{"id":"https://openalex.org/W2954917564","doi":"https://doi.org/10.1155/2019/9876013","title":"Bifurcation Analysis of an SIR Model with Logistic Growth, Nonlinear Incidence, and Saturated Treatment","display_name":"Bifurcation Analysis of an SIR Model with Logistic Growth, Nonlinear Incidence, and Saturated Treatment","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2954917564","doi":"https://doi.org/10.1155/2019/9876013","mag":"2954917564"},"language":"en","primary_location":{"id":"doi:10.1155/2019/9876013","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/9876013","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/9876013.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2019/9876013.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066746973","display_name":"\u00c1ngel P\u00e9rez","orcid":"https://orcid.org/0000-0002-6273-2405"},"institutions":[{"id":"https://openalex.org/I23878562","display_name":"Autonomous University of Yucat\u00e1n","ror":"https://ror.org/032p1n739","country_code":"MX","type":"education","lineage":["https://openalex.org/I23878562"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"\u00c1ngel G. C. P\u00e9rez","raw_affiliation_strings":["Facultad de Matem\u00e1ticas, Universidad Aut\u00f3noma de Yucat\u00e1n, Anillo Perif\u00e9rico Norte, Tablaje Catastral 13615, C.P. 97119, M\u00e9rida, Yucat\u00e1n"],"raw_orcid":"https://orcid.org/0000-0002-6273-2405","affiliations":[{"raw_affiliation_string":"Facultad de Matem\u00e1ticas, Universidad Aut\u00f3noma de Yucat\u00e1n, Anillo Perif\u00e9rico Norte, Tablaje Catastral 13615, C.P. 97119, M\u00e9rida, Yucat\u00e1n","institution_ids":["https://openalex.org/I23878562"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052042372","display_name":"Eric \u00c1vila-Vales","orcid":"https://orcid.org/0000-0001-9522-6712"},"institutions":[{"id":"https://openalex.org/I23878562","display_name":"Autonomous University of Yucat\u00e1n","ror":"https://ror.org/032p1n739","country_code":"MX","type":"education","lineage":["https://openalex.org/I23878562"]},{"id":"https://openalex.org/I4210139820","display_name":"Universidad de Norteam\u00e9rica","ror":"https://ror.org/03m69ak30","country_code":"MX","type":"education","lineage":["https://openalex.org/I4210139820"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Eric Avila-Vales","raw_affiliation_strings":["Facultad de Matemticas, Universidad Autnoma de Yucatn, Anillo Perifrico Norte, Tablaje Catastral 13615, C.P. 97119, Mrida, Yucatn, Mexico","Facultad de Matem\u00e1ticas, Universidad Aut\u00f3noma de Yucat\u00e1n, Anillo Perif\u00e9rico Norte, Tablaje Catastral 13615, C.P. 97119, M\u00e9rida, Yucat\u00e1n"],"raw_orcid":"https://orcid.org/0000-0001-9522-6712","affiliations":[{"raw_affiliation_string":"Facultad de Matemticas, Universidad Autnoma de Yucatn, Anillo Perifrico Norte, Tablaje Catastral 13615, C.P. 97119, Mrida, Yucatn, Mexico","institution_ids":["https://openalex.org/I4210139820"]},{"raw_affiliation_string":"Facultad de Matem\u00e1ticas, Universidad Aut\u00f3noma de Yucat\u00e1n, Anillo Perif\u00e9rico Norte, Tablaje Catastral 13615, C.P. 97119, M\u00e9rida, Yucat\u00e1n","institution_ids":["https://openalex.org/I23878562"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025477236","display_name":"Gerardo Garc\u00eda-Almeida","orcid":"https://orcid.org/0000-0001-8376-031X"},"institutions":[{"id":"https://openalex.org/I23878562","display_name":"Autonomous University of Yucat\u00e1n","ror":"https://ror.org/032p1n739","country_code":"MX","type":"education","lineage":["https://openalex.org/I23878562"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Gerardo Emilio Garc\u00eda-Almeida","raw_affiliation_strings":["Facultad de Matem\u00e1ticas, Universidad Aut\u00f3noma de Yucat\u00e1n, Anillo Perif\u00e9rico Norte, Tablaje Catastral 13615, C.P. 97119, M\u00e9rida, Yucat\u00e1n"],"raw_orcid":"https://orcid.org/0000-0001-8376-031X","affiliations":[{"raw_affiliation_string":"Facultad de Matem\u00e1ticas, Universidad Aut\u00f3noma de Yucat\u00e1n, Anillo Perif\u00e9rico Norte, Tablaje Catastral 13615, C.P. 97119, M\u00e9rida, Yucat\u00e1n","institution_ids":["https://openalex.org/I23878562"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5052042372"],"corresponding_institution_ids":["https://openalex.org/I23878562","https://openalex.org/I4210139820"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":4.279,"has_fulltext":true,"cited_by_count":30,"citation_normalized_percentile":{"value":0.93964623,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"2019","issue":"1","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":0.9998999834060669,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.991599977016449,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9853000044822693,"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/bifurcation","display_name":"Bifurcation","score":0.7159236669540405},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6369816064834595},{"id":"https://openalex.org/keywords/logistic-function","display_name":"Logistic function","score":0.5837209224700928},{"id":"https://openalex.org/keywords/logistic-regression","display_name":"Logistic regression","score":0.5315423011779785},{"id":"https://openalex.org/keywords/incidence","display_name":"Incidence (geometry)","score":0.515112578868866},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42577800154685974},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.37774980068206787},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3470969796180725},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.30153316259384155},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13207370042800903},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07863408327102661}],"concepts":[{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.7159236669540405},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6369816064834595},{"id":"https://openalex.org/C180802074","wikidata":"https://www.wikidata.org/wiki/Q1052379","display_name":"Logistic function","level":2,"score":0.5837209224700928},{"id":"https://openalex.org/C151956035","wikidata":"https://www.wikidata.org/wiki/Q1132755","display_name":"Logistic regression","level":2,"score":0.5315423011779785},{"id":"https://openalex.org/C61511704","wikidata":"https://www.wikidata.org/wiki/Q1671857","display_name":"Incidence (geometry)","level":2,"score":0.515112578868866},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42577800154685974},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.37774980068206787},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3470969796180725},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.30153316259384155},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13207370042800903},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07863408327102661},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2019/9876013","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/9876013","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/9876013.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:9876013","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2019/9876013.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:2f441e1242a0433eb1ef01f5b4213b39","is_oa":false,"landing_page_url":"https://doaj.org/article/2f441e1242a0433eb1ef01f5b4213b39","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2019 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2019/9876013","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/9876013","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/9876013.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8500000238418579,"display_name":"Good health and well-being","id":"https://metadata.un.org/sdg/3"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320326060","display_name":"Universidad Aut\u00f3noma de Yucat\u00e1n","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2954917564.pdf","grobid_xml":"https://content.openalex.org/works/W2954917564.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1993534484","https://openalex.org/W2007892796","https://openalex.org/W2015074865","https://openalex.org/W2021321360","https://openalex.org/W2057313753","https://openalex.org/W2081696580","https://openalex.org/W2085451305","https://openalex.org/W2088827616","https://openalex.org/W2089876099","https://openalex.org/W2112680994","https://openalex.org/W2126084338","https://openalex.org/W2147274601","https://openalex.org/W2155247719","https://openalex.org/W2321291885","https://openalex.org/W2398128155","https://openalex.org/W2545008996","https://openalex.org/W2598770997","https://openalex.org/W2607267260","https://openalex.org/W2912545311","https://openalex.org/W4293079218"],"related_works":["https://openalex.org/W2171482902","https://openalex.org/W2129863591","https://openalex.org/W1983481117","https://openalex.org/W1596769710","https://openalex.org/W2024251235","https://openalex.org/W2923497059","https://openalex.org/W2978363435","https://openalex.org/W4394896199","https://openalex.org/W2363171232","https://openalex.org/W2061411662"],"abstract_inverted_index":{"There":[0],"is":[1],"a":[2,54,108],"wide":[3],"range":[4],"of":[5,16,31,38,80,85,111,117,123],"works":[6],"that":[7,142,149],"have":[8],"proposed":[9],"mathematical":[10],"models":[11,46,155],"to":[12,128,158],"describe":[13],"the":[14,29,36,69,77,83,96,118],"spread":[15],"infectious":[17],"diseases":[18],"within":[19],"human":[20],"populations.":[21],"Based":[22],"on":[23],"such":[24],"models,":[25],"researchers":[26],"can":[27,156],"evaluate":[28],"effect":[30],"applying":[32],"different":[33],"strategies":[34],"for":[35,76],"treatment":[37,62,101],"diseases.":[39],"In":[40],"this":[41],"article,":[42],"we":[43],"generalize":[44],"previous":[45],"by":[47],"studying":[48],"an":[49],"SIR":[50],"epidemic":[51,154],"model":[52,106],"with":[53],"nonlinear":[55],"incidence":[56],"rate,":[57,63],"saturated":[58],"Holling":[59],"type":[60],"II":[61],"and":[64,73,82,88,100,120,131],"logistic":[65],"growth.":[66],"We":[67,91],"compute":[68],"basic":[70],"reproduction":[71],"number":[72],"determine":[74],"conditions":[75],"local":[78],"stability":[79],"equilibria":[81,124],"existence":[84],"backward":[86],"bifurcation":[87,110,133],"Hopf":[89],"bifurcation.":[90],"also":[92],"show":[93],"that,":[94],"when":[95],"disease":[97],"transmission":[98],"rate":[99],"parameter":[102],"are":[103,125],"varied,":[104],"our":[105,144],"undergoes":[107],"Bogdanov\u2010Takens":[109],"codimension":[112],"2":[113],"or":[114],"3.":[115],"Simulations":[116],"solutions":[119],"numerical":[121],"continuation":[122],"carried":[126],"out":[127],"generate":[129],"2D":[130],"3D":[132],"diagrams,":[134],"as":[135,137],"well":[136],"several":[138],"related":[139],"phase":[140],"portraits":[141],"illustrate":[143],"results.":[145],"Our":[146],"work":[147],"shows":[148],"incorporating":[150],"these":[151],"factors":[152],"into":[153],"lead":[157],"very":[159],"complex":[160],"dynamics.":[161]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3}],"updated_date":"2026-06-04T09:04:59.091469","created_date":"2025-10-10T00:00:00"}