We examine a model for a disease with SIR-type dynamics circulating in a population living on two or more patches between any pair of which migration is allowed. We suppose that a pulse vaccination strategy (PVS) is carried out on each patch. Conditions are derived on each PVS such that the disease will be eradicated on all patches. The PVS on one patch is assumed to be essentially independent of the PVS on the other patches except in so far as they are all performed simultaneously. This independence is of practical value when we bear in mind that the patches may represent regions or countries with autonomous public health authorities, which may make individual decisions about the days appropriate for a vaccination pulse to occur in their own region or country. Simulations corroborate our theoretical results.