{"id":"https://openalex.org/W4386896286","doi":"https://doi.org/10.1142/s0218127423300288","title":"Stability Switches, Hopf Bifurcation and Chaotic Dynamics in Simple Epidemic Model with State-Dependent Delay","display_name":"Stability Switches, Hopf Bifurcation and Chaotic Dynamics in Simple Epidemic Model with State-Dependent Delay","publication_year":2023,"publication_date":"2023-09-15","ids":{"openalex":"https://openalex.org/W4386896286","doi":"https://doi.org/10.1142/s0218127423300288"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127423300288","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127423300288","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5057620086","display_name":"Redouane Qesmi","orcid":"https://orcid.org/0000-0001-9213-5313"},"institutions":[{"id":"https://openalex.org/I81605866","display_name":"Sidi Mohamed Ben Abdellah University","ror":"https://ror.org/04efg9a07","country_code":"MA","type":"education","lineage":["https://openalex.org/I81605866"]}],"countries":["MA"],"is_corresponding":true,"raw_author_name":"Redouane Qesmi","raw_affiliation_strings":["Superior School of Technology, Sidi Mohamed Ben Abdellah University, Fez 30000, Morocco"],"raw_orcid":"https://orcid.org/0000-0001-9213-5313","affiliations":[{"raw_affiliation_string":"Superior School of Technology, Sidi Mohamed Ben Abdellah University, Fez 30000, Morocco","institution_ids":["https://openalex.org/I81605866"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030154675","display_name":"Jane M. Heffernan","orcid":"https://orcid.org/0000-0001-9502-1688"},"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":"Jane M. Heffernan","raw_affiliation_strings":["Department of Mathematics and Statistics, York University, Toronto, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, York University, Toronto, Canada","institution_ids":["https://openalex.org/I192455969"]}]},{"author_position":"last","author":{"id":null,"display_name":"Jianhong Wu","orcid":null},"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, Department of Mathematics and Statistics, York University, Toronto, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics, York University, Toronto, Canada","institution_ids":["https://openalex.org/I192455969"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5057620086"],"corresponding_institution_ids":["https://openalex.org/I81605866"],"apc_list":null,"apc_paid":null,"fwci":0.8434,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.7515824,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"33","issue":"11","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/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9955000281333923,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9750000238418579,"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/chaotic","display_name":"Chaotic","score":0.7314602136611938},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.7159572243690491},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.6871606707572937},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6196646094322205},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.5750108361244202},{"id":"https://openalex.org/keywords/transcritical-bifurcation","display_name":"Transcritical bifurcation","score":0.5745763778686523},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.478863924741745},{"id":"https://openalex.org/keywords/biological-applications-of-bifurcation-theory","display_name":"Biological applications of bifurcation theory","score":0.46597597002983093},{"id":"https://openalex.org/keywords/period-doubling-bifurcation","display_name":"Period-doubling bifurcation","score":0.452629953622818},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.42672374844551086},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4237472414970398},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41366010904312134},{"id":"https://openalex.org/keywords/basic-reproduction-number","display_name":"Basic reproduction number","score":0.41221123933792114},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3774828612804413},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19905990362167358},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18139922618865967},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.16576293110847473},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.11646163463592529}],"concepts":[{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.7314602136611938},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.7159572243690491},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.6871606707572937},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6196646094322205},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.5750108361244202},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.5745763778686523},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.478863924741745},{"id":"https://openalex.org/C174914120","wikidata":"https://www.wikidata.org/wiki/Q4914973","display_name":"Biological applications of bifurcation theory","level":5,"score":0.46597597002983093},{"id":"https://openalex.org/C194271172","wikidata":"https://www.wikidata.org/wiki/Q2181373","display_name":"Period-doubling bifurcation","level":4,"score":0.452629953622818},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.42672374844551086},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4237472414970398},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41366010904312134},{"id":"https://openalex.org/C204264503","wikidata":"https://www.wikidata.org/wiki/Q901464","display_name":"Basic reproduction number","level":3,"score":0.41221123933792114},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3774828612804413},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19905990362167358},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18139922618865967},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.16576293110847473},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.11646163463592529},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127423300288","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127423300288","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8600000143051147,"display_name":"Good health and well-being","id":"https://metadata.un.org/sdg/3"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W116939097","https://openalex.org/W1511286968","https://openalex.org/W1535375949","https://openalex.org/W1765463781","https://openalex.org/W1937028141","https://openalex.org/W1985068938","https://openalex.org/W1996995731","https://openalex.org/W2002944058","https://openalex.org/W2008866301","https://openalex.org/W2013322007","https://openalex.org/W2018484210","https://openalex.org/W2022101730","https://openalex.org/W2022774266","https://openalex.org/W2023354629","https://openalex.org/W2033644556","https://openalex.org/W2036374024","https://openalex.org/W2037941375","https://openalex.org/W2039958572","https://openalex.org/W2042391826","https://openalex.org/W2054429774","https://openalex.org/W2057598198","https://openalex.org/W2073532412","https://openalex.org/W2079871064","https://openalex.org/W2082163258","https://openalex.org/W2082901059","https://openalex.org/W2089876099","https://openalex.org/W2090026851","https://openalex.org/W2094003690","https://openalex.org/W2094631910","https://openalex.org/W2104606876","https://openalex.org/W2148301044","https://openalex.org/W2150154539","https://openalex.org/W2303402394","https://openalex.org/W2474672359","https://openalex.org/W2491783108","https://openalex.org/W2523388279","https://openalex.org/W2605543710","https://openalex.org/W2939484461","https://openalex.org/W3102837034","https://openalex.org/W3106120518","https://openalex.org/W3110861178","https://openalex.org/W4239975174","https://openalex.org/W4243174912"],"related_works":["https://openalex.org/W2546487931","https://openalex.org/W2978098199","https://openalex.org/W2054978396","https://openalex.org/W4214875847","https://openalex.org/W2143208590","https://openalex.org/W2751270551","https://openalex.org/W4285005170","https://openalex.org/W3015096850","https://openalex.org/W2087441007","https://openalex.org/W1984861030"],"abstract_inverted_index":{"Dynamic":[0],"behavior":[1],"investigations":[2],"of":[3,13,16,37,53,68,75,96,105,116,124,139,149],"infectious":[4],"disease":[5],"models":[6],"are":[7],"central":[8],"to":[9,49,56,144,156],"improve":[10],"our":[11,42],"understanding":[12],"emerging":[14],"characteristics":[15],"model":[17,26,36,152],"states":[18],"interaction.":[19],"Here,":[20],"we":[21],"consider":[22],"a":[23,28,46,57,106,117],"Susceptible-Infected":[24],"(SI)":[25],"with":[27],"general":[29],"state-dependent":[30,140],"delay,":[31],"which":[32],"covers":[33],"an":[34],"immuno-epidemiological":[35],"pathogen":[38],"transmission,":[39],"developed":[40],"in":[41,61,92],"early":[43],"study,":[44],"using":[45],"threshold":[47],"delay":[48],"examine":[50],"the":[51,62,66,79,93,97,103,114,121,125,131,137,147,150],"effects":[52],"multiple":[54],"exposures":[55],"pathogen.":[58],"The":[59,90],"analysis":[60],"previous":[63],"work":[64],"showed":[65],"appearance":[67],"forward":[69],"as":[70,72],"well":[71],"backward":[73,126],"bifurcations":[74],"endemic":[76],"equilibria":[77],"when":[78],"basic":[80],"reproductive":[81],"ratio":[82],"[Formula:":[83],"see":[84],"text]":[85],"is":[86,142],"less":[87],"than":[88],"unity.":[89],"analysis,":[91],"present":[94],"work,":[95],"endemically":[98],"infected":[99],"equilibrium":[100],"behavior,":[101],"through":[102],"study":[104],"second":[107],"order":[108],"exponential":[109],"polynomial":[110],"characteristic":[111],"equation,":[112],"concludes":[113],"existence":[115],"Hopf":[118],"bifurcation":[119,127],"on":[120],"upper":[122],"branch":[123],"diagram":[128],"and":[129,153,162],"gives":[130],"criteria":[132],"for":[133],"stability":[134],"switches.":[135],"Furthermore,":[136],"inclusion":[138],"delays":[141],"shown":[143],"entirely":[145],"change":[146],"dynamics":[148],"SI":[151],"give":[154],"rise":[155],"rich":[157],"behaviors":[158],"including":[159],"periodic,":[160],"torus":[161],"chaotic":[163],"dynamics.":[164]},"counts_by_year":[{"year":2025,"cited_by_count":3}],"updated_date":"2026-04-28T14:05:53.105641","created_date":"2025-10-10T00:00:00"}