{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T16:51:21Z","timestamp":1769878281869,"version":"3.49.0"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1009351","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2021,9,10]],"date-time":"2021-09-10T00:00:00Z","timestamp":1631232000000}}],"reference-count":67,"publisher":"Public Library of Science (PLoS)","issue":"8","license":[{"start":{"date-parts":[[2021,8,30]],"date-time":"2021-08-30T00:00:00Z","timestamp":1630281600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Borealis AI Fellowship"},{"name":"NSERC-Discovery Grant","award":["RGPIN-2019-04067"],"award-info":[{"award-number":["RGPIN-2019-04067"]}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Decision-making about pandemic mitigation often relies upon simulation modelling. Models of disease transmission through networks of contacts\u2013between individuals or between population centres\u2013are increasingly used for these purposes. Real-world contact networks are rich in structural features that influence infection transmission, such as tightly-knit local communities that are weakly connected to one another. In this paper, we propose a new flow-based edge-betweenness centrality method for detecting bottleneck edges that connect nodes in contact networks. In particular, we utilize convex optimization formulations based on the idea of diffusion with p-norm network flow. Using simulation models of COVID-19 transmission through real network data at both individual and county levels, we demonstrate that targeting bottleneck edges identified by the proposed method reduces the number of infected cases by up to 10% more than state-of-the-art edge-betweenness methods. Furthermore, the proposed method is orders of magnitude faster than existing methods.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1009351","type":"journal-article","created":{"date-parts":[[2021,8,30]],"date-time":"2021-08-30T17:38:11Z","timestamp":1630345091000},"page":"e1009351","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":5,"title":["Targeted pandemic containment through identifying local contact network bottlenecks"],"prefix":"10.1371","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5335-3729","authenticated-orcid":true,"given":"Shenghao","family":"Yang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7085-6013","authenticated-orcid":true,"given":"Priyabrata","family":"Senapati","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0891-0255","authenticated-orcid":true,"given":"Di","family":"Wang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6214-6601","authenticated-orcid":true,"given":"Chris T.","family":"Bauch","sequence":"additional","affiliation":[]},{"given":"Kimon","family":"Fountoulakis","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2021,8,30]]},"reference":[{"issue":"39","key":"pcbi.1009351.ref001","doi-asserted-by":"crossref","first-page":"24575","DOI":"10.1073\/pnas.2014385117","article-title":"Local lockdowns outperform global lockdown on the far side of the COVID-19 epidemic curve","volume":"117","author":"VA Karatayev","year":"2020","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"19","key":"pcbi.1009351.ref002","doi-asserted-by":"crossref","first-page":"E497","DOI":"10.1503\/cmaj.200476","article-title":"Mathematical modelling of COVID-19 transmission and mitigation strategies in the population of Ontario, Canada","volume":"192","author":"AR Tuite","year":"2020","journal-title":"CMAJ"},{"issue":"1","key":"pcbi.1009351.ref003","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1371\/journal.pcbi.1008619","article-title":"Predictions of COVID-19 dynamics in the UK: Short-term forecasting and analysis of potential exit strategies","volume":"17","author":"MJ Keeling","year":"2021","journal-title":"PLOS Computational Biology"},{"key":"pcbi.1009351.ref004","first-page":"1","article-title":"Modelling COVID-19","author":"A Vespignani","year":"2020","journal-title":"Nature Reviews Physics"},{"key":"pcbi.1009351.ref005","doi-asserted-by":"crossref","first-page":"588","DOI":"10.1038\/s41562-020-0898-6","article-title":"Social network-based distancing strategies to flatten the COVID-19 curve in a post-lockdown world","author":"P Block","year":"2020","journal-title":"Nature Human Behaviour"},{"key":"pcbi.1009351.ref006","article-title":"Modeling COVID-19 on a network: super-spreaders, testing and containment","author":"O Reich","year":"2020","journal-title":"medRxiv"},{"issue":"6489","key":"pcbi.1009351.ref007","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":"6490","key":"pcbi.1009351.ref008","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"},{"key":"pcbi.1009351.ref009","article-title":"A Global Dataset of Human Mobility","author":"HF Chan","year":"2020","journal-title":"Center for Research in Economics, Management and the Arts (CREMA)"},{"issue":"4","key":"pcbi.1009351.ref010","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1137\/S0036144500371907","article-title":"The Mathematics of Infectious Diseases","volume":"42","author":"HW Hethcote","year":"2000","journal-title":"SIAM Review"},{"key":"pcbi.1009351.ref011","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.epidem.2014.07.003","article-title":"Eight challenges for network epidemic models","volume":"10","author":"L Pellis","year":"2015","journal-title":"Epidemics"},{"issue":"21","key":"pcbi.1009351.ref012","doi-asserted-by":"crossref","first-page":"218701","DOI":"10.1103\/PhysRevLett.105.218701","article-title":"Thresholds for epidemic spreading in networks","volume":"105","author":"C Castellano","year":"2010","journal-title":"Physical review letters"},{"issue":"2","key":"pcbi.1009351.ref013","doi-asserted-by":"crossref","first-page":"e1000280","DOI":"10.1371\/journal.pcbi.1000280","article-title":"Social contact networks and disease eradicability under voluntary vaccination","volume":"5","author":"A Perisic","year":"2009","journal-title":"PLOS Computational Biology"},{"issue":"4","key":"pcbi.1009351.ref014","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1098\/rsif.2005.0051","article-title":"Networks and epidemic models","volume":"2","author":"MJ Keeling","year":"2005","journal-title":"Journal of the Royal Society Interface"},{"issue":"1354","key":"pcbi.1009351.ref015","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1098\/rspb.1995.0009","article-title":"Invasion, stability and evolution to criticality in spatially extended, artificial host\u2014pathogen ecologies","volume":"259","author":"D Rand","year":"1995","journal-title":"Proceedings of the Royal Society of London Series B: Biological Sciences"},{"issue":"2","key":"pcbi.1009351.ref016","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/j.mbs.2005.06.005","article-title":"The spread of infectious diseases in spatially structured populations: an invasory pair approximation","volume":"198","author":"CT Bauch","year":"2005","journal-title":"Mathematical Biosciences"},{"issue":"6","key":"pcbi.1009351.ref017","doi-asserted-by":"crossref","first-page":"908","DOI":"10.1209\/epl\/i2004-10286-2","article-title":"Efficient local strategies for vaccination and network attack","volume":"68","author":"P Holme","year":"2004","journal-title":"EPL (Europhysics Letters)"},{"issue":"2","key":"pcbi.1009351.ref018","doi-asserted-by":"crossref","first-page":"780","DOI":"10.1016\/j.physa.2007.08.054","article-title":"Effective vaccination strategies for realistic social networks","volume":"386","author":"JC Miller","year":"2007","journal-title":"Physica A: Statistical Mechanics and its Applications"},{"key":"pcbi.1009351.ref019","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.jtbi.2013.01.006","article-title":"The importance of contact network topology for the success of vaccination strategies","volume":"325","author":"J Ma","year":"2013","journal-title":"Journal of theoretical biology"},{"issue":"3","key":"pcbi.1009351.ref020","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1002945","article-title":"Policy resistance undermines superspreader vaccination strategies for influenza","volume":"9","author":"CR Wells","year":"2013","journal-title":"PLOS Computational Biology"},{"issue":"4","key":"pcbi.1009351.ref021","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1371\/journal.pcbi.1000736","article-title":"Dynamics and Control of Diseases in Networks with Community Structure","volume":"6","author":"M Salath\u00e9","year":"2010","journal-title":"PLOS Computational Biology"},{"issue":"1","key":"pcbi.1009351.ref022","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.socnet.2004.11.009","article-title":"A measure of betweenness centrality based on random walks","volume":"27","author":"MEJ Newman","year":"2005","journal-title":"Social Networks"},{"key":"pcbi.1009351.ref023","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1007\/978-3-540-31856-9_44","volume-title":"STACS 2005","author":"U Brandes","year":"2005"},{"issue":"1","key":"pcbi.1009351.ref024","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1080\/15427951.2009.10129177","article-title":"Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters","volume":"6","author":"J Leskovec","year":"2009","journal-title":"Internet Mathematics"},{"key":"pcbi.1009351.ref025","doi-asserted-by":"crossref","first-page":"012821","DOI":"10.1103\/PhysRevE.91.012821","article-title":"Think Locally, Act Locally: Detection of Small, Medium-Sized, and Large Communities in Large Networks","volume":"91","author":"LGS Jeub","year":"2015","journal-title":"Physical Review E"},{"key":"pcbi.1009351.ref026","unstructured":"Fountoulakis K, Wang D, Yang S. p-Norm Flow Diffusion for Local Graph Clustering. In: III HD, Singh A, editors. Proceedings of the 37th International Conference on Machine Learning. vol. 119 of Proceedings of Machine Learning Research. PMLR; 2020. p. 3222\u20133232. Available from: http:\/\/proceedings.mlr.press\/v119\/fountoulakis20a.html."},{"key":"pcbi.1009351.ref027","doi-asserted-by":"crossref","first-page":"176","DOI":"10.2307\/270732","article-title":"Technique for analyzing overlapping memberships","volume":"4","author":"P Bonacich","year":"1972","journal-title":"Sociological methodology"},{"issue":"5","key":"pcbi.1009351.ref028","doi-asserted-by":"crossref","first-page":"1170","DOI":"10.1086\/228631","article-title":"Power and centrality: A family of measures","volume":"92","author":"P Bonacich","year":"1987","journal-title":"American journal of sociology"},{"key":"pcbi.1009351.ref029","doi-asserted-by":"crossref","DOI":"10.1038\/s41598-017-06619-9","article-title":"Network-Centric Interventions to Contain the Syphilis Epidemic in San Francisco","volume":"7","author":"D Juher","year":"2017","journal-title":"Scientific Reports"},{"key":"pcbi.1009351.ref030","first-page":"35","volume-title":"A Betweenness Centrality Guided Clustering Algorithm and Its Applications to Cancer Diagnosis","author":"J Ramasamy","year":"2017"},{"key":"pcbi.1009351.ref031","first-page":"1","volume-title":"2010 IEEE International Symposium on Parallel Distributed Processing (IPDPS)","author":"S Jin","year":"2010"},{"key":"pcbi.1009351.ref032","unstructured":"Carpenter T, Karakostas G, Shallcross D. Practical Issues and Algorithms for Analyzing Terrorist Networks 1. In: Proceedings of the Western Simulation MultiConference; 2002."},{"issue":"3","key":"pcbi.1009351.ref033","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1257\/jep.32.3.259","article-title":"Social Connectedness: Measurement, Determinants, and Effects","volume":"32","author":"M Bailey","year":"2018","journal-title":"Journal of Economic Perspectives"},{"key":"pcbi.1009351.ref034","article-title":"How Connected Is Your Community to Everywhere Else in America?","author":"E Badger","year":"2018","journal-title":"The New York Times"},{"issue":"7","key":"pcbi.1009351.ref035","article-title":"Epidemic Wave Dynamics Attributable to Urban Community Structure: A Theoretical Characterization of Disease Transmission in a Large Network","volume":"17","author":"AG Hoen","year":"2015","journal-title":"Journal of Medical Internet Research"},{"issue":"7","key":"pcbi.1009351.ref036","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1004928","article-title":"Disease surveillance on complex social networks","volume":"12","author":"JL Herrera","year":"2016","journal-title":"PLOS Computational Biology"},{"issue":"6988","key":"pcbi.1009351.ref037","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1038\/nature02541","article-title":"Modelling disease outbreaks in realistic urban social networks","volume":"429","author":"S Eubank","year":"2004","journal-title":"Nature"},{"key":"pcbi.1009351.ref038","article-title":"Synthetic data products for societal infrastructures and proto-populations: Data set 1.0","author":"K Bisset","year":"2006","journal-title":"TR-06-006, Network Dynamics and Simulation"},{"key":"pcbi.1009351.ref039","author":"K Fountoulakis","year":"2019","journal-title":"LocalGraphClustering API"},{"key":"pcbi.1009351.ref040","author":"K Fountoulakis","year":"2018","journal-title":"A Short Introduction to Local Graph Clustering Methods and Software"},{"key":"pcbi.1009351.ref041","unstructured":"Inc PT. Collaborative data science; 2015. Available from: https:\/\/plotly.com."},{"key":"pcbi.1009351.ref042","doi-asserted-by":"crossref","first-page":"056109","DOI":"10.1103\/PhysRevE.65.056109","article-title":"Attack vulnerability of complex networks","volume":"65","author":"P Holme","year":"2002","journal-title":"Phys Rev E"},{"key":"pcbi.1009351.ref043","doi-asserted-by":"crossref","first-page":"061911","DOI":"10.1103\/PhysRevE.84.061911","article-title":"Suppressing epidemics with a limited amount of immunization units","volume":"84","author":"CM Schneider","year":"2011","journal-title":"Phys Rev E"},{"issue":"2","key":"pcbi.1009351.ref044","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1109\/JPROC.2016.2637349","article-title":"An Optimization Approach to Locally-Biased Graph Algorithms","volume":"105","author":"K Fountoulakis","year":"2017","journal-title":"Proceedings of the IEEE"},{"issue":"1","key":"pcbi.1009351.ref045","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/080744888","article-title":"A Local Clustering Algorithm for Massive Graphs and Its Application to Nearly Linear Time Graph Partitioning","volume":"42","author":"DA Spielman","year":"2013","journal-title":"SIAM Journal on Scientific Computing"},{"key":"pcbi.1009351.ref046","first-page":"475","article-title":"Local Graph Partitioning using PageRank Vectors","author":"R Andersen","year":"2006","journal-title":"Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science"},{"key":"pcbi.1009351.ref047","unstructured":"Zhu ZA, Lattanzi S, Mirrokni VS. A Local Algorithm for Finding Well-Connected Clusters. In: Proceedings of the 30th International Conference on Machine Learning; 2013. p. 396\u2013404."},{"key":"pcbi.1009351.ref048","first-page":"235","author":"R Andersen","year":"2009","journal-title":"Finding sparse cuts locally using evolving sets"},{"issue":"1\u20132","key":"pcbi.1009351.ref049","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1007\/s10107-017-1214-8","article-title":"Variational Perspective on Local Graph Clustering","volume":"174","author":"K Fountoulakis","year":"2019","journal-title":"Math Program"},{"key":"pcbi.1009351.ref050","first-page":"651","article-title":"An algorithm for improving graph partitions","author":"R Andersen","year":"2008","journal-title":"Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms"},{"key":"pcbi.1009351.ref051","doi-asserted-by":"crossref","unstructured":"Orecchia L, Zhu ZA. Flow-based algorithms for local graph clustering. In: Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms; 2014. p. 1267\u20131286.","DOI":"10.1137\/1.9781611973402.94"},{"key":"pcbi.1009351.ref052","author":"K Fountoulakis","year":"2020","journal-title":"Flow-based Algorithms for Improving Clusters: A Unifying Framework, Software, and Performance"},{"key":"pcbi.1009351.ref053","unstructured":"Wang D, Fountoulakis K, Henzinger M, Mahoney MW, Rao S. Capacity Releasing Diffusion for Speed and Locality. In: Proceedings of the 34th International Conference on Machine Learning. vol. 70; 2017. p. 3607\u20132017."},{"issue":"2","key":"pcbi.1009351.ref054","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1080\/0022250X.2001.9990249","article-title":"A faster algorithm for betweenness centrality","volume":"25","author":"U Brandes","year":"2001","journal-title":"The Journal of Mathematical Sociology"},{"key":"pcbi.1009351.ref055","doi-asserted-by":"crossref","unstructured":"Hagberg AA, Schult DA, Swart PJ. Exploring Network Structure, Dynamics, and Function using NetworkX. In: Varoquaux G, Vaught T, Millman J, editors. Proceedings of the 7th Python in Science Conference. Pasadena, CA USA; 2008. p. 11\u201315.","DOI":"10.25080\/TCWV9851"},{"issue":"1-2","key":"pcbi.1009351.ref056","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.ecolmodel.2006.04.023","article-title":"A standard protocol for describing individual-based and agent-based models","volume":"198","author":"V Grimm","year":"2006","journal-title":"Ecological modelling"},{"issue":"23","key":"pcbi.1009351.ref057","doi-asserted-by":"crossref","first-page":"2760","DOI":"10.1016\/j.ecolmodel.2010.08.019","article-title":"The ODD protocol: a review and first update","volume":"221","author":"V Grimm","year":"2010","journal-title":"Ecological modelling"},{"key":"pcbi.1009351.ref058","doi-asserted-by":"crossref","first-page":"577","DOI":"10.7326\/M20-0504","article-title":"The Incubation Period of Coronavirus Disease 2019 (COVID-19) From Publicly Reported Confirmed Cases: Estimation and Application","volume":"172","author":"SA Lauer","year":"2020","journal-title":"Annals of internal medicine"},{"key":"pcbi.1009351.ref059","doi-asserted-by":"crossref","first-page":"e197","DOI":"10.1017\/S0950268820001995","article-title":"Does incubation period of COVID-19 vary with age? A study of epidemiologically linked cases in Singapore","volume":"148","author":"WYT Tan","year":"2020","journal-title":"Epidemiology and Infection"},{"key":"pcbi.1009351.ref060","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1186\/s13643-021-01648-y","article-title":"The incubation period during the pandemic of COVID-19: a systematic review and meta-analysis","volume":"10","author":"W Dhouib","year":"2021","journal-title":"Systematic Reviews"},{"key":"pcbi.1009351.ref061","article-title":"Serial interval of novel coronavirus (COVID-19) infections","author":"H Nishiura","year":"2020","journal-title":"International Journal of Infectious Diseases"},{"issue":"2","key":"pcbi.1009351.ref062","doi-asserted-by":"crossref","first-page":"538","DOI":"10.3390\/jcm9020538","article-title":"Incubation period and other epidemiological characteristics of 2019 novel coronavirus infections with right truncation: a statistical analysis of publicly available case data","volume":"9","author":"ML N","year":"2020","journal-title":"Journal of clinical medicine"},{"issue":"11","key":"pcbi.1009351.ref063","doi-asserted-by":"crossref","first-page":"1039","DOI":"10.1093\/aje\/kwg251","article-title":"The interval between successive cases of an infectious disease","volume":"158","author":"PE Fine","year":"2003","journal-title":"American journal of epidemiology"},{"key":"pcbi.1009351.ref064","article-title":"The reproductive number of COVID-19 is higher compared to SARS coronavirus","author":"Y Liu","year":"2020","journal-title":"Journal of travel medicine"},{"issue":"7","key":"pcbi.1009351.ref065","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1371\/journal.pcbi.1008031","article-title":"Estimation of country-level basic reproductive ratios for novel Coronavirus (SARS-CoV-2\/COVID-19) using synthetic contact matrices","volume":"16","author":"J Hilton","year":"2020","journal-title":"PLOS Computational Biology"},{"issue":"1","key":"pcbi.1009351.ref066","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1090\/S0273-0979-06-01148-7","article-title":"Contact network epidemiology: Bond percolation applied to infectious disease prediction and control","volume":"44","author":"LA Meyers","year":"2007","journal-title":"Bulletin of the American Mathematical Society"},{"issue":"12","key":"pcbi.1009351.ref067","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.14778\/2994509.2994522","article-title":"Parallel Local Graph Clustering","volume":"9","author":"J Shun","year":"2016","journal-title":"Proceedings of the VLDB Endowment"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1009351","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2021,9,10]],"date-time":"2021-09-10T00:00:00Z","timestamp":1631232000000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1009351","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,7]],"date-time":"2024-09-07T12:10:30Z","timestamp":1725711030000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1009351"}},"subtitle":[],"editor":[{"given":"Benjamin Muir","family":"Althouse","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2021,8,30]]},"references-count":67,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2021,8,30]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1009351","relation":{"new_version":[{"id-type":"doi","id":"10.1371\/journal.pcbi.1009351","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,30]]}}}