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A beta-Poisson model for infectious disease transmission
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Hilton, Joe and Hall, Ian (2024) A beta-Poisson model for infectious disease transmission. PLoS Computational Biology, 20 (2). e1011856. doi:10.1371/journal.pcbi.1011856 ISSN 1553-7358.
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Official URL: http://doi.org/10.1371/journal.pcbi.1011856
Abstract
Outbreaks of emerging and zoonotic infections represent a substantial threat to human health and well-being. These outbreaks tend to be characterised by highly stochastic transmission dynamics with intense variation in transmission potential between cases. The negative binomial distribution is commonly used as a model for transmission in the early stages of an epidemic as it has a natural interpretation as the convolution of a Poisson contact process and a gamma-distributed infectivity. In this study we expand upon the negative binomial model by introducing a beta-Poisson mixture model in which infectious individuals make contacts at the points of a Poisson process and then transmit infection along these contacts with a beta-distributed probability. We show that the negative binomial distribution is a limit case of this model, as is the zero-inflated Poisson distribution obtained by combining a Poisson-distributed contact process with an additional failure probability. We assess the beta-Poisson model’s applicability by fitting it to secondary case distributions (the distribution of the number of subsequent cases generated by a single case) estimated from outbreaks covering a range of pathogens and geographical settings. We find that while the beta-Poisson mixture can achieve a closer to fit to data than the negative binomial distribution, it is consistently outperformed by the negative binomial in terms of Akaike Information Criterion, making it a suboptimal choice on parsimonious grounds. The beta-Poisson performs similarly to the negative binomial model in its ability to capture features of the secondary case distribution such as overdispersion, prevalence of superspreaders, and the probability of a case generating zero subsequent cases. Despite this possible shortcoming, the beta-Poisson distribution may still be of interest in the context of intervention modelling since its structure allows for the simulation of measures which change contact structures while leaving individual-level infectivity unchanged, and vice-versa.
Item Type: | Journal Article | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Life Sciences (2010- ) | ||||||
Journal or Publication Title: | PLoS Computational Biology | ||||||
Publisher: | Public Library of Science | ||||||
ISSN: | 1553-7358 | ||||||
Official Date: | 8 February 2024 | ||||||
Dates: |
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Volume: | 20 | ||||||
Number: | 2 | ||||||
Article Number: | e1011856 | ||||||
DOI: | 10.1371/journal.pcbi.1011856 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
Date of first compliant deposit: | 19 March 2024 | ||||||
Date of first compliant Open Access: | 19 March 2024 |
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