In Figure 5A , we plot the mean containment fraction (averaging the containment fraction over all 1000 scenarios), as ring vaccination capacity varies, for the two levels of workplace/social group contact finding probabilities (0.8 and 0.9), and for the two levels of monitored diagnosis rate among initially asymptomatic contacts (1 day -1 and 8 day -1 ). For low levels of ring vaccination (traceable contacts per day), the epidemic is almost never contained, but for ring vaccination levels near 50-60 per day (5-6 per index case per day), the average containment fraction Figure 4 Stochastic variability is illustrated by plotting the number of infectives over time over multiple replications. In this example, most simulations exhibit rapid containment of smallpox. The mean number of cases (averaging over simulations) is influenced by a small number of simulations exhibiting an uncontained epidemic. The parameters are the same as in Figure 3A , except that contacts of contacts are not traced in these replications. 