Herd immunity thresholds for SARS-CoV-2 estimated from unfolding epidemics

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Abstract

Variation in individual susceptibility or frequency of exposure to infection accelerates the rate at which populations acquire immunity by natural infection. Individuals that are more susceptible or more frequently exposed tend to be infected earlier and hence more quickly selected out of the susceptible pool, decelerating the incidence of new infections as the epidemic progresses. Eventually, susceptible numbers become low enough to prevent epidemic growth or, in other words, the herd immunity threshold (HIT) is reached. We have recently proposed a method whereby mathematical models, with gamma distributions of susceptibility or exposure to SARS-CoV-2, are fitted to epidemic curves to estimate coefficients of individual variation among epidemiological parameters of interest. In the initial study we estimated HIT around 25-29% for the original Wuhan virus in England and Scotland. Here we explore the limits of applicability of the method using Spain and Portugal as case studies. Results are robust and consistent with England and Scotland, in the case of Spain, but fail in Portugal due to particularities of the dataset. We describe failures, identify their causes, and propose methodological extensions.

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  1. SciScore for 10.1101/2020.07.23.20160762: (What is this?)

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

    Table 1: Rigor

    NIH rigor criteria are not applicable to paper type.

    Table 2: Resources

    Software and Algorithms
    SentencesResources
    Parameter estimation was performed with the software MATLAB, using PESTO
    PESTO
    suggested: (PESTO, RRID:SCR_016891)
    Core models implemented in MATLAB available from: https://github.com/mgmgomes1/covid
    MATLAB
    suggested: (MATLAB, RRID:SCR_001622)

    Results from OddPub: Thank you for sharing your code and 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.

    About SciScore

    SciScore is an automated tool that is designed to assist expert reviewers by finding and presenting formulaic information scattered throughout a paper in a standard, easy to digest format. SciScore checks for the presence and correctness of RRIDs (research resource identifiers), and for rigor criteria such as sex and investigator blinding. For details on the theoretical underpinning of rigor criteria and the tools shown here, including references cited, please follow this link.

  2. Keith Klugman

    Review 1: "Herd immunity thresholds for SARS-CoV-2 estimated from unfolding epidemics"

    Reviewers find that this study presents important concepts surrounding heterogeneous transmission rates and their effects on herd immunity thresholds, but suggest that there are major flaws in the modeling assumptions that produce misleading results.

  3. Pieter Trapman

    Review 2: "Herd immunity thresholds for SARS-CoV-2 estimated from unfolding epidemics"

    Reviewers find that this study presents important concepts surrounding heterogeneous transmission rates and their effects on herd immunity thresholds, but suggest that there are major flaws in the modeling assumptions that produce misleading results.

  4. SciScore for 10.1101/2020.07.23.20160762: (What is this?)

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

    Table 1: Rigor

    NIH rigor criteria are not applicable to paper type.

    Table 2: Resources

    Antibodies
    SentencesResources
    We emphasise that seroprevalence estimates generally lie slightly below our cumulative infection curves (Extended Data Figure 9) consistently with recent findings that a substantial fraction of infected individual does not exhibit detectable antibodies13.
    antibodies13
    suggested: None
    Software and Algorithms
    SentencesResources
    Parameter estimation was performed with the software Matlab, using PESTO (Parameter EStimation Toolbox)37, and assuming the reported case data can be accurately described by a Poisson process.
    Matlab
    suggested: (MATLAB, SCR_001622)

    Data from additional tools added to each annotation on a weekly basis.

    About SciScore

    SciScore is an automated tool that is designed to assist expert reviewers by finding and presenting formulaic information scattered throughout a paper in a standard, easy to digest format. SciScore is not a substitute for expert review. SciScore checks for the presence and correctness of RRIDs (research resource identifiers) in the manuscript, and detects sentences that appear to be missing RRIDs. SciScore also checks to make sure that rigor criteria are addressed by authors. It does this by detecting sentences that discuss criteria such as blinding or power analysis. SciScore does not guarantee that the rigor criteria that it detects are appropriate for the particular study. Instead it assists authors, editors, and reviewers by drawing attention to sections of the manuscript that contain or should contain various rigor criteria and key resources. For details on the results shown here, including references cited, please follow this link.