In general, in a network-structured model, the number of secondary cases caused by an index case in a completely susceptible population is not a useful index of epidemic potential [41, 42] (for a simple example, see [43] ), since (for instance) an individual could infect everyone in his or her household, and not cause a widespread epidemic unless between-household transmission were sufficiently frequent. Rather than constructing the appropriate generalized basic reproduction number for our model (leading to highly cumbersome expressions), we chose an alternative (ad hoc) index of epidemic potential. For any given scenario of interest, we simulated the introduction of 10 index cases at random into a population of size 10000, and operationally defined "containment" to occur whenever the final size of the epidemic was less than 500 cases within 250 days (we showed, in the discussion of Figure   Smallpox stages used in the simulation model Figure 1 Smallpox stages used in the simulation model. Flat and ordinary smallpox rashes are indicated with more dots than modified and "mild" smallpox, suggesting potentially greater infectiousness. Hemorrhagic smallpox is indicated by horizontal line shading. Further details are provided in Table  6 . 5A below, that in nearly all cases, the 250-day window differs very little from a 1000-day window). Because we simulate a disease with a finite duration on a finite and nonrenewing population, epidemic extinction always occurs in finite time.