The effect of delay on contact tracing

•The branching approximation with contact tracing of a stochastic epidemic model is analysed.•Approximations for the probability to be infectious at a given age of infection and the reproduction number are derived.•The effect of the tracing delay on infections with latency period are investigated.•The effect of stochasticity in the tracing delay is discussed.

We consider a model for an infectious disease in the onset of an outbreak. We introduce contact tracing incorporating a tracing delay. The effect of randomness in the delay and the effect of the length of this delay in comparison to the infectious period of the disease respectively to a latency period on the effect of tracing, given e.g. by the change of the reproduction number, is analyzed. We focus particularly on the effect of randomness in the tracing delay.