We used these parameters to simulate smallpox epidemics beginning with 10 cases, for a variety of levels of ring vaccination capacity per day (contact tracing capacity per day), as shown in Figure 3A . In this Figure, we assume that the population size is 10000, and that the epidemic began with 10 infected individuals. The mean household size is assumed to be 4, the mean size of the workplace/social contact group is 8, and contacts of contacts are traced. We assume that each day, the number of contacts that can be traced and vaccinated as a result of case investigation is 0, 10, 20, 30 and 40 per day; the probability of finding a workplace/social contact is assumed to be 80%. The Table 1 .