We consider the optimal control through immunization of an epidemic spread by carriers alone. Costs are taken to be a weighted sum of the number of infected cases, the area under the corners’ trajectory and the total expended immunization effort, and optimal policies are of the bang-bang (on-off) type. The underlying model, first proposed by Weiss, is treated in both its deterministic and stochastic forms, and in the case of the latter, the accuracy of a sub-optimal policy for which more complete analytic results can be found is investigated