Influence of Imperfect Vaccination of Highly Connected Individuals on the Median Smallpox Outbreak Size. Each point was obtained from 1,000 simulations. Initial value: 100 index cases in a population of 100,000. Targeted vaccination: (a) a random sample of 10% of the population is asked to name 20 casual contacts each; (b) these contacts are sorted by frequency; (c) the most frequently named person is first scheduled for vaccination, less frequently named ones follow. The horizontal axis shows what percentage of the population is scheduled for vaccination. Because of vaccination eligibility and/or vaccination efficacy, only a fraction of those scheduled for vaccination can successfully be immunized (percentage immunized is given next to the curves).