{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T10:53:55Z","timestamp":1767178435370,"version":"build-2238731810"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1010281","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2022,7,8]],"date-time":"2022-07-08T00:00:00Z","timestamp":1657238400000}}],"reference-count":97,"publisher":"Public Library of Science (PLoS)","issue":"6","license":[{"start":{"date-parts":[[2022,6,27]],"date-time":"2022-06-27T00:00:00Z","timestamp":1656288000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"General Research Fund of Research Grants Council","award":["C7123-20G"],"award-info":[{"award-number":["C7123-20G"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["31871340"],"award-info":[{"award-number":["31871340"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71974165"],"award-info":[{"award-number":["71974165"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005847","name":"Health and Medical Research Fund","doi-asserted-by":"publisher","award":["COVID190103"],"award-info":[{"award-number":["COVID190103"]}],"id":[{"id":"10.13039\/501100005847","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005847","name":"Health and Medical Research Fund","doi-asserted-by":"publisher","award":["INF-CUHK-1"],"award-info":[{"award-number":["INF-CUHK-1"]}],"id":[{"id":"10.13039\/501100005847","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Chinese University of Hong Kong Grant","award":["PIEF\/Ph2\/COVID\/06"],"award-info":[{"award-number":["PIEF\/Ph2\/COVID\/06"]}]},{"name":"Chinese University of Hong Kong Grant","award":["4054600"],"award-info":[{"award-number":["4054600"]}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>\n                    In the context of infectious disease transmission, high heterogeneity in individual infectiousness indicates that a few index cases can generate large numbers of secondary cases, a phenomenon commonly known as superspreading. The potential of disease superspreading can be characterized by describing the distribution of secondary cases (of each seed case) as a negative binomial (NB) distribution with the dispersion parameter,\n                    <jats:italic>k<\/jats:italic>\n                    . Based on the feature of NB distribution, there must be a proportion of individuals with individual reproduction number of almost 0, which appears restricted and unrealistic. To overcome this limitation, we generalized the compound structure of a Poisson rate and included an additional parameter, and divided the reproduction number into independent and additive fixed and variable components. Then, the secondary cases followed a Delaporte distribution. We demonstrated that the Delaporte distribution was important for understanding the characteristics of disease transmission, which generated new insights distinct from the NB model. By using real-world dataset, the Delaporte distribution provides improvements in describing the distributions of COVID-19 and SARS cases compared to the NB distribution. The model selection yielded increasing statistical power with larger sample sizes as well as conservative type I error in detecting the improvement in fitting with the likelihood ratio (LR) test. Numerical simulation revealed that the control strategy-making process may benefit from monitoring the transmission characteristics under the Delaporte framework. Our findings highlighted that for the COVID-19 pandemic, population-wide interventions may control disease transmission on a general scale before recommending the high-risk-specific control strategies.\n                  <\/jats:p>","DOI":"10.1371\/journal.pcbi.1010281","type":"journal-article","created":{"date-parts":[[2022,6,27]],"date-time":"2022-06-27T13:37:39Z","timestamp":1656337059000},"page":"e1010281","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":10,"title":["Characterizing superspreading potential of infectious disease: Decomposition of individual transmissibility"],"prefix":"10.1371","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8722-6149","authenticated-orcid":true,"given":"Shi","family":"Zhao","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5610-1298","authenticated-orcid":true,"given":"Marc K. C.","family":"Chong","sequence":"additional","affiliation":[]},{"given":"Sukhyun","family":"Ryu","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9002-0483","authenticated-orcid":true,"given":"Zihao","family":"Guo","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0085-7181","authenticated-orcid":true,"given":"Mu","family":"He","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8726-4508","authenticated-orcid":true,"given":"Boqiang","family":"Chen","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6335-2335","authenticated-orcid":true,"given":"Salihu S.","family":"Musa","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1570-7266","authenticated-orcid":true,"given":"Jingxuan","family":"Wang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0687-1187","authenticated-orcid":true,"given":"Yushan","family":"Wu","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3253-654X","authenticated-orcid":true,"given":"Daihai","family":"He","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1223-4595","authenticated-orcid":true,"given":"Maggie H.","family":"Wang","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2022,6,27]]},"reference":[{"issue":"16","key":"pcbi.1010281.ref001","doi-asserted-by":"crossref","first-page":"6146","DOI":"10.1073\/pnas.0307506101","article-title":"Factors that make an infectious disease outbreak controllable","volume":"101","author":"C Fraser","year":"2004","journal-title":"Proc Natl Acad Sci U S A"},{"issue":"5","key":"pcbi.1010281.ref002","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1016\/S1473-3099(15)70135-0","article-title":"Ebola superspreading","volume":"15","author":"CL Althaus","year":"2015","journal-title":"Lancet Infect Dis"},{"issue":"25","key":"pcbi.1010281.ref003","first-page":"14","article-title":"The role of superspreading in Middle East respiratory syndrome coronavirus (MERS-CoV) transmission","volume":"20","author":"AJ Kucharski","year":"2015","journal-title":"Euro surveillance: bulletin Europeen sur les maladies transmissibles = European communicable disease bulletin"},{"issue":"6526","key":"pcbi.1010281.ref004","article-title":"Transmission heterogeneities, kinetics, and controllability of SARS-CoV-2","volume":"371","author":"K Sun","year":"2021","journal-title":"Science"},{"issue":"2","key":"pcbi.1010281.ref005","doi-asserted-by":"crossref","first-page":"256","DOI":"10.3201\/eid1002.030732","article-title":"Superspreading SARS events, Beijing, 2003","volume":"10","author":"Z Shen","year":"2004","journal-title":"Emerg Infect Dis"},{"issue":"40","key":"pcbi.1010281.ref006","doi-asserted-by":"crossref","first-page":"20920","DOI":"10.2807\/1560-7917.ES2014.19.40.20920","article-title":"Transmission dynamics and control of Ebola virus disease outbreak in Nigeria, July to September 2014","volume":"19","author":"FO Fasina","year":"2014","journal-title":"Eurosurveillance"},{"issue":"9913","key":"pcbi.1010281.ref007","first-page":"189","volume":"383","author":"DN Fisman","year":"2014","journal-title":"Nuanced risk assessment for emerging infectious diseases"},{"issue":"1","key":"pcbi.1010281.ref008","doi-asserted-by":"crossref","first-page":"69","DOI":"10.7326\/M20-5008","article-title":"Transmission of SARS-CoV-2: a review of viral, host, and environmental factors","volume":"174","author":"EA Meyerowitz","year":"2021","journal-title":"Annals of internal medicine"},{"key":"pcbi.1010281.ref009","volume-title":"Mathematical epidemiology of infectious diseases: model building, analysis and interpretation","author":"O Diekmann","year":"2000"},{"issue":"5627","key":"pcbi.1010281.ref010","doi-asserted-by":"crossref","first-page":"1966","DOI":"10.1126\/science.1086616","article-title":"Transmission dynamics and control of severe acute respiratory syndrome","volume":"300","author":"M Lipsitch","year":"2003","journal-title":"Science"},{"issue":"5","key":"pcbi.1010281.ref011","doi-asserted-by":"crossref","first-page":"e1002993","DOI":"10.1371\/journal.pcbi.1002993","article-title":"Inference of R(0) and transmission heterogeneity from the size distribution of stuttering chains","volume":"9","author":"S Blumberg","year":"2013","journal-title":"PLoS Comput Biol"},{"issue":"12","key":"pcbi.1010281.ref012","doi-asserted-by":"crossref","first-page":"3163","DOI":"10.1093\/cid\/ciaa790","article-title":"Reconstruction of Transmission Pairs for Novel Coronavirus Disease 2019 (COVID-19) in Mainland China: Estimation of Superspreading Events, Serial Interval, and Hazard of Infection","volume":"71","author":"XK Xu","year":"2020","journal-title":"Clin Infect Dis"},{"issue":"1","key":"pcbi.1010281.ref013","doi-asserted-by":"crossref","first-page":"25","DOI":"10.3201\/eid1001.030553","article-title":"Severe acute respiratory syndrome, Beijing, 2003","volume":"10","author":"W Liang","year":"2004","journal-title":"Emerging infectious diseases"},{"issue":"25","key":"pcbi.1010281.ref014","first-page":"7","article-title":"Preliminary epidemiological assessment of MERS-CoV outbreak in South Korea, May to June 2015","volume":"20","author":"BJ Cowling","year":"2015","journal-title":"Euro surveillance: bulletin Europeen sur les maladies transmissibles = European communicable disease bulletin"},{"issue":"6202","key":"pcbi.1010281.ref015","doi-asserted-by":"crossref","first-page":"1369","DOI":"10.1126\/science.1259657","article-title":"Genomic surveillance elucidates Ebola virus origin and transmission during the 2014 outbreak","volume":"345","author":"SK Gire","year":"2014","journal-title":"Science"},{"issue":"10227","key":"pcbi.1010281.ref016","doi-asserted-by":"crossref","first-page":"e47","DOI":"10.1016\/S0140-6736(20)30462-1","article-title":"Secondary attack rate and superspreading events for SARS-CoV-2","volume":"395","author":"Y Liu","year":"2020","journal-title":"The Lancet"},{"issue":"11","key":"pcbi.1010281.ref017","doi-asserted-by":"crossref","first-page":"1714","DOI":"10.1038\/s41591-020-1092-0","article-title":"Clustering and superspreading potential of SARS-CoV-2 infections in Hong Kong","volume":"26","author":"DC Adam","year":"2020","journal-title":"Nat Med"},{"issue":"36","key":"pcbi.1010281.ref018","doi-asserted-by":"crossref","first-page":"22430","DOI":"10.1073\/pnas.2011802117","article-title":"Characterizing superspreading events and age-specific infectiousness of SARS-CoV-2 transmission in Georgia, USA","volume":"117","author":"MSY Lau","year":"2020","journal-title":"Proc Natl Acad Sci U S A"},{"issue":"10","key":"pcbi.1010281.ref019","doi-asserted-by":"crossref","first-page":"3705","DOI":"10.3390\/ijerph17103705","article-title":"Evaluating Transmission Heterogeneity and Super-Spreading Event of COVID-19 in a Metropolis of China","volume":"17","author":"Y Zhang","year":"2020","journal-title":"Int J Environ Res Public Health"},{"issue":"5627","key":"pcbi.1010281.ref020","doi-asserted-by":"crossref","first-page":"1961","DOI":"10.1126\/science.1086478","article-title":"Transmission dynamics of the etiological agent of SARS in Hong Kong: impact of public health interventions","volume":"300","author":"S Riley","year":"2003","journal-title":"Science"},{"issue":"7066","key":"pcbi.1010281.ref021","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1038\/438293a","article-title":"Epidemiology: dimensions of superspreading","volume":"438","author":"AP Galvani","year":"2005","journal-title":"Nature"},{"issue":"1","key":"pcbi.1010281.ref022","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1186\/s12916-015-0450-0","article-title":"Transmission characteristics of MERS and SARS in the healthcare setting: a comparative study","volume":"13","author":"G Chowell","year":"2015","journal-title":"BMC Med"},{"issue":"22","key":"pcbi.1010281.ref023","doi-asserted-by":"crossref","first-page":"2081","DOI":"10.1056\/NEJMoa2008457","article-title":"Presymptomatic SARS-CoV-2 infections and transmission in a skilled nursing facility","volume":"382","author":"MM Arons","year":"2020","journal-title":"N Engl J Med"},{"issue":"1","key":"pcbi.1010281.ref024","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/ncomms2922","article-title":"Aerosol transmission is an important mode of influenza A virus spread","volume":"4","author":"BJ Cowling","year":"2013","journal-title":"Nature communications"},{"issue":"5","key":"pcbi.1010281.ref025","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1093\/aje\/kwr122","article-title":"Influenza transmission in households during the 1918 pandemic","volume":"174","author":"C Fraser","year":"2011","journal-title":"American journal of epidemiology"},{"issue":"4","key":"pcbi.1010281.ref026","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1016\/j.chom.2015.09.013","article-title":"MERS, SARS, and Ebola: the role of super-spreaders in infectious disease","volume":"18","author":"G Wong","year":"2015","journal-title":"Cell Host Microbe"},{"issue":"7","key":"pcbi.1010281.ref027","doi-asserted-by":"crossref","first-page":"1628","DOI":"10.3201\/eid2607.200764","article-title":"COVID-19 outbreak associated with air conditioning in restaurant, Guangzhou, China, 2020","volume":"26","author":"J Lu","year":"2020","journal-title":"Emerging infectious diseases"},{"key":"pcbi.1010281.ref028","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/j.ijid.2020.03.031","article-title":"Transmission potential and severity of COVID-19 in South Korea","volume":"93","author":"E Shim","year":"2020","journal-title":"International Journal of Infectious Diseases"},{"issue":"7066","key":"pcbi.1010281.ref029","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":"1","key":"pcbi.1010281.ref030","doi-asserted-by":"crossref","first-page":"1558","DOI":"10.1186\/s12889-020-09624-2","article-title":"Low dispersion in the infectiousness of COVID-19 cases implies difficulty in control","volume":"20","author":"D He","year":"2020","journal-title":"BMC Public Health"},{"issue":"14","key":"pcbi.1010281.ref031","doi-asserted-by":"crossref","DOI":"10.1073\/pnas.2016623118","article-title":"Overdispersion in COVID-19 increases the effectiveness of limiting nonrepetitive contacts for transmission control","volume":"118","author":"K Sneppen","year":"2021","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"11","key":"pcbi.1010281.ref032","doi-asserted-by":"crossref","first-page":"e3000897","DOI":"10.1371\/journal.pbio.3000897","article-title":"Superspreading events in the transmission dynamics of SARS-CoV-2: Opportunities for interventions and control","volume":"18","author":"BM Althouse","year":"2020","journal-title":"PLoS Biol"},{"issue":"7","key":"pcbi.1010281.ref033","doi-asserted-by":"crossref","first-page":"ofab350","DOI":"10.1093\/ofid\/ofab350","article-title":"Temporal Changes in the Risk of Superspreading Events of Coronavirus Disease 2019","volume":"8","author":"J-S Lim","year":"2021","journal-title":"Open Forum Infectious Diseases"},{"issue":"11","key":"pcbi.1010281.ref034","doi-asserted-by":"crossref","first-page":"118301","DOI":"10.1103\/PhysRevLett.126.118301","article-title":"COVID-19 superspreading suggests mitigation by social network modulation","volume":"126","author":"BF Nielsen","year":"2021","journal-title":"Phys Rev Lett"},{"key":"pcbi.1010281.ref035","doi-asserted-by":"crossref","first-page":"239","DOI":"10.12688\/wellcomeopenres.16344.1","article-title":"Implication of backward contact tracing in the presence of overdispersed transmission in COVID-19 outbreaks","volume":"5","author":"A. Endo","year":"2020","journal-title":"Wellcome open research"},{"key":"pcbi.1010281.ref036","doi-asserted-by":"crossref","first-page":"100430","DOI":"10.1016\/j.epidem.2020.100430","article-title":"Chopping the tail: How preventing superspreading can help to maintain COVID-19 control","volume":"34","author":"MP Kain","year":"2021","journal-title":"Epidemics"},{"key":"pcbi.1010281.ref037","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/S0025-5564(02)00108-6","article-title":"Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission","volume":"180","author":"P van den Driessche","year":"2002","journal-title":"Math Biosci"},{"issue":"9893","key":"pcbi.1010281.ref038","doi-asserted-by":"crossref","first-page":"694","DOI":"10.1016\/S0140-6736(13)61492-0","article-title":"Interhuman transmissibility of Middle East respiratory syndrome coronavirus: estimation of pandemic risk","volume":"382","author":"R Breban","year":"2013","journal-title":"The Lancet"},{"issue":"2","key":"pcbi.1010281.ref039","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/S1473-3099(20)30840-9","article-title":"Estimating the COVID-19 R number: a bargain with the devil?","volume":"21","author":"CT Bauch","year":"2021","journal-title":"The Lancet Infectious Diseases"},{"issue":"10","key":"pcbi.1010281.ref040","doi-asserted-by":"crossref","first-page":"e1004452","DOI":"10.1371\/journal.ppat.1004452","article-title":"Detecting differential transmissibilities that affect the size of self-limited outbreaks","volume":"10","author":"S Blumberg","year":"2014","journal-title":"PLoS Pathog"},{"issue":"4","key":"pcbi.1010281.ref041","first-page":"2000058","article-title":"Pattern of early human-to-human transmission of Wuhan 2019 novel coronavirus (2019-nCoV), December 2019 to January 2020","volume":"25","author":"J Riou","year":"2020","journal-title":"Euro surveillance: bulletin Europeen sur les maladies transmissibles = European communicable disease bulletin"},{"issue":"9913","key":"pcbi.1010281.ref042","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/S0140-6736(13)62123-6","article-title":"Nuanced risk assessment for emerging infectious diseases","volume":"383","author":"DN Fisman","year":"2014","journal-title":"The Lancet"},{"issue":"1","key":"pcbi.1010281.ref043","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3201\/eid2501.171901","article-title":"Complexity of the basic reproduction number (R0)","volume":"25","author":"PL Delamater","year":"2019","journal-title":"Emerging infectious diseases"},{"issue":"2","key":"pcbi.1010281.ref044","doi-asserted-by":"crossref","first-page":"e180","DOI":"10.1371\/journal.pone.0000180","article-title":"Maximum likelihood estimation of the negative binomial dispersion parameter for highly overdispersed data, with applications to infectious diseases","volume":"2","author":"JO Lloyd-Smith","year":"2007","journal-title":"PLoS One"},{"issue":"2","key":"pcbi.1010281.ref045","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.jtbi.2008.02.038","article-title":"The effect of superspreading on epidemic outbreak size distributions","volume":"253","author":"T Garske","year":"2008","journal-title":"J Theor Biol"},{"issue":"1","key":"pcbi.1010281.ref046","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s12874-021-01225-w","article-title":"Inferencing superspreading potential using zero-truncated negative binomial model: exemplification with COVID-19","volume":"21","author":"S Zhao","year":"2021","journal-title":"BMC Med Res Methodol"},{"issue":"9","key":"pcbi.1010281.ref047","doi-asserted-by":"crossref","first-page":"e674","DOI":"10.1016\/S2468-2667(21)00167-5","article-title":"Effects of adjusting public health, travel, and social measures during the roll-out of COVID-19 vaccination: a modelling study","volume":"6","author":"K Leung","year":"2021","journal-title":"The Lancet Public Health"},{"key":"pcbi.1010281.ref048","first-page":"87","article-title":"Quelques probl\u00e8mes de statistiques math\u00e9matiques poses par l\u2019Assurance Automobile et le Bonus pour non sinistre","volume":"227","author":"PJ Delaporte","year":"1960","journal-title":"Bulletin Trimestriel de l\u2019Institut des Actuaires Fran\u00e7ais"},{"key":"pcbi.1010281.ref049","volume-title":"Risk analysis: a quantitative guide","author":"D. Vose","year":"2008"},{"issue":"2","key":"pcbi.1010281.ref050","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1093\/biostatistics\/4.2.279","article-title":"Branching process models for surveillance of infectious diseases controlled by mass vaccination","volume":"4","author":"CP Farrington","year":"2003","journal-title":"Biostatistics"},{"issue":"8","key":"pcbi.1010281.ref051","doi-asserted-by":"crossref","first-page":"e758","DOI":"10.1371\/journal.pone.0000758","article-title":"Estimating Individual and Household Reproduction Numbers in an Emerging Epidemic","volume":"2","author":"C. Fraser","year":"2007","journal-title":"PLoS One"},{"key":"pcbi.1010281.ref052","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/978-3-540-78911-6","volume-title":"Lecture notes in mathematical epidemiology","author":"F Brauer","year":"2008"},{"issue":"47","key":"pcbi.1010281.ref053","doi-asserted-by":"crossref","first-page":"873","DOI":"10.1098\/rsif.2009.0386","article-title":"The construction of next-generation matrices for compartmental epidemic models","volume":"7","author":"O Diekmann","year":"2010","journal-title":"Journal of the Royal Society Interface"},{"issue":"8","key":"pcbi.1010281.ref054","doi-asserted-by":"crossref","first-page":"911","DOI":"10.1016\/S1473-3099(20)30287-5","article-title":"Epidemiology and transmission of COVID-19 in 391 cases and 1286 of their close contacts in Shenzhen, China: a retrospective cohort study","volume":"20","author":"Q Bi","year":"2020","journal-title":"The Lancet Infectious Diseases"},{"key":"pcbi.1010281.ref055","doi-asserted-by":"crossref","first-page":"5039","DOI":"10.1016\/j.csbj.2021.08.045","article-title":"Superspreading and heterogeneity in transmission of SARS, MERS, and COVID-19: a systematic review","volume":"19","author":"J Wang","year":"2021","journal-title":"Computational and Structural Biotechnology Journal"},{"issue":"1","key":"pcbi.1010281.ref056","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1073\/pnas.94.1.338","article-title":"Heterogeneities in the transmission of infectious agents: implications for the design of control programs","volume":"94","author":"ME Woolhouse","year":"1997","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"67","key":"pcbi.1010281.ref057","doi-asserted-by":"crossref","first-page":"67","DOI":"10.12688\/wellcomeopenres.15842.3","article-title":"Estimating the overdispersion in COVID-19 transmission using outbreak sizes outside China","volume":"5","author":"A Endo","year":"2020","journal-title":"Wellcome Open Research"},{"issue":"70","key":"pcbi.1010281.ref058","doi-asserted-by":"crossref","first-page":"209","DOI":"10.2307\/2276207","article-title":"Methods of measuring the concentration of wealth","volume":"9","author":"MO Lorenz","year":"1905","journal-title":"Publications of the American statistical association"},{"issue":"7238","key":"pcbi.1010281.ref059","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1038\/nature07840","article-title":"Initial community evenness favours functionality under selective stress","volume":"458","author":"L Wittebolle","year":"2009","journal-title":"Nature"},{"key":"pcbi.1010281.ref060","unstructured":"Centre for Health Protection. Summary of data and outbreak situation of the Severe Respiratory Disease associated with a Novel Infectious Agent, Centre for Health Protection, the government of Hong Kong. 2020 [cited 2021]. https:\/\/www.chp.gov.hk\/en\/features\/102465.html."},{"key":"pcbi.1010281.ref061","unstructured":"Centre for Health Protection. The collection of Press Releases by the Centre for Health Protection (CHP) of Hong Kong. 2020 [cited 2020]. https:\/\/www.chp.gov.hk\/en\/media\/116\/index.html."},{"key":"pcbi.1010281.ref062","unstructured":"The Government of Tianjin. Tianjin Municipal People\u2019s Government, China. http:\/\/www.tj.gov.cn\/xw\/ztzl\/tjsyqfk\/yqtb\/."},{"key":"pcbi.1010281.ref063","doi-asserted-by":"crossref","DOI":"10.1201\/b16018","volume-title":"Bayesian data analysis","author":"A Gelman","year":"2013"},{"key":"pcbi.1010281.ref064","volume-title":"Ecological models and data in R","author":"BM Bolker","year":"2008"},{"issue":"7","key":"pcbi.1010281.ref065","doi-asserted-by":"crossref","first-page":"1968","DOI":"10.1177\/0962280217746442","article-title":"Modeling the spread of Middle East respiratory syndrome coronavirus in Saudi Arabia","volume":"27","author":"Q Lin","year":"2018","journal-title":"Stat Methods Med Res"},{"issue":"1","key":"pcbi.1010281.ref066","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1186\/s12916-020-01615-9","article-title":"Real-time monitoring the transmission potential of COVID-19 in Singapore, March 2020","volume":"18","author":"A Tariq","year":"2020","journal-title":"BMC Med"},{"key":"pcbi.1010281.ref067","doi-asserted-by":"crossref","first-page":"taac025","DOI":"10.1093\/jtm\/taac025","article-title":"Superspreading potential of SARS-CoV-2 Delta variants under intensive disease control measures in China","author":"S Zhao","year":"2022","journal-title":"J Travel Med"},{"issue":"1","key":"pcbi.1010281.ref068","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/S1473-3099(13)70304-9","article-title":"Middle East respiratory syndrome coronavirus: quantification of the extent of the epidemic, surveillance biases, and transmissibility","volume":"14","author":"S Cauchemez","year":"2014","journal-title":"The Lancet infectious diseases"},{"key":"pcbi.1010281.ref069","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":"J Theor Biol"},{"key":"pcbi.1010281.ref070","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/978-3-540-78911-6_10","volume-title":"Mathematical epidemiology","author":"P. Yan","year":"2008"},{"issue":"3","key":"pcbi.1010281.ref071","doi-asserted-by":"crossref","first-page":"682","DOI":"10.2307\/3212112","article-title":"The total progeny in a branching process and a related random walk","volume":"6","author":"M. Dwass","year":"1969","journal-title":"J Appl Probab"},{"issue":"5958","key":"pcbi.1010281.ref072","doi-asserted-by":"crossref","first-page":"1362","DOI":"10.1126\/science.1177345","article-title":"Epidemic dynamics at the human-animal interface","volume":"326","author":"JO Lloyd-Smith","year":"2009","journal-title":"Science"},{"issue":"5673","key":"pcbi.1010281.ref073","doi-asserted-by":"crossref","first-page":"968","DOI":"10.1126\/science.1096898","article-title":"Public health risk from the avian H5N1 influenza epidemic","volume":"304","author":"NM Ferguson","year":"2004","journal-title":"Science"},{"issue":"3","key":"pcbi.1010281.ref074","doi-asserted-by":"crossref","first-page":"e148","DOI":"10.1016\/S2589-7500(20)30293-4","article-title":"Mask-wearing and control of SARS-CoV-2 transmission in the USA: a cross-sectional study","volume":"3","author":"B Rader","year":"2021","journal-title":"The Lancet Digital Health"},{"issue":"7","key":"pcbi.1010281.ref075","doi-asserted-by":"crossref","first-page":"437","DOI":"10.7326\/0003-4819-151-7-200910060-00142","article-title":"Facemasks and hand hygiene to prevent influenza transmission in households: a cluster randomized trial","volume":"151","author":"BJ Cowling","year":"2009","journal-title":"Annals of internal medicine"},{"issue":"9","key":"pcbi.1010281.ref076","doi-asserted-by":"crossref","first-page":"2267","DOI":"10.3201\/eid2609.201932","article-title":"Effects of proactive social distancing on COVID-19 outbreaks in 58 cities, China","volume":"26","author":"Z Du","year":"2020","journal-title":"Emerging infectious diseases"},{"issue":"18","key":"pcbi.1010281.ref077","doi-asserted-by":"crossref","first-page":"e45","DOI":"10.1056\/NEJMc2009790","article-title":"From a Sprint to a Marathon in Hong Kong","volume":"382","author":"GM Leung","year":"2020","journal-title":"N Engl J Med"},{"issue":"6490","key":"pcbi.1010281.ref078","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1126\/science.abb4218","article-title":"The effect of human mobility and control measures on the COVID-19 epidemic in China","volume":"368","author":"MU Kraemer","year":"2020","journal-title":"Science"},{"issue":"6489","key":"pcbi.1010281.ref079","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1126\/science.aba9757","article-title":"The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak","volume":"368","author":"M Chinazzi","year":"2020","journal-title":"Science"},{"issue":"8","key":"pcbi.1010281.ref080","first-page":"CD013699","article-title":"Digital contact tracing technologies in epidemics: a rapid review","volume":"8","author":"A Anglemyer","year":"2020","journal-title":"Cochrane Database Syst Rev"},{"issue":"11","key":"pcbi.1010281.ref081","doi-asserted-by":"crossref","first-page":"879","DOI":"10.7326\/M20-2671","article-title":"Contact Settings and Risk for Transmission in 3410 Close Contacts of Patients With COVID-19 in Guangzhou, China: A Prospective Cohort Study","volume":"173","author":"L Luo","year":"2020","journal-title":"Annals of internal medicine"},{"issue":"13","key":"pcbi.1010281.ref082","doi-asserted-by":"crossref","first-page":"1199","DOI":"10.1056\/NEJMoa2001316","article-title":"Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus-Infected Pneumonia","volume":"382","author":"Q Li","year":"2020","journal-title":"N Engl J Med"},{"issue":"1829","key":"pcbi.1010281.ref083","doi-asserted-by":"crossref","first-page":"20200265","DOI":"10.1098\/rstb.2020.0265","article-title":"Novel coronavirus 2019-nCoV (COVID-19): early estimation of epidemiological parameters and epidemic size estimates","volume":"376","author":"JM Read","year":"2021","journal-title":"Philosophical Transactions of the Royal Society B"},{"issue":"10225","key":"pcbi.1010281.ref084","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1016\/S0140-6736(20)30260-9","article-title":"Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study","volume":"395","author":"JT Wu","year":"2020","journal-title":"Lancet"},{"issue":"2","key":"pcbi.1010281.ref085","doi-asserted-by":"crossref","first-page":"388","DOI":"10.3390\/jcm9020388","article-title":"Estimating the Unreported Number of Novel Coronavirus (2019-nCoV) Cases in China in the First Half of January 2020: A Data-Driven Modelling Analysis of the Early Outbreak","volume":"9","author":"S Zhao","year":"2020","journal-title":"Journal of Clinical Medicine"},{"issue":"5634","key":"pcbi.1010281.ref086","doi-asserted-by":"crossref","first-page":"804","DOI":"10.1126\/science.1086726","article-title":"Measles outbreaks in a population with declining vaccine uptake","volume":"301","author":"VA Jansen","year":"2003","journal-title":"Science"},{"issue":"23","key":"pcbi.1010281.ref087","first-page":"20824","article-title":"Assessment of the Middle East respiratory syndrome coronavirus (MERS-CoV) epidemic in the Middle East and risk of international spread using a novel maximum likelihood analysis approach","volume":"19","author":"C Poletto","year":"2014","journal-title":"Euro surveillance: bulletin Europeen sur les maladies transmissibles = European communicable disease bulletin"},{"issue":"181","key":"pcbi.1010281.ref088","doi-asserted-by":"crossref","first-page":"20210444","DOI":"10.1098\/rsif.2021.0444","article-title":"Sub-spreading events limit the reliable elimination of heterogeneous epidemics","volume":"18","author":"KV Parag","year":"2021","journal-title":"Journal of The Royal Society Interface"},{"key":"pcbi.1010281.ref089","unstructured":"World Health Organization, Coronavirus disease 2019 (COVID-19) situation reports. 2021 [cited 2021]. https:\/\/www.who.int\/emergencies\/diseases\/novel-coronavirus-2019\/situation-reports."},{"issue":"6491","key":"pcbi.1010281.ref090","doi-asserted-by":"crossref","first-page":"eabb6936","DOI":"10.1126\/science.abb6936","article-title":"Quantifying SARS-CoV-2 transmission suggests epidemic control with digital contact tracing","volume":"368","author":"L Ferretti","year":"2020","journal-title":"Science"},{"issue":"1","key":"pcbi.1010281.ref091","doi-asserted-by":"crossref","first-page":"e26836","DOI":"10.2196\/26836","article-title":"Digital contact tracing based on a graph database algorithm for emergency management during the COVID-19 epidemic: Case study","volume":"9","author":"Z Mao","year":"2021","journal-title":"JMIR mHealth and uHealth"},{"key":"pcbi.1010281.ref092","first-page":"1","article-title":"Temporal dynamics in viral shedding and transmissibility of COVID-19","author":"X He","year":"2020","journal-title":"Nat Med"},{"issue":"8","key":"pcbi.1010281.ref093","doi-asserted-by":"crossref","DOI":"10.1073\/pnas.2017962118","article-title":"Modeling SARS-CoV-2 viral kinetics and association with mortality in hospitalized patients from the French COVID cohort","volume":"118","author":"N N\u00e9ant","year":"2021","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"6490","key":"pcbi.1010281.ref094","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1126\/science.abb3221","article-title":"Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV-2)","volume":"368","author":"R Li","year":"2020","journal-title":"Science"},{"issue":"8","key":"pcbi.1010281.ref095","doi-asserted-by":"crossref","first-page":"567","DOI":"10.7326\/M20-0358","article-title":"Reporting, Epidemic Growth, and Reproduction Numbers for the 2019 Novel Coronavirus (2019-nCoV) Epidemic","volume":"172","author":"AR Tuite","year":"2020","journal-title":"Annals of Internal Medicine"},{"issue":"2","key":"pcbi.1010281.ref096","doi-asserted-by":"crossref","DOI":"10.3390\/jcm9020419","article-title":"The Rate of Underascertainment of Novel Coronavirus (2019-nCoV) Infection: Estimation Using Japanese Passengers Data on Evacuation Flights","volume":"9","author":"H Nishiura","year":"2020","journal-title":"Journal of Clinical Medicine"},{"issue":"36","key":"pcbi.1010281.ref097","doi-asserted-by":"crossref","first-page":"22597","DOI":"10.1073\/pnas.2005476117","article-title":"Estimating unobserved SARS-CoV-2 infections in the United States","volume":"117","author":"TA Perkins","year":"2020","journal-title":"Proceedings of the National Academy of Sciences"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1010281","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2022,7,8]],"date-time":"2022-07-08T00:00:00Z","timestamp":1657238400000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1010281","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,8]],"date-time":"2022-07-08T14:22:09Z","timestamp":1657290129000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1010281"}},"subtitle":[],"editor":[{"given":"Gerardo","family":"Chowell","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2022,6,27]]},"references-count":97,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2022,6,27]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1010281","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,27]]}}}