We have formulated a model of the importation of an infectious disease from a source region to an at-risk country that permits a comprehensive analysis of the effect of border control measures. Our results are most relevant to the early stage of a pandemic when most cases are contained within a single source region. Once the pandemic has spread to several countries, models with greater complexity and ability to more realistically model global mixing patterns [6] [7] [8] are required. Our model is developed with a pandemic-strain of influenza in mind, but could apply to any emerging infectious disease that is transmitted from person to person. We have assumed a Poisson distribution for the number of secondary infections, which a natural choice when each infected individual has the same infectivity profile. A distribution with a larger variance is appropriate when individuals vary substantially in their infectiousness. Our results are conservative in the sense that they give an upper bound for the probability that an infected traveler manages to initiate an epidemic, compared to an offspring distribution with a greater variance but the same reproduction number [14] .