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.