While Figure 6 illustrates the possibility that rapid contact tracing may be of decisive importance in some scenarios (parameter set choices), this is not always the case. For some parameter sets, the probability of tracing contacts (household or workplace/social) may be too low, or the transmission rate too high, for more rapid contact tracing to make any difference. Conversely, for other parameter sets, the smallpox transmission rate may be so low that smallpox is easily contained even with slow contact tracing. While rapid contact tracing is never harmful, overall, how typical are the results of Figure 6 (in which rapid contact tracing was important in ensuring the efficacy of ring vaccination)? To address this question, we simulated the growth of smallpox for the 1000 "calibrated" scenarios we used in Figure 5A and 5B. As before, we assumed ten initial cases, and (as in Figure 6 ) that 30 ring vaccinations were possible per day; then we simulated 100 epidemics assuming one day to find a household contact (and 2 days to find a workplace/social contact). We then simulated 100 epidemics assuming that it takes five days to find a household contact and 10 days to find a workplace/social contact (as in Figure 6 ). For each of these 1000 scenarios, we calculated the fraction of simulations for which the total number of cases is 500 or less within 250 days, i.e. the containment fraction. For nearly all scenarios (parameter set choices), the containment fraction was smaller (sometimes much smaller) when the contact finding time is faster (since faster contact finding, all else being equal, improves smallpox control, as illustrated in Figure 6 ). However, for 64.5% of the scenarios (parameter set choices) examined, the difference was less than 2.5% in absolute terms (smallpox was either contained or not contained depending on other factors, and rapid contact tracing did not make the difference). On the other hand, for 18.7% of the scenarios examined, the absolute difference in the containment probability was 20% or more; thus, a substantial difference in containment probability is occa-Faster contact tracing Figure 6 Faster contact tracing may improve the efficacy of ring vaccination. We assume the same baseline parameters as in Figure 3A (e.g. households of size 4, workplace/social groups of size 8, 95% of household contacts traceable, 80% of workplace/social contacts traceable), and 30 ring vaccinations available per day (with contacts of contacts not traced). The fast scenario corresponds to an average one day delay for household and two days for workplace/social contacts (as in Figure 3A ); the slow scenario corresponds to an average five day delay for household and ten day delay for workplace/ social contacts. This figure shows the average of one hundred realizations starting with ten index cases. Effect of more rapid diagnosis Public awareness of smallpox, leading to more rapid isolation and identification, may play an important role in eliminating the epidemic, as illustrated by the scenarios in Figure 7 . We assumed 20 ring vaccinations possible per day, a capacity too small to contain the epidemic in the absence of increased surveillance or diagnosis; the black line in the figure shows the steeply rising average number of cases for the first 100 days. If, however, surveillance or public awareness of the symptoms of smallpox increases the diagnosis rate by 50% (multiplies the baseline diagnosis rates by 1.5), containment becomes possible (blue line); with a doubling of the diagnosis rate (red line) the peak number of cases is lower still. In these scenarios, increased diagnostic rates markedly improve the ability of ring vaccination to control the epidemic, this suggest that any ring vaccination effort be accompanied by increased public awareness and surveillance.