consider random perturbations of a general eco-epidemiological model. We
prove the existence of a global random attractor, the persistence of
susceptibles preys and provide conditions for the simultaneous extinction of
infectives and predators. We also discuss the dynamics of the corresponding
random epidemiological $SI$ and predator-prey models. We obtain for this cases
a global random attractor, prove the prevalence of susceptibles/preys and
provide conditions for the extinctions of infectives/predators.
