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The Role of Directionality, Heterogeneity, and Correlations in Epidemic Risk and Spread

Authors: Antoine Allard https://orcid.org/0000-0002-8208-9920, Cristopher Moore, Samuel V. Scarpino, Benjamin M. Althouse https://orcid.org/0000-0002-5464-654X, and Laurent Hébert-DufresneAuthors Info & Affiliations
https://doi.org/10.1137/20M1383811
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Abstract

Most models of epidemic spread, including many designed specifically for COVID-19, implicitly assume mass-action contact patterns and undirected contact networks, meaning that the individuals most likely to spread the disease are also the most at risk of contracting it from others. Here, we review results from the theory of random directed graphs which show that many important quantities, including the reproduction number and the epidemic size, depend sensitively on the joint distribution of in- and out-degrees (``risk” and “spread''), including their heterogeneity and the correlation between them. By considering joint distributions of various kinds, we elucidate why some types of heterogeneity cause a deviation from the standard Kermack--McKendrick analysis of SIR models, i.e., so-called mass-action models where contacts are homogeneous and random, and why some do not. We also show that some structured SIR models informed by realistic complex contact patterns among types of individuals (age or activity) are simply mixtures of Poisson processes and tend not to deviate significantly from the simplest mass-action model. Finally, we point out some possible policy implications of this directed structure, both for contact tracing strategy and for interventions designed to prevent superspreading events. In particular, directed graphs have a forward and a backward version of the classic “friendship paradox''---forward edges tend to lead to individuals with high risk, while backward edges lead to individuals with high spread---such that a combination of both forward and backward contact tracing is necessary to find superspreading events and prevent future cascades of infection.

Keywords

  1. contact network epidemiology
  2. epidemic percolation networks
  3. generating functions
  4. directed graphs
  5. friendship paradox
  6. contact tracing
  7. compartmental models
  8. Poisson mixture models

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Information & Authors

Information

Published In

cover image SIAM Review
SIAM Review
Volume 65 • Issue 2 • May 2023
Pages: 471 - 492
DOI: 10.1137/20M1383811
ISSN (online): 1095-7200

Copyright

© 2023, Laurent Hébert-Dufresne. Published by SIAM under the terms of the Creative Commons 4.0 license. This work is licensed under a Creative Commons Attribution 4.0 International License.

History

Submitted: 2 December 2020
Accepted: 9 February 2022
Published online: 9 May 2023

Keywords

  1. contact network epidemiology
  2. epidemic percolation networks
  3. generating functions
  4. directed graphs
  5. friendship paradox
  6. contact tracing
  7. compartmental models
  8. Poisson mixture models

Authors

Affiliations

Laurent Hébert-Dufresne
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Funding Information

Canada First Research Excellence Fund
Natural Sciences and Engineering Research Council of Canada : 2019-05183
Bill and Melinda Gates Foundation
Northeastern University
National Institutes of Health
National Science Foundation https://doi.org/10.13039/100000001 : IIS-1838251

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