{"id":"https://openalex.org/W3028059896","doi":"https://doi.org/10.1137/20m1383811","title":"The Role of Directionality, Heterogeneity, and Correlations in Epidemic Risk and Spread","display_name":"The Role of Directionality, Heterogeneity, and Correlations in Epidemic Risk and Spread","publication_year":2023,"publication_date":"2023-05-01","ids":{"openalex":"https://openalex.org/W3028059896","doi":"https://doi.org/10.1137/20m1383811","mag":"3028059896"},"language":"en","primary_location":{"id":"doi:10.1137/20m1383811","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1383811","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027136376","display_name":"Antoine Allard","orcid":"https://orcid.org/0000-0002-8208-9920"},"institutions":[{"id":"https://openalex.org/I111236770","display_name":"University of Vermont","ror":"https://ror.org/0155zta11","country_code":"US","type":"education","lineage":["https://openalex.org/I111236770"]},{"id":"https://openalex.org/I43406934","display_name":"Universit\u00e9 Laval","ror":"https://ror.org/04sjchr03","country_code":"CA","type":"education","lineage":["https://openalex.org/I43406934"]}],"countries":["CA","US"],"is_corresponding":false,"raw_author_name":"Antoine Allard","raw_affiliation_strings":["Centre interdisciplinaire en mod\u00e9lisation math\u00e9matique, Universit\u00e9 Laval, Qu\u00e9bec (Qu\u00e9bec), Canada G1V 0A6","D\u00e9partement de physique, de g\u00e9nie physique et d'optique, Universit\u00e9 Laval, Qu\u00e9bec (Qu\u00e9bec), Canada G1V 0A6","Vermont Complex Systems Center, University of Vermont, Burlington, VT 05405, USA"],"raw_orcid":"https://orcid.org/0000-0002-8208-9920","affiliations":[{"raw_affiliation_string":"Centre interdisciplinaire en mod\u00e9lisation math\u00e9matique, Universit\u00e9 Laval, Qu\u00e9bec (Qu\u00e9bec), Canada G1V 0A6","institution_ids":["https://openalex.org/I43406934"]},{"raw_affiliation_string":"D\u00e9partement de physique, de g\u00e9nie physique et d'optique, Universit\u00e9 Laval, Qu\u00e9bec (Qu\u00e9bec), Canada G1V 0A6","institution_ids":["https://openalex.org/I43406934"]},{"raw_affiliation_string":"Vermont Complex Systems Center, University of Vermont, Burlington, VT 05405, USA","institution_ids":["https://openalex.org/I111236770"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008033989","display_name":"Cristopher Moore","orcid":"https://orcid.org/0000-0002-2062-1942"},"institutions":[{"id":"https://openalex.org/I1308548392","display_name":"Santa Fe Institute","ror":"https://ror.org/01arysc35","country_code":"US","type":"funder","lineage":["https://openalex.org/I1308548392"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cristopher Moore","raw_affiliation_strings":["Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA","institution_ids":["https://openalex.org/I1308548392"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026230453","display_name":"Samuel V. Scarpino","orcid":"https://orcid.org/0000-0001-5716-2770"},"institutions":[{"id":"https://openalex.org/I111236770","display_name":"University of Vermont","ror":"https://ror.org/0155zta11","country_code":"US","type":"education","lineage":["https://openalex.org/I111236770"]},{"id":"https://openalex.org/I118636833","display_name":"Rockefeller Foundation","ror":"https://ror.org/03sfkwk85","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I118636833"]},{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]},{"id":"https://openalex.org/I1308548392","display_name":"Santa Fe Institute","ror":"https://ror.org/01arysc35","country_code":"US","type":"funder","lineage":["https://openalex.org/I1308548392"]},{"id":"https://openalex.org/I2801753046","display_name":"Prevention Institute","ror":"https://ror.org/02xdygm42","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I2801753046"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Samuel V. Scarpino","raw_affiliation_strings":["Network Science Institute, Northeastern University, Boston, MA 02115, USA","Pandemic Prevention Institute, Rockefeller Foundation, Washington, DC, USA","Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA","Vermont Complex Systems Center, University of Vermont, Burlington, VT 05405, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Network Science Institute, Northeastern University, Boston, MA 02115, USA","institution_ids":["https://openalex.org/I12912129"]},{"raw_affiliation_string":"Pandemic Prevention Institute, Rockefeller Foundation, Washington, DC, USA","institution_ids":["https://openalex.org/I118636833","https://openalex.org/I2801753046"]},{"raw_affiliation_string":"Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA","institution_ids":["https://openalex.org/I1308548392"]},{"raw_affiliation_string":"Vermont Complex Systems Center, University of Vermont, Burlington, VT 05405, USA","institution_ids":["https://openalex.org/I111236770"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049359232","display_name":"Benjamin M. Althouse","orcid":"https://orcid.org/0000-0002-5464-654X"},"institutions":[{"id":"https://openalex.org/I10052268","display_name":"New Mexico State University","ror":"https://ror.org/00hpz7z43","country_code":"US","type":"education","lineage":["https://openalex.org/I10052268"]},{"id":"https://openalex.org/I174135032","display_name":"Bellevue College","ror":"https://ror.org/05gr4yv49","country_code":"US","type":"education","lineage":["https://openalex.org/I174135032"]},{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Benjamin M. Althouse","raw_affiliation_strings":["New Mexico State University, Las Cruces, NM 88003, USA","Truveta, Inc., Bellevue, WA, USA","University of Washington, Seattle, WA 98105, USA"],"raw_orcid":"https://orcid.org/0000-0002-5464-654X","affiliations":[{"raw_affiliation_string":"New Mexico State University, Las Cruces, NM 88003, USA","institution_ids":["https://openalex.org/I10052268"]},{"raw_affiliation_string":"Truveta, Inc., Bellevue, WA, USA","institution_ids":["https://openalex.org/I174135032"]},{"raw_affiliation_string":"University of Washington, Seattle, WA 98105, USA","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035455593","display_name":"Laurent H\u00e9bert\u2010Dufresne","orcid":"https://orcid.org/0000-0002-0008-3673"},"institutions":[{"id":"https://openalex.org/I111236770","display_name":"University of Vermont","ror":"https://ror.org/0155zta11","country_code":"US","type":"education","lineage":["https://openalex.org/I111236770"]},{"id":"https://openalex.org/I43406934","display_name":"Universit\u00e9 Laval","ror":"https://ror.org/04sjchr03","country_code":"CA","type":"education","lineage":["https://openalex.org/I43406934"]}],"countries":["CA","US"],"is_corresponding":false,"raw_author_name":"Laurent H\u00e9bert-Dufresne","raw_affiliation_strings":["Department of Computer Science, University of Vermont, Burlington, VT 05405, USA","D\u00e9partement de physique, de g\u00e9nie physique et d'optique, Universit\u00e9 Laval, Qu\u00e9bec (Qu\u00e9bec), Canada G1V 0A6","Vermont Complex Systems Center, University of Vermont, Burlington, VT 05405, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Vermont, Burlington, VT 05405, USA","institution_ids":["https://openalex.org/I111236770"]},{"raw_affiliation_string":"D\u00e9partement de physique, de g\u00e9nie physique et d'optique, Universit\u00e9 Laval, Qu\u00e9bec (Qu\u00e9bec), Canada G1V 0A6","institution_ids":["https://openalex.org/I43406934"]},{"raw_affiliation_string":"Vermont Complex Systems Center, University of Vermont, Burlington, VT 05405, USA","institution_ids":["https://openalex.org/I111236770"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":9,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3787,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.9267527,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"65","issue":"2","first_page":"471","last_page":"492"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10410","display_name":"COVID-19 epidemiological studies","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10410","display_name":"COVID-19 epidemiological studies","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/directionality","display_name":"Directionality","score":0.8528695702552795},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.39856189489364624},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3985435962677002},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.27822962403297424},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2696154713630676},{"id":"https://openalex.org/keywords/genetics","display_name":"Genetics","score":0.073272705078125}],"concepts":[{"id":"https://openalex.org/C29648211","wikidata":"https://www.wikidata.org/wiki/Q1995607","display_name":"Directionality","level":2,"score":0.8528695702552795},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.39856189489364624},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3985435962677002},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.27822962403297424},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2696154713630676},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.073272705078125}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m1383811","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1383811","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Good health and well-being","score":0.8500000238418579,"id":"https://metadata.un.org/sdg/3"}],"awards":[{"id":"https://openalex.org/G3142655727","display_name":"Translational Research to Prevent and Control Global Infectious Diseases (Translational Global Infectious Diseases Research Center, TGIR).","funder_award_id":"1p20gm125498-01","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G44508553","display_name":"Translational Research to Prevent and Control Global Infectious Diseases(Translational Global Infectious Diseases Research Center, TGIR)","funder_award_id":"3p20gm125498-07s1","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G6338031445","display_name":null,"funder_award_id":"2019-05183","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G8437291228","display_name":"BIGDATA: F: Collaborative Research: Mining for Patterns in Graphs and High-Dimensional Data: Achieving the Limits","funder_award_id":"1838251","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306137","display_name":"Bill and Melinda Gates Foundation","ror":"https://ror.org/0456r8d26"},{"id":"https://openalex.org/F4320326644","display_name":"Canada First Research Excellence Fund","ror":null},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W76152643","https://openalex.org/W1606697907","https://openalex.org/W1986482847","https://openalex.org/W1987070596","https://openalex.org/W1987182838","https://openalex.org/W1987881677","https://openalex.org/W1989960380","https://openalex.org/W2004826528","https://openalex.org/W2005391019","https://openalex.org/W2011935659","https://openalex.org/W2012173272","https://openalex.org/W2030539428","https://openalex.org/W2037565977","https://openalex.org/W2041685353","https://openalex.org/W2043793275","https://openalex.org/W2044351514","https://openalex.org/W2069251911","https://openalex.org/W2069576934","https://openalex.org/W2078259918","https://openalex.org/W2078980460","https://openalex.org/W2093616570","https://openalex.org/W2096334666","https://openalex.org/W2114126556","https://openalex.org/W2140240219","https://openalex.org/W2144301074","https://openalex.org/W2144543245","https://openalex.org/W2148301044","https://openalex.org/W2151700392","https://openalex.org/W2158599675","https://openalex.org/W2169015768","https://openalex.org/W2196655855","https://openalex.org/W2309645253","https://openalex.org/W2334206889","https://openalex.org/W2472052094","https://openalex.org/W2589194541","https://openalex.org/W2606564740","https://openalex.org/W2894472942","https://openalex.org/W2964035435","https://openalex.org/W3004710867","https://openalex.org/W3008294222","https://openalex.org/W3013215798","https://openalex.org/W3015840999","https://openalex.org/W3016519974","https://openalex.org/W3017966133","https://openalex.org/W3021186497","https://openalex.org/W3021923959","https://openalex.org/W3022047883","https://openalex.org/W3083989168","https://openalex.org/W3094962431","https://openalex.org/W3103149358","https://openalex.org/W3105224959","https://openalex.org/W3119859287","https://openalex.org/W3130225502","https://openalex.org/W3158732255","https://openalex.org/W3159931889","https://openalex.org/W4235019172","https://openalex.org/W4252394414"],"related_works":["https://openalex.org/W2624817431","https://openalex.org/W2950752483","https://openalex.org/W2794987474","https://openalex.org/W4232225082","https://openalex.org/W33032069","https://openalex.org/W1599251874","https://openalex.org/W2029088481","https://openalex.org/W2334790377","https://openalex.org/W8218121","https://openalex.org/W2473013794"],"abstract_inverted_index":{"Most":[0],"models":[1,112,129],"of":[2,47,71,88,96,106,138,146,167,193,219,236],"epidemic":[3,63],"spread,":[4],"including":[5,57,77],"many":[6,54],"designed":[7,179],"specifically":[8],"for":[9,172,177],"COVID-19,":[10],"implicitly":[11],"assume":[12],"mass-action":[13,111,158],"contact":[14,18,134,173,224],"patterns":[15,135],"and":[16,61,75,80,117,119,149,176,190,222,232],"undirected":[17],"networks,":[19],"meaning":[20],"that":[21,53,125,216],"the":[22,28,32,45,58,62,68,81,102,156,194],"individuals":[23,139,203,212],"most":[24,33],"likely":[25],"to":[26,36,152,180,200,202,211,228],"spread":[27],"disease":[29],"are":[30,115,143],"also":[31,123],"at":[34],"risk":[35],"receive":[37],"it":[38],"from":[39,44,101,155],"others.Here,":[40],"we":[41,91,160],"review":[42],"results":[43],"theory":[46],"random":[48],"directed":[49,169,185],"graphs":[50,186],"which":[51],"show":[52,124],"important":[55],"quantities,":[56],"reproduction":[59],"number":[60],"size,":[64],"depend":[65],"sensitively":[66],"on":[67],"joint":[69,86],"distribution":[70],"in-and":[72],"out-degrees":[73],"(\"risk\"":[74],"\"spread\"),":[76],"their":[78],"heterogeneity":[79,97],"correlation":[82],"between":[83],"them.By":[84],"considering":[85],"distributions":[87],"various":[89],"kinds,":[90],"elucidate":[92],"why":[93],"some":[94,120,126,163],"types":[95,137],"cause":[98],"a":[99,188,217],"deviation":[100],"standard":[103],"Kermack-McKendrick":[104],"analysis":[105],"SIR":[107,128],"models,":[108],"i.e.,":[109],"so-called":[110],"where":[113],"contacts":[114],"homogeneous":[116],"random,":[118],"do":[121],"not.We":[122],"structured":[127],"informed":[130],"by":[131],"realistic":[132],"complex":[133],"among":[136],"(age":[140],"or":[141],"activity)":[142],"simply":[144],"mixtures":[145],"Poisson":[147],"processes":[148],"tend":[150,199],"not":[151],"deviate":[153],"significantly":[154],"simplest":[157],"model.Finally,":[159],"point":[161],"out":[162],"possible":[164],"policy":[165],"implications":[166],"this":[168],"structure,":[170],"both":[171,220],"tracing":[174,225],"strategy":[175],"interventions":[178],"prevent":[181,233],"superspreading":[182,230],"events.In":[183],"particular,":[184],"have":[187],"forward":[189,221],"backward":[191,208,223],"version":[192],"classic":[195],"\"friendship":[196],"paradox\"-forward":[197],"edges":[198,209],"lead":[201,210],"with":[204,213],"high":[205,214],"risk,":[206],"while":[207],"spread-such":[215],"combination":[218],"is":[226],"necessary":[227],"find":[229],"events":[231],"future":[234],"cascades":[235],"infection.":[237]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":7},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":4}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}
