{"id":"https://openalex.org/W4225980147","doi":"https://doi.org/10.3934/nhm.2022009","title":"A martingale formulation for stochastic compartmental susceptible-infected-recovered (SIR) models to analyze finite size effects in COVID-19 case studies","display_name":"A martingale formulation for stochastic compartmental susceptible-infected-recovered (SIR) models to analyze finite size effects in COVID-19 case studies","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4225980147","doi":"https://doi.org/10.3934/nhm.2022009"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2022009","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=c1293b1e-1752-4b20-b9ef-43e70dee17c7","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.aimsciences.org/article/exportPdf?id=c1293b1e-1752-4b20-b9ef-43e70dee17c7","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100445622","display_name":"Xia Li","orcid":"https://orcid.org/0000-0003-3050-8529"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"funder","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xia Li","raw_affiliation_strings":["Department of Mathematics, University of California, Los Angeles"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Los Angeles","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049890851","display_name":"Chuntian Wang","orcid":"https://orcid.org/0000-0002-3888-7589"},"institutions":[{"id":"https://openalex.org/I17301866","display_name":"University of Alabama","ror":"https://ror.org/03xrrjk67","country_code":"US","type":"funder","lineage":["https://openalex.org/I17301866"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chuntian Wang","raw_affiliation_strings":["UA Department of Mathematics, The University of Alabama"],"affiliations":[{"raw_affiliation_string":"UA Department of Mathematics, The University of Alabama","institution_ids":["https://openalex.org/I17301866"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100348509","display_name":"Hao Li","orcid":"https://orcid.org/0000-0001-8502-2556"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"funder","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hao Li","raw_affiliation_strings":["Department of Mathematics, University of California, Los Angeles"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Los Angeles","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090707978","display_name":"Andrea L. Bertozzi","orcid":"https://orcid.org/0000-0003-0396-7391"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"funder","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrea L. Bertozzi","raw_affiliation_strings":["Departments of Mathematics and Mechanical and Aerospace Engineering, University of California, Los Angeles"],"affiliations":[{"raw_affiliation_string":"Departments of Mathematics and Mechanical and Aerospace Engineering, University of California, Los Angeles","institution_ids":["https://openalex.org/I161318765"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":0,"max":59},"biblio":{"volume":"17","issue":"3","first_page":"311","last_page":"311"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10410","display_name":"COVID-19 epidemiological studies","score":0.9999,"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":0.9999,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9929,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9807,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-modelling","display_name":"Stochastic modelling","score":0.45681795}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6014706},{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.58001894},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5255876},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.47875753},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.45681795},{"id":"https://openalex.org/C91229774","wikidata":"https://www.wikidata.org/wiki/Q193885","display_name":"Infinitesimal","level":2,"score":0.42608792},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.39707392},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.24239314},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.160485},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14801854},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2022009","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=c1293b1e-1752-4b20-b9ef-43e70dee17c7","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2022009","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=c1293b1e-1752-4b20-b9ef-43e70dee17c7","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/3","score":0.82,"display_name":"Good health and well-being"}],"grants":[],"datasets":[],"versions":[],"referenced_works_count":57,"referenced_works":["https://openalex.org/W1531264907","https://openalex.org/W1536721400","https://openalex.org/W1537236879","https://openalex.org/W1538558414","https://openalex.org/W1995522593","https://openalex.org/W2002882243","https://openalex.org/W2036332207","https://openalex.org/W20373697","https://openalex.org/W2042321087","https://openalex.org/W2065017532","https://openalex.org/W2072895797","https://openalex.org/W207440351","https://openalex.org/W2088942147","https://openalex.org/W2092076434","https://openalex.org/W2093564649","https://openalex.org/W2099700798","https://openalex.org/W2116944637","https://openalex.org/W2148301044","https://openalex.org/W2166893822","https://openalex.org/W2169987437","https://openalex.org/W2198369554","https://openalex.org/W2293609966","https://openalex.org/W2506354201","https://openalex.org/W2787890375","https://openalex.org/W2790110384","https://openalex.org/W2793186588","https://openalex.org/W2795333180","https://openalex.org/W2795682996","https://openalex.org/W2810761244","https://openalex.org/W2829041456","https://openalex.org/W2880606878","https://openalex.org/W2884242497","https://openalex.org/W2885182116","https://openalex.org/W2886102496","https://openalex.org/W2901549144","https://openalex.org/W2954836603","https://openalex.org/W2963530303","https://openalex.org/W2964097150","https://openalex.org/W2967349558","https://openalex.org/W3008443627","https://openalex.org/W3008842543","https://openalex.org/W3022439851","https://openalex.org/W3023441241","https://openalex.org/W3040134252","https://openalex.org/W3101614988","https://openalex.org/W3101915710","https://openalex.org/W3106535680","https://openalex.org/W3126546596","https://openalex.org/W4213329537","https://openalex.org/W4230843050","https://openalex.org/W4232705268","https://openalex.org/W4245159036","https://openalex.org/W4254741854","https://openalex.org/W4256711960","https://openalex.org/W4292049208","https://openalex.org/W4294309872","https://openalex.org/W78182575"],"related_works":["https://openalex.org/W4310398783","https://openalex.org/W2385510272","https://openalex.org/W2385204246","https://openalex.org/W2370818987","https://openalex.org/W2370598571","https://openalex.org/W2361379965","https://openalex.org/W2355499472","https://openalex.org/W2350226651","https://openalex.org/W2349230259","https://openalex.org/W2348667803"],"abstract_inverted_index":{"<p":[0],"style='text-indent:20px;'>Deterministic":[1],"compartmental":[2],"models":[3,16],"for":[4,19,107],"infectious":[5],"diseases":[6],"give":[7],"the":[8,44,54,72,96,108,114,158,168],"mean":[9],"behaviour":[10],"of":[11,56,59,84,113,127,141,147,163],"stochastic":[12,74,89,109,115],"agent-based":[13],"models.":[14],"These":[15],"work":[17],"well":[18],"counterfactual":[20],"studies":[21,146],"in":[22,153],"which":[23],"a":[24,80,85,88,124],"fully":[25],"mixed":[26],"large-scale":[27],"population":[28,120],"is":[29,133],"relevant.":[30],"However,":[31],"with":[32,95],"finite":[33],"size":[34,50,129],"populations,":[35],"chance":[36],"variations":[37],"may":[38],"lead":[39],"to":[40],"significant":[41],"departures":[42],"from":[43,53],"mean.":[45],"In":[46,67],"real-life":[47],"applications,":[48],"<i>finite":[49,128],"effects</i>":[51],"arise":[52],"variance":[55],"individual":[57],"realizations":[58],"an":[60,104,161],"epidemic":[61],"course":[62],"about":[63],"its":[64],"fluid":[65],"limit.":[66],"this":[68],"article,":[69],"we":[70,102,122],"consider":[71],"classical":[73,97],"Susceptible-Infected-Recovered":[75],"(SIR)":[76],"model,":[77],"and":[78,87,101,137],"derive":[79],"martingale":[81],"formulation":[82],"consisting":[83],"deterministic":[86,92,98],"component.":[90],"The":[91],"part":[93],"coincides":[94],"SIR":[99],"model":[100],"provide":[103,123],"upper":[105],"bound":[106],"part.":[110],"Through":[111],"analysis":[112],"component":[116],"depending":[117],"on":[118],"varying":[119],"size,":[121],"theoretical":[125,142],"explanation":[126],"effects</i>.":[130],"Our":[131],"theory":[132,159],"supported":[134],"by":[135],"quantitative":[136],"direct":[138],"numerical":[139],"simulations":[140],"infinitesimal":[143],"variance.":[144],"Case":[145],"coronavirus":[148],"disease":[149],"2019":[150],"(COVID-19)":[151],"transmission":[152],"smaller":[154],"populations":[155],"illustrate":[156],"that":[157,166],"provides":[160],"envelope":[162],"possible":[164],"outcomes":[165],"includes":[167],"field":[169],"data.</p>":[170]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W4225980147","counts_by_year":[],"updated_date":"2025-02-26T04:06:05.778642","created_date":"2022-05-05"}