Our results support ring vaccination against epidemics of smallpox (even assuming high rates of transmission to close contacts), but do note that stochastically, for severe (rapidly transmissible) smallpox, scenarios of loss of control are seen, with resulting widespread epidemics. In scenarios in which the transmission potential of smallpox is smaller, such loss-of-control scenarios occur less frequently (results not shown). Mass vaccination campaigns, when conducted quickly and with very high coverage, do not result in loss of control in our model. Nevertheless, fewer deaths due to smallpox result when ring vaccination is conducted along with mass vaccination.