The effect of single-step tracing can be measured by the effective reproduction ratio R q , the average number of new infections per infected. Whereas the rate of being traced backwards at time t since infection (due to detection of any infectee) is equal for all infecteds, the rate of being traced forwards (due to detection of the infector) depends on the generation-time distribution, which in turn depends on the number of traceable generations backwards in the transmission tree (traceable ancestors). Hence, infectives need to be typed according to the number of traceable ancestors j, and R q is the largest eigenvalue of the next-generation matrix K with entries k ij being the expected number of type-i infecteds (with i traceable ancestors) produced per type-j infected [15] . Because type-j infecteds only produce type-0 and type-j+1 infecteds, by untraceable and traceable contacts respectively, all entries other than k 0j and k j+1,j are equal to 0.