{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:11:08Z","timestamp":1787314268500,"version":"build-2736575974"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1011856","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2024,2,29]],"date-time":"2024-02-29T00:00:00Z","timestamp":1709164800000}}],"reference-count":40,"publisher":"Public Library of Science (PLoS)","issue":"2","license":[{"start":{"date-parts":[[2024,2,8]],"date-time":"2024-02-08T00:00:00Z","timestamp":1707350400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>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\u2019s 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.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1011856","type":"journal-article","created":{"date-parts":[[2024,2,8]],"date-time":"2024-02-08T13:51:45Z","timestamp":1707400305000},"page":"e1011856","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":8,"title":["A beta-Poisson model for infectious disease transmission"],"prefix":"10.1371","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2787-3827","authenticated-orcid":true,"given":"Joe","family":"Hilton","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3033-2335","authenticated-orcid":true,"given":"Ian","family":"Hall","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2024,2,8]]},"reference":[{"issue":"4","key":"pcbi.1011856.ref001","doi-asserted-by":"crossref","first-page":"e1004154","DOI":"10.1371\/journal.pcbi.1004154","article-title":"Characterizing the transmission potential of zoonotic infections from minor outbreaks","volume":"11","author":"AJ Kucharski","year":"2015","journal-title":"PLoS computational biology"},{"issue":"7066","key":"pcbi.1011856.ref002","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1038\/nature04153","article-title":"Superspreading and the effect of individual variation on disease emergence","volume":"438","author":"JO Lloyd-Smith","year":"2005","journal-title":"Nature"},{"issue":"5","key":"pcbi.1011856.ref003","doi-asserted-by":"crossref","first-page":"e1002993","DOI":"10.1371\/journal.pcbi.1002993","article-title":"Inference of R0 and transmission heterogeneity from the size distribution of stuttering chains","volume":"9","author":"S Blumberg","year":"2013","journal-title":"PLoS Computational Biology"},{"key":"pcbi.1011856.ref004","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1371\/journal.pone.0000012","article-title":"The Effectiveness of Contact Tracing in Emerging Epidemics","volume":"1","author":"D Klinkenberg","year":"2006","journal-title":"PLOS ONE"},{"key":"pcbi.1011856.ref005","doi-asserted-by":"crossref","first-page":"2565","DOI":"10.1098\/rspb.2003.2554","article-title":"Contact tracing and disease control","volume":"270","author":"KTD Eames","year":"2003","journal-title":"Proc R Soc Lond B"},{"key":"pcbi.1011856.ref006","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1016\/j.idm.2020.12.005","article-title":"Contact tracing\u2014Old models and new challenges","volume":"6","author":"J M\u00fcller","year":"2021","journal-title":"Infectious Disease Modelling"},{"issue":"1","key":"pcbi.1011856.ref007","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0304-4149(94)00034-Q","article-title":"Strong approximations for epidemic models","volume":"55","author":"F Ball","year":"1995","journal-title":"Stochastic processes and their applications"},{"issue":"2","key":"pcbi.1011856.ref008","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1093\/biomet\/61.2.393","article-title":"On parametric estimation for mortal branching processes","volume":"61","author":"N Becker","year":"1974","journal-title":"Biometrika"},{"issue":"132","key":"pcbi.1011856.ref009","doi-asserted-by":"crossref","first-page":"20170115","DOI":"10.1098\/rsif.2017.0115","article-title":"Anticipating the emergence of infectious diseases","volume":"14","author":"TS Brett","year":"2017","journal-title":"Journal of The Royal Society Interface"},{"issue":"1","key":"pcbi.1011856.ref010","doi-asserted-by":"crossref","first-page":"105","DOI":"10.3201\/eid2201.151410","article-title":"Effectiveness of ring vaccination as control strategy for Ebola virus disease","volume":"22","author":"AJ Kucharski","year":"2016","journal-title":"Emerging infectious diseases"},{"key":"pcbi.1011856.ref011","article-title":"Stochastic and spatio-temporal analysis of the Middle East Respiratory Syndrome outbreak in South Korea, 2015","author":"H Lee","year":"2019","journal-title":"Infectious Disease Modelling"},{"key":"pcbi.1011856.ref012","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.jtbi.2011.10.039","article-title":"Estimating the transmission potential of supercritical processes based on the final size distribution of minor outbreaks","volume":"294","author":"H Nishiura","year":"2012","journal-title":"Journal of theoretical biology"},{"issue":"1","key":"pcbi.1011856.ref013","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.mbs.2011.10.009","article-title":"Reproduction numbers for epidemic models with households and other social structures. 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