In three special cases (panels 2A,B,D), with fixed incubation period and/or short infectious period, the proportion of contacts to be traced is at least 121/R 0 pre . This lower limit 121/R 0 pre is due to forwards tracing, when all infecteds that are traceable via their infector, are quarantined before the end of their latent period. Then, the effective reproduction ratio will be equal to the untraceable proportion of R 0 pre , i.e. R q = (12p c )R 0 pre , resulting in p c * = 121/R 0 pre . This is likely to be case with smallpox (panel 2D). However, if the latent period is short, as seen for influenza and possibly FMD, quarantine will occur too late to prevent all infections and more contacts need to be traced.