The first conclusion from our model is that, for a given R 0 pre , the critical tracing probability can take any value depending on all infectious disease characteristics in the model: the latent period, the infectious period, and the detection time distribution. In contrast to some earlier publications on contact tracing [7, 9] , there exists no general expression for p c * as there is for the proportion to vaccinate for effective control in a well-mixed population. For smallpox the relation p c * = 121/R 0 pre holds reasonably well, but for SARS it is smaller, and for influenza and FMD it is larger.