{"id":"https://openalex.org/W7127045265","doi":"https://doi.org/10.53391/2791-8564.1012","title":"Analysis and numerical investigation of a breast cancer treatment model incorporating ketogenic diet and immune boosters via optimal control theory","display_name":"Analysis and numerical investigation of a breast cancer treatment model incorporating ketogenic diet and immune boosters via optimal control theory","publication_year":2025,"publication_date":"2025-12-31","ids":{"openalex":"https://openalex.org/W7127045265","doi":"https://doi.org/10.53391/2791-8564.1012"},"language":"en","primary_location":{"id":"doi:10.53391/2791-8564.1012","doi":"https://doi.org/10.53391/2791-8564.1012","is_oa":true,"landing_page_url":"https://doi.org/10.53391/2791-8564.1012","pdf_url":"https://mmnsa.researchcommons.org/cgi/viewcontent.cgi?article=1012&context=journal","source":{"id":"https://openalex.org/S4386621915","display_name":"Mathematical Modelling and Numerical Simulation with Applications","issn_l":"2791-8564","issn":["2791-8564"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["tr-dizin"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Modelling and Numerical Simulation with Applications","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://mmnsa.researchcommons.org/cgi/viewcontent.cgi?article=1012&context=journal","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5116736755","display_name":"Kunnisai Muniroh","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I177055848","display_name":"University of Brawijaya","ror":"https://ror.org/01wk3d929","country_code":"ID","type":"education","lineage":["https://openalex.org/I177055848"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Kunnisai Muniroh","raw_affiliation_strings":["Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang, Indonesia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang, Indonesia","institution_ids":["https://openalex.org/I177055848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020035450","display_name":"Ummu Habibah","orcid":"https://orcid.org/0000-0002-9460-6374","observed_orcids":["https://orcid.org/0000-0002-9460-6374"]},"institutions":[{"id":"https://openalex.org/I177055848","display_name":"University of Brawijaya","ror":"https://ror.org/01wk3d929","country_code":"ID","type":"education","lineage":["https://openalex.org/I177055848"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Ummu Habibah","raw_affiliation_strings":["Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang, Indonesia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang, Indonesia","institution_ids":["https://openalex.org/I177055848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061505393","display_name":"Wuryansari Muharini Kusumawinahyu","orcid":"https://orcid.org/0000-0001-7307-1537","observed_orcids":["https://orcid.org/0000-0001-7307-1537"]},"institutions":[{"id":"https://openalex.org/I177055848","display_name":"University of Brawijaya","ror":"https://ror.org/01wk3d929","country_code":"ID","type":"education","lineage":["https://openalex.org/I177055848"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Wuryansari Muharini Kusumawinahyu","raw_affiliation_strings":["Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang, Indonesia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang, Indonesia","institution_ids":["https://openalex.org/I177055848"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071552909","display_name":"Nur \u2018Izzati Hamdan","orcid":"https://orcid.org/0000-0002-8333-6153","observed_orcids":["https://orcid.org/0000-0002-8333-6153"]},"institutions":[{"id":"https://openalex.org/I4210138650","display_name":"Universiti Teknologi MARA System","ror":"https://ror.org/030847t23","country_code":"MY","type":"education","lineage":["https://openalex.org/I4210138650","https://openalex.org/I82724352"]},{"id":"https://openalex.org/I82724352","display_name":"Universiti Teknologi MARA","ror":"https://ror.org/05n8tts92","country_code":"MY","type":"education","lineage":["https://openalex.org/I82724352"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Nur\u2019Izzati Hamdan","raw_affiliation_strings":["Faculty of Computer and Mathematical Sciences, University of MARA Technology, Selangor, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Computer and Mathematical Sciences, University of MARA Technology, Selangor, Malaysia","institution_ids":["https://openalex.org/I4210138650","https://openalex.org/I82724352"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.51795047,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"5","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":1.0,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.0,"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/T10336","display_name":"Cancer Cells and Metastasis","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2730","display_name":"Oncology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/breast-cancer","display_name":"breast cancer","score":0.953000009059906},{"id":"https://openalex.org/keywords/tumor-immune-interactions","display_name":"tumor-immune interactions","score":0.765999972820282},{"id":"https://openalex.org/keywords/ketogenic-diet","display_name":"ketogenic diet","score":0.9929999709129333},{"id":"https://openalex.org/keywords/immune-booster","display_name":"immune booster","score":0.9769999980926514},{"id":"https://openalex.org/keywords/cancer-treatment-optimization","display_name":"cancer treatment optimization","score":0.7730000019073486},{"id":"https://openalex.org/keywords/optimal-control","display_name":"optimal control","score":0.8859999775886536},{"id":"https://openalex.org/keywords/pontryagin-s-maximum-principle","display_name":"Pontryagin maximum principle","score":0.8399999737739563},{"id":"https://openalex.org/keywords/treatment-cost-minimization","display_name":"treatment cost minimization","score":0.6359999775886536},{"id":"https://openalex.org/keywords/tumor-growth-inhibition","display_name":"tumor growth inhibition","score":0.6499999761581421},{"id":"https://openalex.org/keywords/immune-enhancement","display_name":"immune enhancement","score":0.5669999718666077}],"concepts":[{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.7411999702453613},{"id":"https://openalex.org/C530470458","wikidata":"https://www.wikidata.org/wiki/Q128581","display_name":"Breast cancer","level":3,"score":0.6880999803543091},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49950000643730164},{"id":"https://openalex.org/C8891405","wikidata":"https://www.wikidata.org/wiki/Q1059","display_name":"Immune system","level":2,"score":0.4731000065803528},{"id":"https://openalex.org/C3019816032","wikidata":"https://www.wikidata.org/wiki/Q2575340","display_name":"Cancer treatment","level":3,"score":0.45820000767707825},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4569000005722046},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.42820000648498535},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4196000099182129},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.4083999991416931},{"id":"https://openalex.org/C2778587478","wikidata":"https://www.wikidata.org/wiki/Q1070684","display_name":"Ketogenic diet","level":3,"score":0.40689998865127563},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4041000008583069},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.3984000086784363},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3479999899864197},{"id":"https://openalex.org/C121608353","wikidata":"https://www.wikidata.org/wiki/Q12078","display_name":"Cancer","level":2,"score":0.3375999927520752},{"id":"https://openalex.org/C186394612","wikidata":"https://www.wikidata.org/wiki/Q7098942","display_name":"Optimal design","level":2,"score":0.31200000643730164},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3086000084877014},{"id":"https://openalex.org/C143998085","wikidata":"https://www.wikidata.org/wiki/Q162555","display_name":"Oncology","level":1,"score":0.29190000891685486},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.2849999964237213},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C2982822547","wikidata":"https://www.wikidata.org/wiki/Q179661","display_name":"Medical treatment","level":2,"score":0.2727000117301941},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26759999990463257},{"id":"https://openalex.org/C39425265","wikidata":"https://www.wikidata.org/wiki/Q7098944","display_name":"Optimal estimation","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C204495892","wikidata":"https://www.wikidata.org/wiki/Q1798304","display_name":"Linear-quadratic-Gaussian control","level":3,"score":0.26330000162124634},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.25999999046325684},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.2581000030040741},{"id":"https://openalex.org/C31010330","wikidata":"https://www.wikidata.org/wiki/Q1914255","display_name":"Maximum principle","level":3,"score":0.2565000057220459},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.25369998812675476}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.53391/2791-8564.1012","doi":"https://doi.org/10.53391/2791-8564.1012","is_oa":true,"landing_page_url":"https://doi.org/10.53391/2791-8564.1012","pdf_url":"https://mmnsa.researchcommons.org/cgi/viewcontent.cgi?article=1012&context=journal","source":{"id":"https://openalex.org/S4386621915","display_name":"Mathematical Modelling and Numerical Simulation with Applications","issn_l":"2791-8564","issn":["2791-8564"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["tr-dizin"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Modelling and Numerical Simulation with Applications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.53391/2791-8564.1012","doi":"https://doi.org/10.53391/2791-8564.1012","is_oa":true,"landing_page_url":"https://doi.org/10.53391/2791-8564.1012","pdf_url":"https://mmnsa.researchcommons.org/cgi/viewcontent.cgi?article=1012&context=journal","source":{"id":"https://openalex.org/S4386621915","display_name":"Mathematical Modelling and Numerical Simulation with Applications","issn_l":"2791-8564","issn":["2791-8564"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["tr-dizin"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Modelling and Numerical Simulation with Applications","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Good health and well-being","id":"https://metadata.un.org/sdg/3","score":0.8371999859809875}],"sustainable_development_goals_aurora":[{"display_name":"Good health and well-being","id":"https://metadata.un.org/sdg/3","score":0.7594215869903564}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7127045265.pdf","grobid_xml":"https://content.openalex.org/works/W7127045265.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"develops":[2],"a":[3,26,81,100,159,174],"mathematical":[4],"model":[5,22],"to":[6,45,121],"investigate":[7],"breast":[8],"cancer":[9,167],"dynamics":[10,169],"by":[11],"incorporating":[12],"tumor\u2013immune":[13],"interactions,":[14],"ketogenic":[15],"diet":[16],"effects,":[17],"and":[18,33,65,86,116,147,161,170],"medical":[19],"treatment.":[20],"The":[21,58,68,138,155],"is":[23,61],"formulated":[24],"as":[25,173],"system":[27,83],"of":[28,84,151],"nonlinear":[29],"ordinary":[30],"differential":[31],"equations":[32],"analyzed":[34],"within":[35],"an":[36],"optimal":[37],"control":[38,41,110],"framework.":[39],"Time-dependent":[40],"variables":[42],"are":[43,73,91,141],"introduced":[44],"represent":[46],"treatment":[47,129,153,168],"strategies":[48,130],"aimed":[49],"at":[50,135],"minimizing":[51],"tumor":[52,114],"progression":[53],"while":[54],"reducing":[55],"therapeutic":[56],"costs.":[57,137],"model\u2019s":[59],"well-posedness":[60],"established":[62],"through":[63],"positivity":[64],"boundedness":[66],"analysis.":[67],"necessary":[69],"conditions":[70],"for":[71,165,176],"optimality":[72],"derived":[74],"using":[75,93],"Pontryagin\u2019s":[76],"Minimum":[77],"Principle,":[78],"resulting":[79],"in":[80],"coupled":[82],"state":[85],"adjoint":[87],"equations.":[88],"Numerical":[89],"solutions":[90],"obtained":[92],"the":[94,108,128,132,144,149],"fourth-order":[95],"Runge\u2013Kutta":[96],"method":[97],"combined":[98],"with":[99,131,143],"forward\u2013backward":[101],"sweep":[102],"algorithm.":[103],"Simulation":[104],"results":[105,146],"demonstrate":[106],"that":[107],"proposed":[109,156],"strategy":[111],"effectively":[112],"suppresses":[113],"growth":[115],"enhances":[117],"immune":[118],"response":[119],"compared":[120],"uncontrolled":[122],"scenarios.":[123],"Cost-effectiveness":[124],"analysis":[125],"also":[126],"shows":[127],"greatest":[133],"impact":[134],"minimum":[136],"numerical":[139],"findings":[140],"consistent":[142],"analytical":[145],"highlight":[148],"importance":[150],"optimized":[152],"scheduling.":[154],"framework":[157],"provides":[158],"reliable":[160],"computationally":[162],"efficient":[163],"approach":[164],"analyzing":[166],"may":[171],"serve":[172],"basis":[175],"further":[177],"extensions":[178],"involving":[179],"parameter":[180],"estimation":[181],"or":[182],"data-driven":[183],"studies.":[184]},"counts_by_year":[],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2026-02-03T00:00:00"}