Scenario c illustrates that vaccination prior to the discontinuation of routine vaccination does play a role in smallpox control by ring vaccination; there were more decontainment scenarios (5/100) when no prior Transmission prior to the rash Figure 8 Transmission prior to the rash makes epidemic control more difficult. The figure shows a expanding smallpox epidemic assuming differing levels of infectivity prior to the rash. We assume all parameters are the same as in Figure 3A (and that the ring vaccination capacity is 40 per day). Infectivity prior to the rash is modeled as the relative infectivity during the short (1 day) period of oropharyngeal lesions just prior to the rash (compared to the infectivity during the first week of the rash), and as the relative infectivity during the prodromal period (relative to the period just prior to the rash). For scenario a, relative infectivity during the prodromal period and just prior to the rash is the same as during the first week of the rash, for scenario b, the relative infectivity just prior to the rash is the same as during the first week of the rash, but during the prodromal period is 4% (as in Figure 3A ) of this value, and for scenario c, the relative infectivity just prior to the rash is 20% of the infectivity during the first week of the rash, and during the prodromal period is 20% of this value (these two parameters are the same as in Figure 3A ). Additional scenarios, assuming 40 ring vaccinations or con-tact tracings possible per day, and that contacts of contacts are traced; all parameters are identical to those in Figure 3A unless otherwise indicated Figure 9 Additional scenarios, assuming 40 ring vaccinations or contact tracings possible per day, and that contacts of contacts are traced; all parameters are identical to those in Figure 3A unless otherwise indicated. The figure shows the average of 100 replications of five scenarios (Case a repeats the result from Figure 3A for reference); the numbers in parentheses in the legend are the corresponding fraction of the 100 scenarios for which decontainment occurred. For case b, we assumed that flat and hemorrhagic smallpox cases took four times as long on average to diagnose as ordinary cases; for case c., we assumed that no one in the population had prior protection (as opposed to 25% for Figure 3A) ; for case d, we assumed that an additional 10% of individuals (13% instead of 3%) would develop mild smallpox (with 75% developing ordinary smallpox instead of 85% as in Figure 3A ); and for case e, we assumed that the vaccine is completely ineffective and provides no protection against infection. protection exists in the population. The results suggest that prior vaccination aids in the control of smallpox, but that it is not strictly necessary for control (in this scenario, 95% of the replications exhibited containment). In Figure  3A , we assumed 25% of individuals had protection due to vaccination prior to the discontinuation of routine vaccination; in scenario c of Figure 9 , we assumed this fraction was zero.