The relevance of this finding can be seen in Figure 2 , which shows how the targeted immunization influences the simulation results of an outbreak which starts with 100 index cases in a population of 100,000 individuals. We start with a highly over-simplified situation in which we assume that we can ask everybody in the population to supply the names of all casual contacts, and later progress towards more realistic scenarios. The contacts are first sorted by frequency and then scheduled for vaccination, starting with the most frequently named person. As described in detail in the Methods section, detected cases are isolated or are asked to stay at home or to seclude themselves from contacts with other individuals (if all 500 isolation units are occupied); their contacts are traced and taken under surveillance. If only case isolation and contact tracing are used to fight against the outbreak, the large initial attack overwhelms the public health resources and the smallpox outbreak afflicts more than 50% of the population. When additionally targeting the vaccination on the most frequently named contacts, an immunization coverage of only 4% yields a median outbreak of less than 1,600 cases; a vaccination coverage of 6% can further reduce the median to less than 1,300 cases with a worst case scenario of under 1,700 cases. Asking everybody in the population is clearly an unrealistic task for any public health system. We will next explore how the results change, if only a small random fraction of the population is asked to name all casual contacts. Figure 3 shows how the median outbreak size changes if only a small random sample is asked. The horizontal axis again shows what percentage of the population is vaccinated, whereby immunization begins with the most frequently named contact. If we are willing to vaccinate 10% of the population, it suffices to ask a random sample of 4% of the population for their contacts in order to obtain a median outbreak size of less than 2,000 cases. For the highly optimistic goal of having a median outbreak size of less than 1,000 cases, we have to ask 10% of the population to supply the names of their contacts.