The effectiveness of backward contact tracing in networks

Abstract

Effective control of an epidemic relies on the rapid discovery and isolation of infected individuals. Because many infectious diseases spread through interaction, contact tracing is widely used to facilitate case discovery and control. However, what determines the efficacy of contact tracing has not been fully understood. Here we reveal that, compared with 'forward' tracing (tracing to whom disease spreads), 'backward' tracing (tracing from whom disease spreads) is profoundly more effective. The effectiveness of backward tracing is due to simple but overlooked biases arising from the heterogeneity in contacts. We argue that, even if the directionality of infection is unknown, it is possible to perform backward-aiming contact tracing. Using simulations on both synthetic and high-resolution empirical contact datasets, we show that strategically executed contact tracing can prevent a substantial fraction of transmissions with a higher efficiency-in terms of prevented cases per isolation-than case isolation alone. Our results call for a revision of current contact-tracing strategies so that they leverage all forms of bias. It is particularly crucial that we incorporate backward and deep tracing in a digital context while adhering to the privacy-preserving requirements of these new platforms.

Fig. 1 |. Schematic illustration of backward contact tracing.

a, A transmission event occurs from a ‘parent’ to a ‘focal node’ (or an offspring). b, The disease spreads from an infected node to its neighbours through edges in networks. c, The spread of disease can be represented as a transmission tree with directed edges from parents to offspring. d, Backward tracing is likely to sample parents with many offspring; for example, node 11 is more likely to be sampled than node 10 by backward tracing. e, Contact tracing can also be conducted for a bipartite network of people and gatherings. As for the contact network, a high-degree gathering is more likely to be ‘infected’ and to be traced with the same logic.

Fig. 2 |. Backward and frequency-based contact tracings are effective at reaching hub nodes.

a,b, We simulate the SEIR model on a BA network composed of 250,000 nodes. We sample the infected nodes with probability 0.1 and trace their parents at time t = 10. In a, the blue and orange lines respectively indicate the complementary cumulative distribution function (CCDF) for the degree of the sampled nodes and their parents, which follow G₁ and G₂, respectively. Frequency-based contact tracing (b)—isolating the most frequently traced nodes—can reach nodes with a degree similar to the parents without knowing who infects whom. c,d, As for the contact network, both backward (c) and frequency-based (d) contact tracing can reach large degree nodes for people-gathering networks. e, The bias due to backward tracing is present even in a relatively homogeneous network. We simulate the SEIR model on a temporal contact network of university students and sample all infected nodes and their parents. The infected and parent nodes have degree distributions that closely follow G₁ and G₂ for the unweighted aggregated network, respectively. f, As for the contact and people-gathering networks, frequency-based contact tracing is effective at reaching large degree nodes.

Fig. 3 |. Effectiveness of contact tracing for networks with a heterogeneous degree distribution.

a–l, People contact networks (a–f) and people-gathering networks (g–l) are generated by the BA and the configuration model, respectively. Contact tracing (a) lowers the peak of infection by more than 70% of that for case isolation. The effectiveness (b) stands out even if we can trace a few nodes. The efficacy of contact tracing (c) is substantially enhanced when the detection probability is increased. Compared with case isolation (p_t = 0), contact tracing (p_t > 0) isolates fewer nodes (d) while preventing more cases (e,f). Contact tracing is therefore highly cost-efficient in terms of the number of prevented cases per isolation. The plots in g–l correspond to those in a–f, but for people-gathering networks. Contact tracing is also highly effective for people-gathering networks (g). Each point indicates the average value for 30 simulations. The translucent bands indicate the 95% confidence interval estimated by a bootstrapping with 10⁴ resamples.

Fig. 4 |. Effectiveness of contact tracing for the student physical contact network.

An infected node is discovered and isolated with probability p_s. Contact tracing isolates the most frequent n close contacts in the contact list. We isolate n = 3, 10 or all close contacts, as indicated by ‘n = 3’, ‘n = 10’ or ‘all’, respectively. a, Contact tracing reduces the peak of infections more than case isolation. b, Even if we trace and isolate a few nodes, it is as effective as isolating all contacts. c, The effectiveness is more pronounced when we can detect more infected nodes. d–f, Contact tracing isolates more nodes (d) and prevents more cases (e,f) as we trace more contacts. Contact tracing is not efficient when tracing probability is large. Although contact tracing is highly effective and efficient, massive contact tracing may have a diminishing return. Each point indicates the average value for 1,000 simulations. The translucent bands indicate the 95% confidence interval estimated by a bootstrapping with 10⁴ resamples.

Fig. 5 |. Control of an outbreak using contact tracing in heterogeneous networks.

We use randomized BA networks, where each of 250,000 nodes has a degree of at least 2, and attempt to control the spread of a disease with transmissibility T using tracing probability P, which successfully isolates a given sibling of a new case with probability 1 − f. Symbols show the average of 100 Monte Carlo simulations, and solid lines show the results of our analytical formalism. a, Using perfect contact tracing f = 0, the probability of sustained transmissions goes down monotonically with more contact tracing, but without undergoing the usual sharp epidemic transition. b, With f = 0, the regime of smeared epidemic transition increases with the frequency of contact tracing. At a high frequency of contact tracing, we find the probability of sustained transmission remains low, even for high values of transmissibility well beyond the epidemic threshold. c, We fix transmissibility at T = 0.3 and look at the robustness of different contact tracing probability P to imperfect tracing by varying the probability f that isolation fails.