{"id":"https://openalex.org/W2800687609","doi":"https://doi.org/10.1155/2018/6801475","title":"A Fractional-Order Model for HIV Dynamics in a Two-Sex Population","display_name":"A Fractional-Order Model for HIV Dynamics in a Two-Sex Population","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2800687609","doi":"https://doi.org/10.1155/2018/6801475","mag":"2800687609"},"language":"en","primary_location":{"id":"doi:10.1155/2018/6801475","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2018/6801475","pdf_url":"http://downloads.hindawi.com/journals/ijmms/2018/6801475.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://downloads.hindawi.com/journals/ijmms/2018/6801475.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Fatmawati","orcid":"https://orcid.org/0000-0002-3562-6789"},"institutions":[{"id":"https://openalex.org/I205133468","display_name":"Airlangga University","ror":"https://ror.org/04ctejd88","country_code":"ID","type":"education","lineage":["https://openalex.org/I205133468"]}],"countries":["ID"],"is_corresponding":true,"raw_author_name":"Fatmawati","raw_affiliation_strings":["Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya 60115, Indonesia"],"raw_orcid":"https://orcid.org/0000-0002-3562-6789","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya 60115, Indonesia","institution_ids":["https://openalex.org/I205133468"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001791760","display_name":"Endrik Mifta Shaiful","orcid":null},"institutions":[{"id":"https://openalex.org/I205133468","display_name":"Airlangga University","ror":"https://ror.org/04ctejd88","country_code":"ID","type":"education","lineage":["https://openalex.org/I205133468"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Endrik Mifta Shaiful","raw_affiliation_strings":["Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya 60115, Indonesia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya 60115, Indonesia","institution_ids":["https://openalex.org/I205133468"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091060348","display_name":"Mohammad Imam Utoyo","orcid":"https://orcid.org/0000-0003-2292-8443"},"institutions":[{"id":"https://openalex.org/I205133468","display_name":"Airlangga University","ror":"https://ror.org/04ctejd88","country_code":"ID","type":"education","lineage":["https://openalex.org/I205133468"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Mohammad Imam Utoyo","raw_affiliation_strings":["Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya 60115, Indonesia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya 60115, Indonesia","institution_ids":["https://openalex.org/I205133468"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I205133468"],"apc_list":{"value":1050,"currency":"USD","value_usd":1050},"apc_paid":{"value":1050,"currency":"USD","value_usd":1050},"fwci":5.1783,"has_fulltext":true,"cited_by_count":48,"citation_normalized_percentile":{"value":0.95665571,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"2018","issue":null,"first_page":"1","last_page":"11"},"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":0.9994999766349792,"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":0.9994999766349792,"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":0.9994000196456909,"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/T11020","display_name":"Immune Cell Function and Interaction","score":0.9222999811172485,"subfield":{"id":"https://openalex.org/subfields/2403","display_name":"Immunology"},"field":{"id":"https://openalex.org/fields/24","display_name":"Immunology and Microbiology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.6151266694068909},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5939145088195801},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.588071346282959},{"id":"https://openalex.org/keywords/human-immunodeficiency-virus","display_name":"Human immunodeficiency virus (HIV)","score":0.56728196144104},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49571073055267334},{"id":"https://openalex.org/keywords/basic-reproduction-number","display_name":"Basic reproduction number","score":0.4852325916290283},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.44707953929901123},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43533459305763245},{"id":"https://openalex.org/keywords/antiretroviral-therapy","display_name":"Antiretroviral therapy","score":0.43411219120025635},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.4148736298084259},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38527053594589233},{"id":"https://openalex.org/keywords/demography","display_name":"Demography","score":0.37674853205680847},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.3712407946586609},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.357864648103714},{"id":"https://openalex.org/keywords/immunology","display_name":"Immunology","score":0.34045112133026123},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28931209444999695},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.1725407838821411},{"id":"https://openalex.org/keywords/viral-load","display_name":"Viral load","score":0.1510465145111084}],"concepts":[{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.6151266694068909},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5939145088195801},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.588071346282959},{"id":"https://openalex.org/C3013748606","wikidata":"https://www.wikidata.org/wiki/Q15787","display_name":"Human immunodeficiency virus (HIV)","level":2,"score":0.56728196144104},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49571073055267334},{"id":"https://openalex.org/C204264503","wikidata":"https://www.wikidata.org/wiki/Q901464","display_name":"Basic reproduction number","level":3,"score":0.4852325916290283},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.44707953929901123},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43533459305763245},{"id":"https://openalex.org/C2993143319","wikidata":"https://www.wikidata.org/wiki/Q583050","display_name":"Antiretroviral therapy","level":4,"score":0.43411219120025635},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.4148736298084259},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38527053594589233},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.37674853205680847},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.3712407946586609},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.357864648103714},{"id":"https://openalex.org/C203014093","wikidata":"https://www.wikidata.org/wiki/Q101929","display_name":"Immunology","level":1,"score":0.34045112133026123},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28931209444999695},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.1725407838821411},{"id":"https://openalex.org/C142462285","wikidata":"https://www.wikidata.org/wiki/Q2528140","display_name":"Viral load","level":3,"score":0.1510465145111084},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2018/6801475","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2018/6801475","pdf_url":"http://downloads.hindawi.com/journals/ijmms/2018/6801475.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:repository.unair.ac.id:114279","is_oa":false,"landing_page_url":"https://repository.unair.ac.id/114279/1/C15.%20Fulltext.pdf","pdf_url":"https://repository.unair.ac.id/114279/1/C15.%20Fulltext.pdf","source":{"id":"https://openalex.org/S4306400777","display_name":"Universitas Airlangga Repository (Universitas Airlangga)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205133468","host_organization_name":"Airlangga University","host_organization_lineage":["https://openalex.org/I205133468"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:RePEc:hin:jijmms:6801475","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2018/6801475.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:45800a1ed28f4ae2b33563507c13fe0e","is_oa":true,"landing_page_url":"https://doaj.org/article/45800a1ed28f4ae2b33563507c13fe0e","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2018 (2018)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2018/6801475","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2018/6801475","pdf_url":"http://downloads.hindawi.com/journals/ijmms/2018/6801475.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/3","score":0.8799999952316284,"display_name":"Good health and well-being"}],"awards":[{"id":"https://openalex.org/G2079663999","display_name":null,"funder_award_id":"569/UN3/2017","funder_id":"https://openalex.org/F4320325143","funder_display_name":"Universitas Airlangga"}],"funders":[{"id":"https://openalex.org/F4320325143","display_name":"Universitas Airlangga","ror":"https://ror.org/04ctejd88"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2800687609.pdf","grobid_xml":"https://content.openalex.org/works/W2800687609.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1198550170","https://openalex.org/W1963581131","https://openalex.org/W1966674224","https://openalex.org/W1976777314","https://openalex.org/W1978349032","https://openalex.org/W2002216072","https://openalex.org/W2028301294","https://openalex.org/W2036442409","https://openalex.org/W2041572706","https://openalex.org/W2102798763","https://openalex.org/W2112680994","https://openalex.org/W2154271572","https://openalex.org/W2328420549","https://openalex.org/W2567013741","https://openalex.org/W2591254227","https://openalex.org/W2616206390","https://openalex.org/W2622539902","https://openalex.org/W2755562380","https://openalex.org/W4247953052","https://openalex.org/W4249481540","https://openalex.org/W4253062931"],"related_works":["https://openalex.org/W2082446734","https://openalex.org/W4313560640","https://openalex.org/W2253351617","https://openalex.org/W4246784705","https://openalex.org/W3121927021","https://openalex.org/W2089892488","https://openalex.org/W2416906960","https://openalex.org/W2050580331","https://openalex.org/W3049300385","https://openalex.org/W2006097873"],"abstract_inverted_index":{"Human":[0],"Immunodeficiency":[1,21],"Virus":[2],"(HIV)":[3],"is":[4,24,33,58,97,127],"a":[5,75],"virus":[6],"that":[7,16],"attacks":[8],"or":[9],"infects":[10],"cells":[11],"in":[12,41,67,98],"the":[13,25,34,42,49,62,65,68,79,95,99,109,115,118,121,131,135,138,152,155,159],"immune":[14,18],"system":[15],"causes":[17],"decline.":[19],"Acquired":[20],"Syndrome":[22],"(AIDS)":[23],"most":[26],"severe":[27],"stage":[28],"of":[29,44,55,64,78,81,94,117,120,151,154,161],"HIV":[30,82],"infection.":[31],"AIDS":[32,84],"rapidly":[35],"spreading":[36],"and":[37,83,113,169],"becoming":[38],"epidemic":[39],"diseases":[40,66,85],"world":[43],"almost":[45],"complete":[46],"influence":[47],"across":[48],"country.":[50],"A":[51],"mathematical":[52],"model":[53,77,96],"approach":[54],"HIV/AIDS":[56],"dynamic":[57],"needed":[59],"to":[60,129],"predict":[61],"spread":[63,80],"future.":[69],"In":[70],"this":[71],"paper,":[72],"we":[73,142],"presented":[74],"fractional-order":[76],"which":[86],"incorporates":[87],"two-sex":[88],"population.":[89],"The":[90,123],"fractional":[91,156],"derivative":[92],"order":[93,153],"interval":[100],"<mml:math":[101],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[102],"id=\"M1\"><mml:mo":[103],"stretchy=\"false\">(</mml:mo><mml:mn":[104],"fontstyle=\"italic\">0,1</mml:mn><mml:mo":[105],"stretchy=\"false\">]</mml:mo></mml:math>.":[106],"We":[107],"compute":[108],"basic":[110],"reproduction":[111],"number":[112],"prove":[114],"stability":[116],"equilibriums":[119],"model.":[122],"sensitivity":[124],"analysis":[125],"also":[126],"done":[128],"determine":[130],"important":[132],"factor":[133],"controlling":[134],"spread.":[136],"Using":[137],"Adams-type":[139],"predictor-corrector":[140],"method,":[141],"then":[143],"perform":[144],"some":[145],"numerical":[146,172],"simulations":[147],"for":[148],"variation":[149],"values":[150],"derivative.":[157],"Finally,":[158],"effects":[160],"various":[162],"antiretroviral":[163],"therapy":[164],"(ART)":[165],"treatments":[166],"are":[167],"studied":[168],"compared":[170],"with":[171],"approach.":[173]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":1}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}
