Effects of immunization in small-world epidemics

The propagation of model epidemics on a small-world network under the action of immunization is studied. Although the connectivity in this kind of networks is rather uniform, a vaccination strategy focused on the best connected individuals yields a considerable improvement of disease control. The model exhibits a transition from disease localization to propagation as the disorder of the underlying network grows. As a consequence, for fixed disorder, a threshold immunization level exists above which the disease remains localized.