A minimal model for household effects in epidemics

  1. Greg Huber
  2. Mason Kamb
  3. Kyle Kawagoe
  4. Lucy M Li
  5. Boris Veytsman
  6. David Yllanes
  7. Dan Zigmond

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Abstract

Shelter-in-place and other confinement strategies implemented in the current COVID-19 pandemic have created stratified patterns of contacts between people: close contacts within households and more distant contacts between the households. The epidemic transmission dynamics is significantly modified as a consequence. We introduce a minimal model that incorporates these household effects in the framework of mean-field theory and numerical simulations. We show that the reproduction number R 0 depends on the household size in a surprising way: linearly for relatively small households, and as a square root of size for larger households. We discuss the implications of the findings for the lockdown, test, tracing, and isolation policies.

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  1. ScreenIT

    SciScore for 10.1101/2020.07.09.20150227: (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: We detected the following sentences addressing limitations in the study:
    The assumptions underlying the model reveal its natural limitations. For mean-field calculations (but not numerical simulations), we assumed that inside-household dynamics are much faster than the transmission between households. This allowed us to neglect the details of transmission inside households and use an idealized model depending just on the mean time between the first infection and the completely infected household. This also allowed us to neglect secondary between-household infections (i.e., household members of an infected individual getting infected by their outside contacts rather than by the inside ones). Our numerical simulations did not employ this assumption explicitly. However, by selecting a very simple inside-household infection model (pair interactions between household members) we made the assumption implicitly: the details of the inside transmission should not matter if the transmission is fast. Another assumption for the mean-field model is the neglect of random fluctuations: we used mean values to construct the equations. We also neglected the dependence of the time for a household to become infected on the household size. This dependence should be significant for very large “households” (see Appendix). While we use the word “households” throughout this paper, our model may describe situations beyond the simple picture of families waiting out the epidemics together. A dormitory, cruise ship, or even apartment building with a common ventilation system ...

    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. Version published to 10.1088/1478-3975/abb209
  3. Version published to 10.1101/2020.07.09.20150227 on medRxiv