Estimating the Tracing Probability from Contact History at the Onset of an Epidemic

Contact tracing is believed to be an effective method to control infectious diseases. If an infected person is noticed (the index case), one tries to find other infected persons through the contact history of the index case. The distribution of the total number of additionally detected persons per index case is derived, partially by heuristic arguments. The reproduction number influences this distribution only weakly, and the detection rate of index cases even less. This distribution depends mainly on the tracing probability. An estimator for the tracing probability is derived. This estimator is applied to data for tuberculosis and chlamydia.