Automated contact tracing: a game of big numbers in the time of COVID-19

Abstract

One of the more widely advocated solutions for slowing down the spread of COVID-19 has been automated contact tracing. Since proximity data can be collected by personal mobile devices, the natural proposal has been to use this for automated contact tracing providing a major gain over a manual implementation. In this work, we study the characteristics of voluntary and automated contact tracing and its effectiveness for mapping the spread of a pandemic due to the spread of SARS-CoV-2. We highlight the infrastructure and social structures required for automated contact tracing to work. We display the vulnerabilities of the strategy to inadequate sampling of the population, which results in the inability to sufficiently determine significant contact with infected individuals. Of crucial importance will be the participation of a significant fraction of the population for which we derive a minimum threshold. We conclude that relying largely on automated contact tracing without population-wide participation to contain the spread of the SARS-CoV-2 pandemic can be counterproductive and allow the pandemic to spread unchecked. The simultaneous implementation of various mitigation methods along with automated contact tracing is necessary for reaching an optimal solution to contain the pandemic.

Keywords: COVID-19; SARS-CoV-2; contact tracing; disease mitigation.

Figure 1.

A depiction of automated contact tracing. The cross-section is denoted by the dashed circle and is of radius r₀/2. Interactions occur from t = 0 to t = t₀ + ε where ε ≪ t₀. A will be confirmed as COVID-19 positive in the future and C will be notified having come in contact with A. E might be notified if E stays in contact with A for a time period greater than t₀.

Figure 2.

Percentage of the population that needs to be enrolled ($f_e^{\min }$) for automated contact tracing to be successful. Starting from the left, the solid and dashed lines represent $f_c=100\text{\%},80\text{\%}$, respectively, for the first panel, $p_t=35\text{\%},15\text{\%}$ for the second panel, $r_c=75\text{\%},95\text{\%}$ for the third panel and $f_T=50\text{\%},90\text{\%}$ for the fourth panel. For the left two panels, the fraction of truly infected individuals that will be confirmed as infected by testing, r_c is varied between 75% and 95%. For the right two panels, the fraction of people who will confirm they have been tested as infected if they are enrolled, f_c is varied between 70% and 90%. Three cases for the minimum fraction of the individuals at risk that need to be traced are considered with $f_T=50\text{\%},70\text{\%},90\text{\%}$ in orange, green and red, respectively, in the left two panels and similarly, three cases are considered for $p_t=15\text{\%},25\text{\%},35\text{\%}$ in the right two panels. The blue dotted line in the third panel from the left gives the threshold variation of $f_e^{\min }$ with f_T when all other parameters are set to 1. The y-axes are identical for all panels. See text for more details.