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Heterogeneous network epidemics: real-time growth, variance and extinction of infection

Ball, Frank; House, Thomas

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Authors

FRANK BALL frank.ball@nottingham.ac.uk
Professor of Applied Probability

Thomas House



Abstract

© 2017, The Author(s). Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular choice in theoretical studies since it combines the ability to specify the distribution of the number of contacts (degree) with analytical tractability. Here we consider the early real-time behaviour of the Markovian SIR epidemic model on a configuration model network using a multitype branching process. We find closed-form analytic expressions for the mean and variance of the number of infectious individuals as a function of time and the degree of the initially infected individual(s), and write down a system of differential equations for the probability of extinction by time t that are numerically fast compared to Monte Carlo simulation. We show that these quantities are all sensitive to the degree distribution—in particular we confirm that the mean prevalence of infection depends on the first two moments of the degree distribution and the variance in prevalence depends on the first three moments of the degree distribution. In contrast to most existing analytic approaches, the accuracy of these results does not depend on having a large number of infectious individuals, meaning that in the large population limit they would be asymptotically exact even for one initial infectious individual.

Citation

Ball, F., & House, T. (2017). Heterogeneous network epidemics: real-time growth, variance and extinction of infection. Journal of Mathematical Biology, 75(3), 577-619. https://doi.org/10.1007/s00285-016-1092-3

Journal Article Type Article
Acceptance Date Dec 21, 2016
Online Publication Date Jan 17, 2017
Publication Date Sep 1, 2017
Deposit Date Feb 10, 2017
Publicly Available Date Mar 28, 2024
Journal Journal of Mathematical Biology
Print ISSN 0303-6812
Electronic ISSN 1432-1416
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 75
Issue 3
Pages 577-619
DOI https://doi.org/10.1007/s00285-016-1092-3
Keywords SIR epdidemic, configuration model, branching process
Public URL https://nottingham-repository.worktribe.com/output/840001
Publisher URL http://link.springer.com/article/10.1007%2Fs00285-016-1092-3

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