Contact tracing, either manual by questioning diagnosed individuals for recent contacts or by an App keeping track of close contacts, is one out of many measures to reduce spreading. Mathematically this is hard to analyse because future infections of an individual are no longer independent of earlier contacts. In the talk I will describe a stochastic model for a simplified situation, allowing for both manual and digital contact tracing, for which it is possible to obtain results for the initial phase of the epidemic, with focus on the effective reproduction number $R_E$ which determines if contact tracing will prevent an outbreak or not. (Joint work with Dongni Zhang)