  Contact tracing, the practice of isolating individuals who have been in
contact with infected individuals, is an effective and practical way of
containing disease spread. Here, we show that this strategy is particularly
effective in the presence of social groups: Once the disease enters a group,
contact tracing not only cuts direct infection paths but can also pre-emptively
quarantine group members such that it will cut indirect spreading routes. We
show these results by using a deliberately stylized model that allows us to
isolate the effect of contact tracing within the clique structure of the
network where the contagion is spreading. This will enable us to derive
mean-field approximations and epidemic thresholds to demonstrate the efficiency
of contact tracing in social networks with small groups. This analysis shows
that contact tracing in networks with groups is more efficient the larger the
groups are. We show how these results can be understood by approximating the
combination of disease spreading and contact tracing with a complex contagion
process where every failed infection attempt will lead to a lower infection
probability in the following attempts. Our results illustrate how contact
tracing in real-world settings can be more efficient than predicted by models
that treat the system as fully mixed or the network structure as locally
tree-like.
