Mathematically, we represent the course of smallpox according to Figure 1 . We distinguish eight epidemiologically relevant states: (1) just following exposure, during which time vaccination could afford complete protection against disease, (2) a period of several days during which vaccination will not prevent disease, but may still reduce the severity of disease, (3) still prior to the development of symptoms, but too late for vaccination, (4) the beginning of the pre-eruptive period, during which the patient exhibits fever, malaise, and possibly other symptoms, but is not yet infectious, (5) a short period prior to the appearance of the rash, during which the appearance of oropharyngeal lesions will permit variola transmission, (6) the first week of the rash, during which time the patient is most infectious, (7) and (8), succeeding stages of the rash, during which time the patient is less infectious. For each of these states, we assume that conditional on surviving, the waiting time until the next stage is chosen from a uniform distribution as indicated in Appendix 2 [see Additional file: 2], except that the incubation period (the time from infection until Stage 4) is derived from estimates of the incubation distribution of smallpox based on importation cases in Europe [26] (see Appendix 2 [see additional file 2] for details). We chose to sample from a uniform distribution as a simple way to ensure a minimum waiting time in each state; many alternatives to this choice are possible.