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An epidemic model with short-lived mixing groups

Ball, Frank; Neal, Peter

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Professor of Applied Probability

Professor of Statistics


Almost all epidemic models make the assumption that infection is driven by the interaction between pairs of individuals, one of whom is infectious and the other of whom is susceptible. However, in society individuals mix in groups of varying sizes, at varying times, allowing one or more infectives to be in close contact with one or more susceptible individuals at a given point in time. In this paper we study the effect of mixing groups beyond pairs on the transmission of an infectious disease in an SIR (susceptible → infective → recovered) model, both through a branching process approximation for the initial stages of an epidemic with few initial infectives and a functional central limit theorem for the trajectories of the numbers of infectives and susceptibles over time for epidemics with many initial infectives. We also derive central limit theorems for the final size of (i) an epidemic with many initial infectives and (ii) a major outbreak triggered by few initial infectives. We show that, for a given basic reproduction number R0, the distribution of the size of mixing groups has a significant impact on the probability and final size of a major epidemic outbreak. Moreover, the standard pair-based homogeneously mixing epidemic model is shown to represent the worst case scenario, with both the highest probability and the largest final size of a major epidemic.


Ball, F., & Neal, P. (2022). An epidemic model with short-lived mixing groups. Journal of Mathematical Biology, 85(6-7), Article 63.

Journal Article Type Article
Acceptance Date Oct 3, 2022
Online Publication Date Oct 31, 2022
Publication Date Dec 1, 2022
Deposit Date Oct 7, 2022
Publicly Available Date Nov 1, 2023
Journal Journal of Mathematical Biology
Print ISSN 0303-6812
Electronic ISSN 1432-1416
Publisher Springer Science and Business Media LLC
Peer Reviewed Peer Reviewed
Volume 85
Issue 6-7
Article Number 63
Keywords Applied Mathematics; Agricultural and Biological Sciences (miscellaneous); Modeling and Simulation
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