Abstract
We investigate final outcome properties of an SIR (susceptible → infective → recovered) epidemic model defined on a population of large sub-communities in which there is stronger disease transmission within the communities than between them. Our analysis involves approximation of the epidemic process by a chain of within-community large outbreaks spreading between the communities. We derive law of large numbers and central limit type results for the number of individuals and the number of communities affected and the so-called severity of the outbreak. These results are valid as the size of communities tends to infinity, with the number of communities either fixed or also tending to infinity. The weaker between-community connections lead to randomness even in the law of large numbers type limit. As part of our proofs we also obtain a new result concerning the rate of convergence of the expected fraction infected in a standard SIR epidemic to its large-population limit.
Funding Statement
This work was partially supported by a grant from the Simons Foundation and was carried out as a result of the authors’ visit to the Isaac Newton Institute for Mathematical Sciences during the programme Theoretical Foundations for Statistical Network Analysis in 2016 (EPSRC Grant Number EP/K032208/1).
The third author was supported by Vetenskapsrådet (Swedish Research Council), grant 2016-04566.
This work was also supported by a grant from the Knut and Alice Wallenberg Foundation, which enabled the first author to be a guest professor at the Department of Mathematics, Stockholm University.
Acknowledgments
The authors thank an anonymous referee for their very careful reading of our paper and constructive comments, which have improved its presentation.
Current affiliation of the third author is Bernoulli Institute, University of Groningen.
Citation
Frank Ball. David Sirl. Pieter Trapman. "SIR epidemics in populations with large sub-communities." Ann. Appl. Probab. 34 (5) 4408 - 4454, October 2024. https://doi.org/10.1214/24-AAP2070
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