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 networks without clustering.

隔离和联系人跟踪是缓解流行病爆发的流行的特殊做法。但是，目前很少有数学理论可用来评估网络在这些实践的有效性中的作用。在本文中，我们研究在网络空模型（配置模型）中将接触者跟踪和隔离相结合的过程如何影响流行的最终规模。即，我们假设被感染的顶点可以自我隔离并以给定的成功概率来追踪其感染者。反过来，被追踪的感染者感染其他人的可能性较小。我们表明，这种跟踪过程的有效性在很大程度上取决于网络结构。与以前的发现相反，跟踪过程不一定在异构度较高的网络上更有效。