The Impact of Contact Tracing in Clustered Populations

The tracing of potentially infectious contacts has become an important part of the control strategy for many infectious diseases, from early cases of novel infections to endemic sexually transmitted infections. Here, we make use of mathematical models to consider the case of partner notification for sexually transmitted infection, however these models are sufficiently simple to allow more general conclusions to be drawn. We show that, when contact network structure is considered in addition to contact tracing, standard “mass action” models are generally inadequate. To consider the impact of mutual contacts (specifically clustering) we develop an improvement to existing pairwise network models, which we use to demonstrate that ceteris paribus, clustering improves the efficacy of contact tracing for a large region of parameter space. This result is sometimes reversed, however, for the case of highly effective contact tracing. We also develop stochastic simulations for comparison, using simple re-wiring methods that allow the generation of appropriate comparator networks. In this way we contribute to the general theory of network-based interventions against infectious disease.Author Summary: There are multiple ways to control infectious diseases—vaccination and drugs such as antibiotics or anti-virals form part of the pharmaceutical approach, however another route is to stop people infecting each other. This can be done either through general efforts to reduce epidemiologically relevant contacts, or through a more targeted attempt to trace the contacts of known cases who can then be isolated or treated. The impact of this kind of contact tracing is a priori likely to depend strongly on the network of contacts linking people together. In this paper, we develop new mathematical and computational techniques to model the impact of clustering: the probability that any two contacts of a given individual are also linked to each other in the network, creating triangles. Often, and for intuitively understandable reasons, the presence of clustering increases the efficacy of contact tracing, however we show that in the regime of highly effective contact tracing sometimes the opposite is true.