The Effectiveness of Contact Tracing in Emerging Epidemics

Klinkenberg, Don; Fraser, Christophe; Heesterbeek, Hans

The underlying model for infection dynamics is based on the framework of [4] . In our model, t measures time since infection of an individual, which starts with a latent period until t = t lat without transmission of the pathogen. During the infectious period, lasting from t lat to t inf , infecteds give rise to b new infecteds per unit of time, as long as they are not detected. As we are interested in the effectiveness of tracing only, we do not model possible transmission that might occur while being isolated, so transmission 'ceases' after detection of the infected. This leaves us with the basic reproduction ratio prior to detection, defined as the expected number of secondary infections per infected in a susceptible population before detection, R 0 pre . Here we have adjusted the interpretation of the model in [4] , where R 0 is divided in an asymptomatic and a symptomatic part, by adding a detection delay after becoming symptomatic. The part R 0 pre is determined by t lat , t inf , b, and the distribution of the detection time, a Gammadistribution with mean 1 (so time is measured relative to the mean detection time) and shape parameter a. Throughout our analyses, b will be scaled accordingly to achieve a desired value of R 0 pre . This model construction allows a flexible way of exploring different assumptions about the time to detection, the infectious period, and their overlap, and it enables us to evaluate tracing effectiveness for most infections.