Successfully immunizing as much as 80% or 90% of the scheduled individuals may only be possible with one of the new generation vaccines [2] [3] [4] [5] [6] , and even this may already be regarded as over-optimistic by some, yet this assumption already increases the median outbreak size considerably ( Figure 5 ). The disproportionate effect of a few vaccination failures on the simulation result can be Figure 2 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. explained by a closer look at the maximum eigenvalues depicted in Figure 1 : The removal of all highly connected individuals (red curve) is necessary to really incapacitate the transmission network; if only a random sample of 90% of the highly connected individuals are removed (yellow curve), it practically stays intact.