Effectiveness of probabilistic contact tracing in epidemic containment: the role of super-spreaders and transmission path reconstruction

TL;DR

This study quantitatively analyze the diagnostic and social costs associated with these containment measures based on contact tracing, employing three state-of-the-art models of SARS-CoV-2 spreading and reveals a remarkable efficacy of probabilistic contact-tracing techniques in performing backward and multistep tracing and capturing superspreading events.

Abstract

The recent COVID-19 pandemic underscores the significance of early-stage non-pharmacological intervention strategies. The widespread use of masks and the systematic implementation of contact tracing strategies provide a potentially equally effective and socially less impactful alternative to more conventional approaches, such as large-scale mobility restrictions. However, manual contact tracing faces strong limitations in accessing the network of contacts, and the scalability of currently implemented protocols for smartphone-based digital contact tracing becomes impractical during the rapid expansion phases of the outbreaks, due to the surge in exposure notifications and associated tests. A substantial improvement in digital contact tracing can be obtained through the integration of probabilistic techniques for risk assessment that can more effectively guide the allocation of new diagnostic tests. In this study, we first quantitatively analyze the diagnostic and social costs associated with these containment measures based on contact tracing, employing three state-of-the-art models of SARS-CoV-2 spreading. Our results suggest that probabilistic techniques allow for more effective mitigation at a lower cost. Secondly, our findings reveal a remarkable efficacy of probabilistic contact-tracing techniques in performing backward and multi-step tracing and capturing super-spreading events.

Figures (10)

• Figure 1: Effective epidemic mitigation. Columns labeled (a), (b), and (c) show, respectively, the behavior in time of the effective reproduction number $R_{t}$ (see the Supplementary Information for a detailed description), the cumulative number of diagnostic tests, and the cumulative number of infected individuals. For the Covasim model (first row), simulations are run on a population of $70\,000$ people, for $T=100$ days. Each simulation starts with $N_{pz}=30$ patients zero, all in the exposed state, and each day half of the unidentified symptomatic individuals are observed ($p_{sym} = 50 \%$), while tracing-based interventions start after $t_{i} = 14$ days. For the StEM model (second row), simulations are performed on the urban area of Tübingen for $T = 100$ days, and the number of initial cases $N_{pz}$ is 6 (1 in the exposed state, 2 in the asymptomatic state, and 3 of them are pre-symptomatic individuals). The same fraction of the symptomatic individuals is observed ($p_{sym} = 50 \%$), with interventions starting at $t_{i} = 14$. In the StEM model, households are confined whenever a member is tested positive. Lines reflect the average behavior of the metrics computed from $20$ realizations of the Covasim population model and $30$ realizations of the StEM mobility model. The shaded regions indicate the associated standard error.
• Figure 2: Spreading reduction, social, and diagnostic cost. Panels (a.1) and (b.1) show the reduction measure of the epidemic spreading as a function of the number of medical tests performed daily during the simulations; panels (a.2) and (b.2) display $N_{Q}$, the percentage of the confined individuals due to the different confinement strategies as a function of the reduction (see Ref. barrat2021effect). These quantities are computed for $T= 100$ and $T = 150$ for StEM and Covasim respectively, when the number of infected individuals reaches a plateau in the corresponding uncontrolled simulations. For StEM (Covasim), the population has a size of $90,546$ ($70,000$) individuals (see Methods). The panels on the top display the two measures associated with the Covasim model, while the panels on the bottom show the results while running StEM dynamics. The reduction measure is formally defined as the difference between the cumulative number of infected in an unconstrained propagation (where only the fixed percentage of symptomatic is confined) and the mitigated one, normalized by the cumulative number of infected in unconstrained dynamics. The higher the reduction, the more effective the containment measure. The size of the markers in panels (a.1) and (b.1) is proportional to the number of quarantines (the quantity plotted in the y-axis of the (a.2) and (b.2) panels), the larger the dots, the larger the number of confined individuals. The color code used in all the panels mirrors the number of tests performed on a daily basis: the darker the color, the larger this number.
• Figure 3: Detection of the super-spreaders. (a) Schematic representation of the experimental setup. A posteriori, the superspreader individuals (the purple nodes) are identified as those responsible for over-dispersed transmissions (see the main text for a proper definition for the three models), here marked as the nodes within the pink shadow. To fairly evaluate the ability of each contact tracing method to detect superspreaders the ROC curves are built only for a subset of the individuals composed of the true superspreaders and susceptible individuals (small light grey nodes). Information about the epidemic dynamics entirely comes from the contact network and the daily observation of a fixed fraction of symptomatic (red nodes). The methods employed to compute the ROC curves are Belief Propagation (BP, orange), Simple Mean Field (SMF, green), Informed Contact Tracing (ICT, blue), Digital Contact Tracing (DCT, purple), Trace-Test-Quarantine (TTQ, pink). The statistics of the AUC associated with the ROC curves obtained by different methods are shown for (b) OpenABM, (c) Covasim, and (d) StEM. Lines are kernel density estimation plots used as guides for the eyes, while mean AUC values are reported in the legend. All parameters used in these simulations are the same as used in the epidemic containment results, except for the time $T$, the number of patients zero $N_{\rm{pz}}$, and the probability of self-testing. These numbers have been tuned to ensure that the maximum number of true positives in the ROC curves is at least a few tens. In particular, the duration of the free epidemic propagation before estimation is set to $T = 15$ for StEM, $T = 30$ for Covasim, and $T = 20$ for OpenABM. The number of initially infected individuals is set to $N_{\rm{pz}} = 200$ for StEM, $N_{\rm{pz}} = 90$ for Covasim and $N_{\rm{pz}} = 100$ for OpenABM. The fraction of observed symptomatic individuals is set to $p_{\rm{sym}} = 0.1$ for StEM and for Covasim, while for OpenABM all severe symptomatic individuals are observed ($p_{\rm{ssym}} = 1.0$) together with a fraction $p_{\rm{msym}} = 0.3$ of mild ones.
• Figure 4: Detection of the one-step, two-step backward, and one-step, multi-step forward tracing. Panels (a.1), (b.1), (c.1), and (d.1) show a schematic representation of the one-step, two-step backward, one-step, and multi-step forward transmissions respectively. See the main text for a formal definition. The second, third, and fourth rows show the histogram of the AUC associated with the detection of the four types of infected individuals, for OpenABM, Covasim, and StEM respectively. The methods used to obtain the ROC curves are Belief Propagation (BP, orange), Simple Mean Field (SMF), Informed Contact Tracing (ICT, blue), Digital Contact Tracing (DCT, purple), and Trace-Test-Quarantine (TTQ, pink). The simulation set-up used for these results is the same exploited for the detection of the super-spreaders illustrated in Figure \ref{['fig:fig3']}. The average AUC is reported in the legend for the methods, while the lines report kernel density estimates to guide the visualization of the histograms.
• Figure S1: Schematic representation of the epidemic dynamics in the three models considered in this work. (a): OpenABM; (b): Covasim. (c): StEM. Color codes identify how these states are considered within the reduction to an effective SIR model (d). Infection events are graphically represented by red dots; each arrow represents a transition between two states, whose waiting time is drawn from certain probability distributions; the probability to undergo one of the different infection pathways is always age-dependent in the three models.