{"id":"https://openalex.org/W7127269763","doi":"https://doi.org/10.1007/s12190-026-02765-4","title":"How delay, isolation and vaccination shape epidemic waves: a bifurcation approach in mathematical epidemiology","display_name":"How delay, isolation and vaccination shape epidemic waves: a bifurcation approach in mathematical epidemiology","publication_year":2026,"publication_date":"2026-02-03","ids":{"openalex":"https://openalex.org/W7127269763","doi":"https://doi.org/10.1007/s12190-026-02765-4"},"language":"en","primary_location":{"id":"doi:10.1007/s12190-026-02765-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s12190-026-02765-4","pdf_url":null,"source":{"id":"https://openalex.org/S199913245","display_name":"Journal of Applied Mathematics and Computing","issn_l":"1226-0061","issn":["1226-0061","1229-9499","1229-9502","1598-5865","1865-2085"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-05563554/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5123815351","display_name":"Mehdi Bouziane","orcid":null},"institutions":[{"id":"https://openalex.org/I177657909","display_name":"Universit\u00e9 de Mostaganem","ror":"https://ror.org/052r04325","country_code":"DZ","type":"education","lineage":["https://openalex.org/I177657909"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Mehdi Bouziane","raw_affiliation_strings":["Department of Mathematics, Higher Normal School of Mostaganem, Mostaganem, 27000, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Higher Normal School of Mostaganem, Mostaganem, 27000, Algeria","institution_ids":["https://openalex.org/I177657909"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124942206","display_name":"Silia Bercisse","orcid":null},"institutions":[{"id":"https://openalex.org/I233209018","display_name":"University of Abou Bekr Belka\u00efd","ror":"https://ror.org/00jsjm362","country_code":"DZ","type":"education","lineage":["https://openalex.org/I233209018"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Silia Bercisse","raw_affiliation_strings":["Laboratoire d\u2019Analyse Nonlin\u00e9aire et Math\u00e9matiques Appliqu\u00e9es, University of Tlemcen, Tlemcen, 13000, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire d\u2019Analyse Nonlin\u00e9aire et Math\u00e9matiques Appliqu\u00e9es, University of Tlemcen, Tlemcen, 13000, Algeria","institution_ids":["https://openalex.org/I233209018"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124242175","display_name":"Abdennasser Chekroun","orcid":null},"institutions":[{"id":"https://openalex.org/I233209018","display_name":"University of Abou Bekr Belka\u00efd","ror":"https://ror.org/00jsjm362","country_code":"DZ","type":"education","lineage":["https://openalex.org/I233209018"]}],"countries":["DZ"],"is_corresponding":true,"raw_author_name":"Abdennasser Chekroun","raw_affiliation_strings":["Laboratoire d\u2019Analyse Nonlin\u00e9aire et Math\u00e9matiques Appliqu\u00e9es, University of Tlemcen, Tlemcen, 13000, Algeria"],"raw_orcid":"https://orcid.org/0000-0001-9245-3274","affiliations":[{"raw_affiliation_string":"Laboratoire d\u2019Analyse Nonlin\u00e9aire et Math\u00e9matiques Appliqu\u00e9es, University of Tlemcen, Tlemcen, 13000, Algeria","institution_ids":["https://openalex.org/I233209018"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041571508","display_name":"Simon Girel","orcid":"https://orcid.org/0000-0001-5154-6327"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210112930","display_name":"Laboratoire Jean-Alexandre Dieudonn\u00e9","ror":"https://ror.org/0274zdr66","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I201841394","https://openalex.org/I4210112930","https://openalex.org/I4210141950"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Simon Girel","raw_affiliation_strings":["Laboratoire J.A.Dieudonn\u00e9, Universit\u00e9 C\u00f4te d\u2019Azur, UMR CNRS-UNS 7351, Nice, 06000, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire J.A.Dieudonn\u00e9, Universit\u00e9 C\u00f4te d\u2019Azur, UMR CNRS-UNS 7351, Nice, 06000, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210112930"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5124242175"],"corresponding_institution_ids":["https://openalex.org/I233209018"],"apc_list":{"value":3390,"currency":"USD","value_usd":3390},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08583932,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"72","issue":"3","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":0.9035999774932861,"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":0.9035999774932861,"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/T10410","display_name":"COVID-19 epidemiological studies","score":0.06939999759197235,"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/T11764","display_name":"Evolution and Genetic Dynamics","score":0.005100000184029341,"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/epidemic-model","display_name":"Epidemic model","score":0.7006999850273132},{"id":"https://openalex.org/keywords/basic-reproduction-number","display_name":"Basic reproduction number","score":0.6384999752044678},{"id":"https://openalex.org/keywords/isolation","display_name":"Isolation (microbiology)","score":0.5921000242233276},{"id":"https://openalex.org/keywords/vaccination","display_name":"Vaccination","score":0.5383999943733215},{"id":"https://openalex.org/keywords/distancing","display_name":"Distancing","score":0.5297999978065491},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5027999877929688},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4925000071525574},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4584999978542328},{"id":"https://openalex.org/keywords/stability-theory","display_name":"Stability theory","score":0.44859999418258667}],"concepts":[{"id":"https://openalex.org/C1627819","wikidata":"https://www.wikidata.org/wiki/Q2572354","display_name":"Epidemic model","level":3,"score":0.7006999850273132},{"id":"https://openalex.org/C204264503","wikidata":"https://www.wikidata.org/wiki/Q901464","display_name":"Basic reproduction number","level":3,"score":0.6384999752044678},{"id":"https://openalex.org/C2775941552","wikidata":"https://www.wikidata.org/wiki/Q25212305","display_name":"Isolation (microbiology)","level":2,"score":0.5921000242233276},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.565500020980835},{"id":"https://openalex.org/C22070199","wikidata":"https://www.wikidata.org/wiki/Q192995","display_name":"Vaccination","level":2,"score":0.5383999943733215},{"id":"https://openalex.org/C31957729","wikidata":"https://www.wikidata.org/wiki/Q5282877","display_name":"Distancing","level":5,"score":0.5297999978065491},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5027999877929688},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49570000171661377},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4925000071525574},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4584999978542328},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.44859999418258667},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.44359999895095825},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.42559999227523804},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.4092999994754791},{"id":"https://openalex.org/C2992243407","wikidata":"https://www.wikidata.org/wiki/Q525512","display_name":"Disease transmission","level":2,"score":0.40220001339912415},{"id":"https://openalex.org/C2781402358","wikidata":"https://www.wikidata.org/wiki/Q182899","display_name":"Quarantine","level":2,"score":0.40119999647140503},{"id":"https://openalex.org/C55610538","wikidata":"https://www.wikidata.org/wiki/Q1502581","display_name":"Transcritical bifurcation","level":5,"score":0.38260000944137573},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.3562999963760376},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.34790000319480896},{"id":"https://openalex.org/C2983030100","wikidata":"https://www.wikidata.org/wiki/Q638328","display_name":"Nonlinear dynamical systems","level":3,"score":0.32089999318122864},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30090001225471497},{"id":"https://openalex.org/C59659247","wikidata":"https://www.wikidata.org/wiki/Q11990","display_name":"Reproduction","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26739999651908875},{"id":"https://openalex.org/C524204448","wikidata":"https://www.wikidata.org/wiki/Q788926","display_name":"Infectious disease (medical specialty)","level":3,"score":0.26739999651908875},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.25540000200271606},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.2549999952316284},{"id":"https://openalex.org/C89623803","wikidata":"https://www.wikidata.org/wiki/Q12184","display_name":"Pandemic","level":5,"score":0.2538999915122986}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s12190-026-02765-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s12190-026-02765-4","pdf_url":null,"source":{"id":"https://openalex.org/S199913245","display_name":"Journal of Applied Mathematics and Computing","issn_l":"1226-0061","issn":["1226-0061","1229-9499","1229-9502","1598-5865","1865-2085"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics and Computing","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-05563554v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05563554","pdf_url":"https://hal.science/hal-05563554/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics and Computing, 2026, 72 (3), pp.112. ⟨10.1007/s12190-026-02765-4⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-05563554v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05563554","pdf_url":"https://hal.science/hal-05563554/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics and Computing, 2026, 72 (3), pp.112. ⟨10.1007/s12190-026-02765-4⟩","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"score":0.8196729421615601,"id":"https://metadata.un.org/sdg/3","display_name":"Good health and well-being"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7127269763.pdf","grobid_xml":"https://content.openalex.org/works/W7127269763.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W2000953228","https://openalex.org/W2012831684","https://openalex.org/W2014133043","https://openalex.org/W2018214960","https://openalex.org/W2034471702","https://openalex.org/W2040554560","https://openalex.org/W2041572706","https://openalex.org/W2045913546","https://openalex.org/W2083225775","https://openalex.org/W2085326283","https://openalex.org/W2090695500","https://openalex.org/W2094534930","https://openalex.org/W2102610172","https://openalex.org/W2112680994","https://openalex.org/W2127435093","https://openalex.org/W2144803946","https://openalex.org/W2161728228","https://openalex.org/W2217328210","https://openalex.org/W2313603370","https://openalex.org/W2341199367","https://openalex.org/W2555815256","https://openalex.org/W2725216843","https://openalex.org/W2796024571","https://openalex.org/W2809129701","https://openalex.org/W2898447963","https://openalex.org/W2978577943","https://openalex.org/W2994322671","https://openalex.org/W3018691224","https://openalex.org/W3049738036","https://openalex.org/W3126478997","https://openalex.org/W3128418047","https://openalex.org/W3157022736","https://openalex.org/W4211202937","https://openalex.org/W4225837764","https://openalex.org/W4290805532","https://openalex.org/W4292156591","https://openalex.org/W4362601378","https://openalex.org/W4390904382","https://openalex.org/W4405999586","https://openalex.org/W4406110287","https://openalex.org/W4408011546","https://openalex.org/W4415694631"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2026-02-04T00:00:00"}