Contact tracing in configuration models

TL;DR

This paper develops a mathematical framework to analyze how contact tracing and quarantining impact epidemic spread on network models, revealing that network structure and clustering significantly influence intervention effectiveness.

Contribution

It introduces a model combining contact tracing and quarantining on configuration networks, highlighting the complex effects of network heterogeneity and clustering on epidemic control.

Findings

Tracing effectiveness varies with network heterogeneity.

Clustering can either enhance or reduce tracing efficiency.

Network structure critically influences epidemic mitigation strategies.

Abstract

Quarantining and contact tracing are popular ad hoc practices for mitigating epidemic outbreaks. However, few mathematical theories are currently available to asses the role of a network in the effectiveness of these practices. In this paper, we study how the final size of an epidemic is influenced by the procedure that combines contact tracing and quarantining on a network null model: the configuration model. Namely, we suppose that infected vertices may self-quarantine and trace their infector with a given success probability. A traced infector is, in turn, less likely to infect others. We show that the effectiveness of such tracing process strongly depends on the network structure. In contrast to previous findings, the tracing procedure is not necessarily more effective on networks with heterogeneous degrees. We also show that network clustering influences the effectiveness of the tracing process in a non-trivial way: depending on the infectiousness parameter, contact tracing on clustered networks may either be more, or less efficient than on network without clustering.