{"id":"https://openalex.org/W7220382170","doi":"https://doi.org/10.64898/2026.09.30.26364380","title":"History-dependent SEIR models: equivalent formulations, fractional foundation, and growth and decay principles","display_name":"History-dependent SEIR models: equivalent formulations, fractional foundation, and growth and decay principles","publication_year":2026,"publication_date":"2026-10-05","ids":{"openalex":"https://openalex.org/W7220382170","doi":"https://doi.org/10.64898/2026.09.30.26364380"},"language":"en","primary_location":{"id":"doi:10.64898/2026.09.30.26364380","doi":"https://doi.org/10.64898/2026.09.30.26364380","is_oa":true,"landing_page_url":"https://doi.org/10.64898/2026.09.30.26364380","pdf_url":"https://www.medrxiv.org/content/medrxiv/early/2026/10/05/2026.09.30.26364380.full.pdf","source":{"id":"https://openalex.org/S3005729997","display_name":"medRxiv","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4310315909"],"host_organization_lineage_names":["Cold Spring Harbor Laboratory Press"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"medRxiv","raw_type":"posted-content"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.medrxiv.org/content/medrxiv/early/2026/10/05/2026.09.30.26364380.full.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103258164","display_name":"Suli Liu","orcid":"https://orcid.org/0000-0002-4354-2665","observed_orcids":["https://orcid.org/0000-0002-4354-2665"]},"institutions":[{"id":"https://openalex.org/I194450716","display_name":"Jilin University","ror":"https://ror.org/00js3aw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I194450716"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Suli Liu","raw_affiliation_strings":["School of Mathematics, Jilin University, Changchun 130012, China"],"raw_orcid":"https://orcid.org/0000-0002-4354-2665","affiliations":[{"raw_affiliation_string":"School of Mathematics, Jilin University, Changchun 130012, China","institution_ids":["https://openalex.org/I194450716"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157617460","display_name":"Jianhong Wu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I192455969","display_name":"York University","ror":"https://ror.org/05fq50484","country_code":"CA","type":"education","lineage":["https://openalex.org/I192455969"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Jianhong Wu","raw_affiliation_strings":["Laboratory for Industrial and Applied Mathematics, York University, Toronto, M3J 1P3, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory for Industrial and Applied Mathematics, York University, Toronto, M3J 1P3, Canada","institution_ids":["https://openalex.org/I192455969"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091595646","display_name":"Yijun Lou","orcid":"https://orcid.org/0000-0003-3864-2001","observed_orcids":["https://orcid.org/0000-0003-3864-2001"]},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Yijun Lou","raw_affiliation_strings":["Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, SAR, China"],"raw_orcid":"https://orcid.org/0000-0003-3864-2001","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, SAR, China","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"last","author":{"id":null,"display_name":"Chen Jia","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Chen Jia","raw_affiliation_strings":["Beijing Research Institute, Harbin Institute of Technology, Beijing 100144, China","School of Mathematics, Harbin Institute of Technology, Harbin 150001, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Research Institute, Harbin Institute of Technology, Beijing 100144, China","institution_ids":["https://openalex.org/I204983213"]},{"raw_affiliation_string":"School of Mathematics, Harbin Institute of Technology, Harbin 150001, China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I204983213"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10410","display_name":"COVID-19 epidemiological studies","score":0.0020000000949949026,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.0013000000035390258,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/seir-model","display_name":"SEIR model","score":0.9079999923706055},{"id":"https://openalex.org/keywords/memory-effects","display_name":"memory effects","score":0.9520000219345093},{"id":"https://openalex.org/keywords/residence-time-distribution","display_name":"residence time distribution","score":0.8100000023841858},{"id":"https://openalex.org/keywords/riemann-liouville-fractional-derivative","display_name":"Riemann-Liouville fractional derivative","score":0.8679999709129333},{"id":"https://openalex.org/keywords/fractional-order-epidemic-model","display_name":"fractional-order epidemic model","score":0.9449999928474426},{"id":"https://openalex.org/keywords/infectious-period-distribution","display_name":"infectious period distribution","score":0.9990000128746033},{"id":"https://openalex.org/keywords/euler-lotka-equation","display_name":"Euler-Lotka equation","score":0.8889999985694885},{"id":"https://openalex.org/keywords/stochastic-orders","display_name":"stochastic ordering","score":0.6600000262260437}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7046999931335449},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.642300009727478},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5738999843597412},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.49079999327659607},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.4708000123500824},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4535999894142151},{"id":"https://openalex.org/C2775913793","wikidata":"https://www.wikidata.org/wiki/Q3030793","display_name":"Residence time (fluid dynamics)","level":2,"score":0.40720000863075256},{"id":"https://openalex.org/C2983335520","wikidata":"https://www.wikidata.org/wiki/Q47537570","display_name":"Growth model","level":2,"score":0.33219999074935913},{"id":"https://openalex.org/C1627819","wikidata":"https://www.wikidata.org/wiki/Q2572354","display_name":"Epidemic model","level":3,"score":0.3089999854564667},{"id":"https://openalex.org/C2781291010","wikidata":"https://www.wikidata.org/wiki/Q178580","display_name":"Period (music)","level":2,"score":0.3066999912261963},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.27079999446868896},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.26649999618530273},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2590000033378601},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.25780001282691956}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.64898/2026.09.30.26364380","doi":"https://doi.org/10.64898/2026.09.30.26364380","is_oa":true,"landing_page_url":"https://doi.org/10.64898/2026.09.30.26364380","pdf_url":"https://www.medrxiv.org/content/medrxiv/early/2026/10/05/2026.09.30.26364380.full.pdf","source":{"id":"https://openalex.org/S3005729997","display_name":"medRxiv","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4310315909"],"host_organization_lineage_names":["Cold Spring Harbor Laboratory Press"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"medRxiv","raw_type":"posted-content"}],"best_oa_location":{"id":"doi:10.64898/2026.09.30.26364380","doi":"https://doi.org/10.64898/2026.09.30.26364380","is_oa":true,"landing_page_url":"https://doi.org/10.64898/2026.09.30.26364380","pdf_url":"https://www.medrxiv.org/content/medrxiv/early/2026/10/05/2026.09.30.26364380.full.pdf","source":{"id":"https://openalex.org/S3005729997","display_name":"medRxiv","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4310315909"],"host_organization_lineage_names":["Cold Spring Harbor Laboratory Press"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"medRxiv","raw_type":"posted-content"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3549048451","display_name":null,"funder_award_id":"12571547","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G355472857","display_name":null,"funder_award_id":"12271020","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3572799349","display_name":null,"funder_award_id":"12301627","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4233426262","display_name":null,"funder_award_id":"12526215","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322174","display_name":"People's Government of Jilin Province","ror":"https://ror.org/02fzqav45"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220382170.pdf","grobid_xml":"https://content.openalex.org/works/W7220382170.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1802192273","https://openalex.org/W4378376467","https://openalex.org/W4392471606","https://openalex.org/W7207641632","https://openalex.org/W2591254227","https://openalex.org/W2040548005","https://openalex.org/W1973106743","https://openalex.org/W7100931190","https://openalex.org/W7160662934","https://openalex.org/W3027681486"],"abstract_inverted_index":{"Abstract":[0],"Non-exponential":[1],"residence":[2],"times":[3],"give":[4],"rise":[5],"to":[6],"history-dependent":[7,28],"or":[8,98],"memory":[9],"effects":[10],"in":[11,94,148,162],"epidemic":[12,109,127],"dynamics,":[13],"yet":[14],"their":[15],"mathematical":[16],"formulations":[17,47],"remain":[18],"fragmented.":[19],"Here":[20],"we":[21,118],"develop":[22],"a":[23,27,53,63,68,81,104],"unified":[24,54],"framework":[25],"for":[26,107],"SEIR":[29],"model":[30,89],"with":[31],"general":[32],"latent-":[33,122],"and":[34,45,48,74,115,123,129,139],"infectious-period":[35,124],"distributions.":[36],"We":[37,57],"first":[38],"establish":[39],"the":[40,43,60,78,88,121,149,163],"equivalence":[41],"between":[42,71],"stage-age":[44],"renewal":[46],"show":[49],"that":[50],"both":[51,136],"admit":[52],"transition-flow":[55,64],"representation.":[56],"then":[58],"introduce":[59],"concept":[61],"of":[62,84,96],"multiplier,":[65],"which":[66],"provides":[67],"direct":[69],"link":[70],"residence-time":[72],"distributions":[73,125],"transition":[75],"flows.":[76],"When":[77],"multiplier":[79],"is":[80],"weighted":[82],"sum":[83],"shifted":[85],"power":[86],"functions,":[87],"admits":[90],"an":[91],"exact":[92],"representation":[93],"terms":[95],"Riemann-Liouville":[97,100],"tempered":[99],"fractional":[101,108],"operators,":[102],"providing":[103],"first-principles":[105],"foundation":[106],"models.":[110],"Finally,":[111],"using":[112],"Euler-Lotka":[113],"equations":[114],"stochastic-order":[116],"arguments,":[117],"characterize":[119],"how":[120],"shape":[126],"growth":[128,138,154],"decay.":[130],"A":[131],"longer":[132],"latent":[133,150],"period":[134,151,165],"slows":[135,156,166],"early":[137,153],"late":[140,157],"decay,":[141,158],"while,":[142],"at":[143],"fixed":[144],"means,":[145],"greater":[146,160],"variability":[147,161],"accelerates":[152],"but":[155],"whereas":[159],"infectious":[164],"both.":[167]},"counts_by_year":[],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-10-06T00:00:00"}