A mathematical assessment of the efficiency of quarantining and contact tracing in curbing the COVID-19 epidemic

  1. Amaury Lambert

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Abstract

In our model of the COVID-19 epidemic, infected individuals can be of four types, according whether they are asymptomatic ( A ) or symptomatic ( I ), and use a contact tracing mobile phone application ( Y ) or not ( N ). We denote by R 0 the average number of secondary infections from a random infected individual. We investigate the effect of non-digital interventions (voluntary isolation upon symptom onset, quarantining private contacts) and of digital interventions (contact tracing thanks to the app), depending on the willingness to quarantine, parameterized by four cooperating probabilities. For a given ‘effective’ R 0 obtained with non-digital interventions, we use non-negative matrix theory and stopping line techniques to characterize mathematically the minimal fraction y 0 of app users needed to curb the epidemic, i.e. , for the epidemic to die out with probability 1. We show that under a wide range of scenarios, the threshold y 0 as a function of R 0 rises steeply from 0 at R 0 = 1 to prohibitively large values (of the order of 60−70% up) whenever R 0 is above 1.3. Our results show that moderate rates of adoption of a contact tracing app can reduce R 0 but are by no means sufficient to reduce it below 1 unless it is already very close to 1 thanks to non-digital interventions.

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    SciScore for 10.1101/2020.05.04.20091009: (What is this?)

    Please note, not all rigor criteria are appropriate for all manuscripts.

    Table 1: Rigor

    Institutional Review Board Statementnot detected.
    Randomizationnot detected.
    Blindingnot detected.
    Power Analysisnot detected.
    Sex as a biological variablenot detected.

    Table 2: Resources

    No key resources detected.

    Results from OddPub: We did not detect open data. We also did not detect open code. Researchers are encouraged to share open data when possible (see Nature blog).

    Results from LimitationRecognizer: An explicit section about the limitations of the techniques employed in this study was not found. We encourage authors to address study limitations.

    Results from TrialIdentifier: No clinical trial numbers were referenced.

    Results from Barzooka: We did not find any issues relating to the usage of bar graphs.

    Results from JetFighter: We did not find any issues relating to colormaps.

    Results from rtransparent:
    • Thank you for including a conflict of interest statement. Authors are encouraged to include this statement when submitting to a journal.
    • Thank you for including a funding statement. Authors are encouraged to include this statement when submitting to a journal.
    • No protocol registration statement was detected.

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  2. Version published to 10.1051/mmnp/2021042
  3. Version published to 10.1101/2020.05.04.20091009 on medRxiv