Social heterogeneity and the COVID-19 lockdown in a multi-group SEIR model

  1. Jean Dolbeault
  2. Gabriel Turinici

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Abstract

The goal of the lockdown is to mitigate and if possible prevent the spread of an epidemic. It consists in reducing social interactions. This is taken into account by the introduction of a factor of reduction of social interactions q, and by decreasing the transmission coefficient of the disease accordingly. Evaluating q is a difficult question and one can ask if it makes sense to compute an average coefficient q for a given population, in order to make predictions on the basic reproduction rate ℛ 0 , the dynamics of the epidemic or the fraction of the population that will have been infected by the end of the epidemic. On a very simple example, we show that the computation of ℛ 0 in a heterogeneous population is not reduced to the computation of an average q but rather to the direct computation of an average coefficient ℛ 0 . Even more interesting is the fact that, in a range of data compatible with the Covid-19 outbreak, the size of the epidemic is deeply modified by social heterogeneity, as is the height of the epidemic peak, while the date at which it is reached mainly depends on the average ℛ 0 coefficient. This paper illustrates more technical results that can be found in [4], with new numerical computations. It is intended to draw the attention on the role of heterogeneities in a population in a very simple case, which might be difficult to apprehend in more realistic but also more complex models.

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    SciScore for 10.1101/2020.05.15.20103010: (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: Thank you for sharing your data.

    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 10.1101/2020.05.15.20103010v2 on medRxiv
  3. Version published to 10.1515/cmb-2020-0115
  4. Version published to 10.1101/2020.05.15.20103010v1 on medRxiv