Epidemic contact tracing via communication traces

Abstract

Traditional contact tracing relies on knowledge of the interpersonal network of physical interactions, where contagious outbreaks propagate. However, due to privacy constraints and noisy data assimilation, this network is generally difficult to reconstruct accurately. Communication traces obtained by mobile phones are known to be good proxies for the physical interaction network, and they may provide a valuable tool for contact tracing. Motivated by this assumption, we propose a model for contact tracing, where an infection is spreading in the physical interpersonal network, which can never be fully recovered; and contact tracing is occurring in a communication network which acts as a proxy for the first. We apply this dual model to a dataset covering 72 students over a 9 month period, for which both the physical interactions as well as the mobile communication traces are known. Our results suggest that a wide range of contact tracing strategies may significantly reduce the final size of the epidemic, by mainly affecting its peak of incidence. However, we find that for low overlap between the face-to-face and communication interaction network, contact tracing is only efficient at the beginning of the outbreak, due to rapidly increasing costs as the epidemic evolves. Overall, contact tracing via mobile phone communication traces may be a viable option to arrest contagious outbreaks.

Figure 1. Average maximum and total infected over .

Average maximum and total number of infected people for a network overlap , while varying the ratio between the number of removed and added edges. The known network (used for contact tracing) is supposed to be a noisy version of the real network (in which epidemics spread), obtained by removing some edges and adding new ones.

Figure 2. Overlap illustration.

Illustration of the overlap in terms of links between the ideal network and the dual network depending on , and . The intersection of the two networks, in blue, is of size and the union is of size .

Figure 3. Static network visualizations of the data.

The static networks obtained by the overall average number of daily mobile phone (a) communication (call and sms) and (b) physical proximity interactions.

Figure 4. Real data-driven network overlap.

(a) Distribution of % overlap between the overall communication and Bluetooth networks on a log-log scale. (b) Monthly variations in the % overlap between the communication and Bluetooth networks averaged over all users.

Figure 5. Theoretical epidemic simulations over varying tracing efforts and network overlap.

(a) The maximum number of infected individuals (representing the peak of the epidemic), (b) its time of occurrence, and (c)-(d) the overall number of infected individuals on log and non-log scales, respectively; all plotted as a function of , with and . The legend shows the range of contact tracing effort, with to . We can see in (a) that contact tracing is effective in reducing the peak number of infected people with to times fewer maximum infected cases between and . We plot a line at , representing a minimal network overlap which corresponds to the values suggested by the analysis of mobile phone data (see figure 4). The greater the overlap between the tracing and disease spreading networks, the more effective the tracing. At the ideal but unrealistic case of 100% overlap, a of 2.5 allows to get times fewer maximum infected people in comparison to the case with . A low overlap such as has little effect on the size of the outbreak (the overall number of infected individuals does not decrease much), but still the peak number of infected cases is lowered. With higher overlap, the peak of infections not only decreases in intensity but also gets delayed (c).

Figure 6. Time varying simulation results of the ideal network scenario and the proposed dual network topology.

The infected population plot as a function of time for (a) and (b) a network overlap of , where , , , . Contact tracing is always beneficial, even when there is a small overlap between and . We observe that contact tracing becomes increasingly effective as the number of infections increases in both network topologies (a) and (b). However, contact tracing becomes decreasingly effective as the number of infections decreases, particularly in the dual network topology case. This can be seen by the worsened effects of the second and sometimes third peaks for the dual network case (e.g., with ).

Figure 7. Time varying simulation results of our proposed contact tracing dual network topology while varying network overlap, .

We observe the changing effects of the time-varying spread over . The difference in infectious spread over time becomes more apparent in the cases with two peaks, where particularly after the second peak, where an increase in network overlap results in fewer infected cases. Note, the log scale employed to make the graphs easily comparable tends to attenuate the differences between curves within a graph.

Figure 8. Average temporal evolution of the tracing effort and the number of infected people with or without contact tracing.

Only the last curve considers the case with complete network overlap () while all other curves are with .

Figure 9. Average maximum and total numbers of infected people against the amount of random tracing effort.

Simulations consider a network overlap of (left) and (right), when the total tracing effort is constant (400).

Figure 10. Simulation of contact tracing over the empirical data with .

Only the real physical proximity interactions are used to obtain and . The physical proximity interactions are obtained by the mobile phone Bluetooth data and are incorporated on (a) a weekly scale, and (b) a daily scales.

Figure 11. Dual network scenario simulated over the real mobile phone data.

Bluetooth physical proximity is used for , phone communication logs are used for tracing, .

Figure 12. Theory versus practice.

Considering the ideal network scenario, we run the simulated contact tracing model with set to the average daily (and weekly) node degree of the data (see figure S1), but consider a simulated network (labeled as ). Two data-driven models are considered with the interactions taken from the Bluetooth proximity logs. For all cases, , and therefore . The real data is considered on weekly and daily scales, and are the real physical interactions logged by the community’s Bluetooth sensors.