{"id":"https://openalex.org/W3082045716","doi":"https://doi.org/10.1109/embc44109.2020.9176529","title":"Using Pad\u00e9 Approximant Method to Solve the Mathematical Model of Tumor-Immune Interactions","display_name":"Using Pad\u00e9 Approximant Method to Solve the Mathematical Model of Tumor-Immune Interactions","publication_year":2020,"publication_date":"2020-07-01","ids":{"openalex":"https://openalex.org/W3082045716","doi":"https://doi.org/10.1109/embc44109.2020.9176529","mag":"3082045716","pmid":"https://pubmed.ncbi.nlm.nih.gov/33018506"},"language":"en","primary_location":{"id":"doi:10.1109/embc44109.2020.9176529","is_oa":false,"landing_page_url":"https://doi.org/10.1109/embc44109.2020.9176529","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 42nd Annual International Conference of the IEEE Engineering in Medicine &amp; Biology Society (EMBC)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5050144413","display_name":"Hesham A. Elkaranshawy","orcid":"https://orcid.org/0000-0002-0616-1732"},"institutions":[{"id":"https://openalex.org/I84524832","display_name":"Alexandria University","ror":"https://ror.org/00mzz1w90","country_code":"EG","type":"education","lineage":["https://openalex.org/I84524832"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Hesham A. Elkaranshawy","raw_affiliation_strings":["Department of Engineering Mathematics and Physics, Alexandria University, Alexandria, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Engineering Mathematics and Physics, Alexandria University, Alexandria, Egypt","institution_ids":["https://openalex.org/I84524832"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006421218","display_name":"Ahmed M. Makhlouf","orcid":"https://orcid.org/0000-0002-5538-3737"},"institutions":[{"id":"https://openalex.org/I84524832","display_name":"Alexandria University","ror":"https://ror.org/00mzz1w90","country_code":"EG","type":"education","lineage":["https://openalex.org/I84524832"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Ahmed M. Makhlouf","raw_affiliation_strings":["Department of Engineering Mathematics and Physics, Alexandria University, Alexandria, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Engineering Mathematics and Physics, Alexandria University, Alexandria, Egypt","institution_ids":["https://openalex.org/I84524832"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090783556","display_name":"Yasmine Abouelseoud","orcid":"https://orcid.org/0000-0002-8888-7309"},"institutions":[{"id":"https://openalex.org/I84524832","display_name":"Alexandria University","ror":"https://ror.org/00mzz1w90","country_code":"EG","type":"education","lineage":["https://openalex.org/I84524832"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Yasmine Abouelseoud","raw_affiliation_strings":["Department of Engineering Mathematics and Physics, Alexandria University, Alexandria, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Engineering Mathematics and Physics, Alexandria University, Alexandria, Egypt","institution_ids":["https://openalex.org/I84524832"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I84524832"],"apc_list":null,"apc_paid":null,"fwci":0.0698,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.45290664,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"4","issue":null,"first_page":"2467","last_page":"2470"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9998000264167786,"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":0.9998000264167786,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9925000071525574,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9603999853134155,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/convergence","display_name":"Convergence (economics)","score":0.7221028804779053},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.6789377927780151},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.664008617401123},{"id":"https://openalex.org/keywords/radius-of-convergence","display_name":"Radius of convergence","score":0.6622360944747925},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5634429454803467},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5487162470817566},{"id":"https://openalex.org/keywords/pad\u00e9-approximant","display_name":"Pad\u00e9 approximant","score":0.5423551201820374},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5364044308662415},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5321490168571472},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5105627775192261},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5049565434455872},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4388176202774048},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3370937705039978},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33682531118392944},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09573131799697876}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7221028804779053},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.6789377927780151},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.664008617401123},{"id":"https://openalex.org/C155568369","wikidata":"https://www.wikidata.org/wiki/Q1428097","display_name":"Radius of convergence","level":3,"score":0.6622360944747925},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5634429454803467},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5487162470817566},{"id":"https://openalex.org/C153150388","wikidata":"https://www.wikidata.org/wiki/Q2452504","display_name":"Pad\u00e9 approximant","level":2,"score":0.5423551201820374},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5364044308662415},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5321490168571472},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5105627775192261},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5049565434455872},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4388176202774048},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3370937705039978},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33682531118392944},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09573131799697876},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D002452","descriptor_name":"Cell Count","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D002452","descriptor_name":"Cell Count","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D002452","descriptor_name":"Cell Count","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D009369","descriptor_name":"Neoplasms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D009369","descriptor_name":"Neoplasms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D009369","descriptor_name":"Neoplasms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1109/embc44109.2020.9176529","is_oa":false,"landing_page_url":"https://doi.org/10.1109/embc44109.2020.9176529","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 42nd Annual International Conference of the IEEE Engineering in Medicine &amp; Biology Society (EMBC)","raw_type":"proceedings-article"},{"id":"pmid:33018506","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33018506","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W634523187","https://openalex.org/W1588906117","https://openalex.org/W1791346221","https://openalex.org/W1970191127","https://openalex.org/W2020122130","https://openalex.org/W2029159090","https://openalex.org/W2040837794","https://openalex.org/W2099571909","https://openalex.org/W2147342239","https://openalex.org/W2173951735","https://openalex.org/W2203267712","https://openalex.org/W2498647973","https://openalex.org/W2510594548","https://openalex.org/W2775828860","https://openalex.org/W2900046418","https://openalex.org/W2963602500","https://openalex.org/W2973039712","https://openalex.org/W3007695633","https://openalex.org/W4243974290","https://openalex.org/W6638224975","https://openalex.org/W6767391537"],"related_works":["https://openalex.org/W2377017989","https://openalex.org/W2059145352","https://openalex.org/W2485604075","https://openalex.org/W2349056005","https://openalex.org/W2595118608","https://openalex.org/W2014356728","https://openalex.org/W2142001093","https://openalex.org/W2359656545","https://openalex.org/W602427772","https://openalex.org/W4240355644"],"abstract_inverted_index":{"A":[0],"mathematical":[1],"model,":[2],"in":[3],"the":[4,16,60,91,115,120],"form":[5],"of":[6,9,54,93,105,117],"a":[7,51,78,102,128,133],"system":[8,35,92],"nonlinear":[10,39],"ordinary":[11],"differential":[12],"equations,":[13],"that":[14],"describes":[15],"interaction":[17,61],"between":[18],"tumor":[19],"cells":[20,24],"and":[21,131],"effective":[22],"immune":[23],"is":[25,45,74,111,125],"proposed.":[26],"An":[27],"exact":[28],"solution":[29,44,48,100,124],"cannot":[30],"be":[31,57],"found":[32],"to":[33,56,66,76,89,95,113],"this":[34,82,99],"like":[36],"many":[37,64],"other":[38],"systems.":[40],"Yet,":[41],"approximate":[42,122],"analytical":[43,123],"explored.":[46],"This":[47],"should":[49],"have":[50],"large":[52,129],"interval":[53,130],"convergence":[55],"acceptable":[58],"because":[59],"can":[62],"take":[63],"days":[65],"reach":[67],"its":[68],"steady":[69],"state.":[70],"Power":[71],"series":[72,79],"method":[73,110],"used":[75,88,112],"obtain":[77],"solution.":[80,140],"In":[81],"process,":[83],"some":[84],"auxiliary":[85],"variables":[86],"are":[87],"transform":[90],"equations":[94],"polynomial":[96],"form.":[97],"However,":[98],"has":[101,132],"small":[103],"radius":[104],"convergence,":[106],"therefore,":[107],"Pad\u00e9":[108],"approximant":[109],"extend":[114],"domain":[116],"convergence.":[118],"Hence,":[119],"obtained":[121],"valid":[126],"over":[127],"remarkable":[134],"accuracy":[135],"when":[136],"compared":[137],"with":[138],"numerical":[139]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
