Hardness of Herd Immunity and Success Probability of Quarantine Measures: A Branching Process Approach

  1. Sujit Kumar Nath

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Abstract

Herd immunity refers to the collective resistance of a population against the spreading of an infection as an epidemic. Understanding the dependencies of herd immunity on various epidemiological parameters is of immense importance for strategizing control measures against an infection in a population. Using an age-dependent branching process model of infection propagation, we obtain interesting functional dependencies of herd immunity on the incubation period of the contagion, contact rate, and the probability of disease transmission from an infected to a susceptible individual. We show that herd immunity is difficult to achieve in case of a high incubation period of the contagion. We derive a method to quantify the success probabilities of quarantine measures to mitigate infection from a population, before achieving herd immunity. We provide a mechanistic derivation of the distribution of generation time from basic principles, which is of central importance to estimate the reproduction number R 0 , but has been assumed in an ad hoc manner in epidemiological studies, by far. This derivation of the generation time distribution has the generality to be applied in the study of many other age-dependent branching processes, such as the growth of bacterial colonies, various problems in evolutionary and population biology etc.

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  1. Version published to 10.1101/2020.10.22.20216481v2 on medRxiv
  2. ScreenIT

    SciScore for 10.1101/2020.10.22.20216481: (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.

    About SciScore

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  3. Version published to 10.1101/2020.10.22.20216481v1 on medRxiv