Influence of Perfect Vaccination of Highly Connected Individuals on a Smallpox Outbreak. Efficacy = 100%. Simulated outbreak sizes, caused by 100 index cases in a population of 100,000: the boxes show 25%, 50%, 75% quantiles, the whiskers show 10% and 90% quantiles and the triangles show minimum and maximum results (for 2% vaccination, the upper limit is not given, as one of the 100 simulations afflicted more than half of the population, as did all simulations for 0% and 1% vaccination). Targeted vaccination: (a) everybody is asked to name all casual contacts; (b) these contacts are sorted by frequency; (c) vaccination starts with the most frequently named person and progresses towards less frequently named ones. The horizontal axis shows what percentage of the population is vaccinated.