In many cases, however, more rapid diagnosis was not required for ring vaccination to be effective. As before, we simulated smallpox epidemics for each of 1000 calibrated scenarios, performing 100 realizations each beginning with 10 index cases, and computed the fraction of scenarios for which the epidemic was always contained (as defined earlier), assuming no change in diagnosis rates. We assumed 80 ring vaccinators per day, contact finding probabilities of 0.95 for households and 0.8 for workplace/social contacts (as in Figure 3A ). Under these assumptions, for 83.4% of the scenarios, the epidemic was contained within 500 total cases in each of the 100 realizations, even with no change in diagnosis rates. Uncertainty analysis (using the 1000 calibrated scenarios, and based on the fraction of 100 replications showing decontainment) revealed the most important parameters which predict the failure of ring vaccination without more rapid diagnosis were the same as we found in the earlier uncertainty analysis; a higher fraction vaccinated before the epidemic, smaller households or workplace/social groups, less transmissibility, lowered infectivity prior to the rash, more rapid diagnosis, and a higher rate of diagnosis for alerted individuals all contribute to a greater containment probability even without an overall increase in the diagnosis rate.