How long is long enough? The impact of the contact tracing interval

Contact tracing is one of the most important non-pharmaceutical control measures for infectious diseases. The corona epidemic revealed that many aspects of contact tracing are still not well understood, from the theoretical as well as from the practical point of view.In the present work, we focus on the tracing interval. The tracing interval is the time interval for which people are asked to give their contacts. The current practical guidelines mainly orient themselves at the infectious interval. In our research we vary this tracing interval and examine its effect on the spread of the disease in the onset. Thereto we setup a differential-difference equation model for the probability to be infectious at a certain age since infection when contact tracing is used. The probability to be infectious is then used to calculate the incidence depending on the tracing interval. Therewith we discuss the impact of contact tracing in dependence on the tracing interval.