We have been assuming that whenever an individual is contacted during an investigation, the individual will be diagnosed more quickly should they subsequently develop symptoms. When transmission is assumed to be very rapid (smallpox is assumed to be highly contagious), most individuals may already be infected when identified through contact tracing from an infective. Using the scenario we examined in Figure 3A , we see that continued surveillance of contacts is an essential component of effective ring vaccination designed to control rapidly spreading smallpox: if smallpox in a contact is not diagnosed any more quickly than for a non-contact, containment by ring vaccination requires over 98% contact finding probabilities for both household and workplace/ social contacts -even if unlimited numbers of ring vaccinators are available; containment cannot be guaranteed by adding additional ring vaccination capacity if the contact finding rates are too low and/or the follow-up for contacts is insufficient. Smallpox which is transmitted less rapidly to contacts would, however, be containable with a lower contact finding probability (results not shown).