In an epidemic where single-step tracing is applied, asymptomatic infecteds can spread the infection until they are detected and isolated. Detected infecteds are asked to name their contactees, and a proportion p c of all contactees will be reported and quarantined. Only when quarantined infecteds are detected themselves, tracing is continued ( Figure 1A) . We determined the critical tracing probability p c * as a function of the latent period for three values of R 0 pre (1.5, 2, and 3). The results are shown in Figure 2 . If the detection time is fixed (a = '), a too large latent period (larger than the detection time) results in a situation where every infected is detected before transmitting the infection, so tracing need not prevent any transmission; hence the maximum t lat of 1 in panels 2B and 2D. If we locate the approximate position of real infections (parameter values in Table 2 ) in Figure 2 , we observe that the long infectious period will be the best approximation for most infections, because we only regard pre-detection transmission and infecteds will often still be infectious at the time of detection. This does not entirely hold for influenza, which therefore fits best between the short and long infectious period. Because of the detection period distributions, smallpox and FMD are best described by panel 2D, whereas SARS and influenza fit best into panel 2C (influenza also into 2A).