{"id":"https://openalex.org/W2049978891","doi":"https://doi.org/10.1137/s0036139999359860","title":"Global Dynamics of an SEIR Epidemic Model with Vertical Transmission","display_name":"Global Dynamics of an SEIR Epidemic Model with Vertical Transmission","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2049978891","doi":"https://doi.org/10.1137/s0036139999359860","mag":"2049978891"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139999359860","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139999359860","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Journal on Applied Mathematics","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/A5018475416","display_name":"Michael Y. Li","orcid":"https://orcid.org/0000-0002-4403-1429"},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Michael Y. Li","raw_affiliation_strings":["University of Alberta"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Alberta","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109396218","display_name":"Hal L. Smith","orcid":null},"institutions":[{"id":"https://openalex.org/I4210152479","display_name":"Statistical Service","ror":"https://ror.org/05vydvf11","country_code":"CY","type":"government","lineage":["https://openalex.org/I4210152479"]}],"countries":["CY"],"is_corresponding":false,"raw_author_name":"Hal L. Smith","raw_affiliation_strings":["CLAS-NS: Mathematics and Statistical Sciences, School of (SMSS)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CLAS-NS: Mathematics and Statistical Sciences, School of (SMSS)","institution_ids":["https://openalex.org/I4210152479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020886237","display_name":"Liancheng Wang","orcid":"https://orcid.org/0000-0002-6567-6138"},"institutions":[{"id":"https://openalex.org/I39815113","display_name":"Georgia Southern University","ror":"https://ror.org/04agmb972","country_code":"US","type":"education","lineage":["https://openalex.org/I39815113"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Liancheng Wang","raw_affiliation_strings":["Georgia Southern University ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Southern University ,","institution_ids":["https://openalex.org/I39815113"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6907,"has_fulltext":false,"cited_by_count":340,"citation_normalized_percentile":{"value":0.89679816,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"62","issue":"1","first_page":"58","last_page":"69"},"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":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9998999834060669,"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":0.9991000294685364,"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"}},{"id":"https://openalex.org/T10410","display_name":"COVID-19 epidemiological studies","score":0.9936000108718872,"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/basic-reproduction-number","display_name":"Basic reproduction number","score":0.821840763092041},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.6093782186508179},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.555549681186676},{"id":"https://openalex.org/keywords/transmission","display_name":"Transmission (telecommunications)","score":0.5529334545135498},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5525710582733154},{"id":"https://openalex.org/keywords/epidemic-model","display_name":"Epidemic model","score":0.5273138880729675},{"id":"https://openalex.org/keywords/demography","display_name":"Demography","score":0.23518610000610352},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10400897264480591}],"concepts":[{"id":"https://openalex.org/C204264503","wikidata":"https://www.wikidata.org/wiki/Q901464","display_name":"Basic reproduction number","level":3,"score":0.821840763092041},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.6093782186508179},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.555549681186676},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.5529334545135498},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5525710582733154},{"id":"https://openalex.org/C1627819","wikidata":"https://www.wikidata.org/wiki/Q2572354","display_name":"Epidemic model","level":3,"score":0.5273138880729675},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.23518610000610352},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10400897264480591},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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":[{"id":"doi:10.1137/s0036139999359860","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139999359860","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Journal on Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/3","display_name":"Good health and well-being","score":0.8500000238418579}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W163591500","https://openalex.org/W228144990","https://openalex.org/W614290300","https://openalex.org/W1510122527","https://openalex.org/W1606697907","https://openalex.org/W1777062577","https://openalex.org/W1837867392","https://openalex.org/W1965567178","https://openalex.org/W1982075903","https://openalex.org/W1982416282","https://openalex.org/W1984819558","https://openalex.org/W1986751706","https://openalex.org/W1989695742","https://openalex.org/W1994606684","https://openalex.org/W1999581374","https://openalex.org/W2008072444","https://openalex.org/W2035143741","https://openalex.org/W2043616341","https://openalex.org/W2044163391","https://openalex.org/W2049529576","https://openalex.org/W2054353417","https://openalex.org/W2055605553","https://openalex.org/W2084318376","https://openalex.org/W2109437952","https://openalex.org/W2125307802","https://openalex.org/W2234807080","https://openalex.org/W2328512274","https://openalex.org/W2502051805"],"related_works":["https://openalex.org/W2002276778","https://openalex.org/W3163183336","https://openalex.org/W2363756920","https://openalex.org/W2787791688","https://openalex.org/W1698381576","https://openalex.org/W4307385600","https://openalex.org/W2353047014","https://openalex.org/W4282842863","https://openalex.org/W2079780715","https://openalex.org/W3039783441"],"abstract_inverted_index":{"We":[0,41],"study":[1],"a":[2,91],"population":[3,14,24],"model":[4],"for":[5],"an":[6,112],"infectious":[7,70],"disease":[8,84,109],"that":[9,43],"spreads":[10],"in":[11,100],"the":[12,32,37,44,51,67,76,83,101,104,108,123,127],"host":[13,23],"through":[15],"both":[16],"horizontal":[17],"and":[18,31,59,69,82,96,107],"vertical":[19,124],"transmission.":[20],"The":[21,120],"total":[22],"is":[25,35,79,97,131],"assumed":[26],"to":[27,126],"have":[28],"constant":[29],"density":[30],"incidence":[33],"term":[34],"of":[36,63,103,122],"bilinear":[38],"mass-action":[39],"form.":[40],"prove":[42],"global":[45],"dynamics":[46],"are":[47,61],"completely":[48],"determined":[49],"by":[50],"basic":[52,128],"reproduction":[53,129],"number":[54,130],"R0":[55,89],"(p,q),":[56],"where":[57],"p":[58],"q":[60],"fractions":[62],"infected":[64],"newborns":[65],"from":[66],"exposed":[68],"classes,":[71],"respectively.":[72],"If":[73,88],"$R_0(p,q)\\le":[74],"1,$":[75],"disease-free":[77],"equilibrium":[78,94,114],"globally":[80,98],"stable":[81,99],"always":[85],"dies":[86],"out.":[87],"(p,q)>1,":[90],"unique":[92],"endemic":[93,113],"exists":[95],"interior":[102],"feasible":[105],"region,":[106],"persists":[110],"at":[111],"state":[115],"if":[116],"it":[117],"initially":[118],"exists.":[119],"contribution":[121],"transmission":[125],"also":[132],"analyzed.":[133]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":18},{"year":2024,"cited_by_count":26},{"year":2023,"cited_by_count":19},{"year":2022,"cited_by_count":22},{"year":2021,"cited_by_count":24},{"year":2020,"cited_by_count":36},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":13},{"year":2017,"cited_by_count":23},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":16},{"year":2013,"cited_by_count":14},{"year":2012,"cited_by_count":15}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}