{"id":"https://openalex.org/W4362669617","doi":"https://doi.org/10.3390/sym15040869","title":"Numerical Simulation for a Hybrid Variable-Order Multi-Vaccination COVID-19 Mathematical Model","display_name":"Numerical Simulation for a Hybrid Variable-Order Multi-Vaccination COVID-19 Mathematical Model","publication_year":2023,"publication_date":"2023-04-06","ids":{"openalex":"https://openalex.org/W4362669617","doi":"https://doi.org/10.3390/sym15040869"},"language":"en","primary_location":{"id":"doi:10.3390/sym15040869","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040869","pdf_url":"https://www.mdpi.com/2073-8994/15/4/869/pdf?version=1680851995","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/4/869/pdf?version=1680851995","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013078094","display_name":"N. H. Sweilam","orcid":"https://orcid.org/0000-0001-7428-5799"},"institutions":[{"id":"https://openalex.org/I145487455","display_name":"Cairo University","ror":"https://ror.org/03q21mh05","country_code":"EG","type":"education","lineage":["https://openalex.org/I145487455"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"Nasser Sweilam","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt"],"raw_orcid":"https://orcid.org/0000-0001-7428-5799","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt","institution_ids":["https://openalex.org/I145487455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051956896","display_name":"Seham M. Al\u2010Mekhlafi","orcid":"https://orcid.org/0000-0003-0351-9679"},"institutions":[{"id":"https://openalex.org/I170535673","display_name":"Sana'a University","ror":"https://ror.org/04hcvaf32","country_code":"YE","type":"education","lineage":["https://openalex.org/I170535673"]},{"id":"https://openalex.org/I186217134","display_name":"Future University in Egypt","ror":"https://ror.org/03s8c2x09","country_code":"EG","type":"education","lineage":["https://openalex.org/I186217134"]}],"countries":["EG","YE"],"is_corresponding":false,"raw_author_name":"Seham Al-Mekhlafi","raw_affiliation_strings":["Department of Engineering Mathematics and Physics, Future University in Egypt, New Cairo 11835, Egypt","Department of Mathematics, Faculty of Education, Sana\u2019a University, Sana\u2019a 1247, Yemen","Department of Mathematics, Faculty of Education, Sana'a University, Sana'a 1247, Yemen"],"raw_orcid":"https://orcid.org/0000-0003-0351-9679","affiliations":[{"raw_affiliation_string":"Department of Engineering Mathematics and Physics, Future University in Egypt, New Cairo 11835, Egypt","institution_ids":["https://openalex.org/I186217134"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Education, Sana\u2019a University, Sana\u2019a 1247, Yemen","institution_ids":["https://openalex.org/I170535673"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Education, Sana'a University, Sana'a 1247, Yemen","institution_ids":["https://openalex.org/I170535673"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037299723","display_name":"R. G. Salama","orcid":null},"institutions":[{"id":"https://openalex.org/I113643904","display_name":"Beni-Suef University","ror":"https://ror.org/05pn4yv70","country_code":"EG","type":"education","lineage":["https://openalex.org/I113643904"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Reem Salama","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef 62521, Egypt","Department of Mathematics, Faculty of Science, Bani Suef University, Bani Suef 62521, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef 62521, Egypt","institution_ids":["https://openalex.org/I113643904"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Bani Suef University, Bani Suef 62521, Egypt","institution_ids":["https://openalex.org/I113643904"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087432269","display_name":"Taghreed A. Assiri","orcid":"https://orcid.org/0000-0003-3911-784X"},"institutions":[{"id":"https://openalex.org/I199693650","display_name":"Umm al-Qura University","ror":"https://ror.org/01xjqrm90","country_code":"SA","type":"education","lineage":["https://openalex.org/I199693650"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Tagreed Assiri","raw_affiliation_strings":["Department of mathematics, Faculty of Science, Umm Al-Qura University, Makkah 21961, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of mathematics, Faculty of Science, Umm Al-Qura University, Makkah 21961, Saudi Arabia","institution_ids":["https://openalex.org/I199693650"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5013078094"],"corresponding_institution_ids":["https://openalex.org/I145487455"],"apc_list":{"value":2400,"currency":"CHF","value_usd":2896},"apc_paid":{"value":2400,"currency":"CHF","value_usd":2896},"fwci":0.8833,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.67034207,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"15","issue":"4","first_page":"869","last_page":"869"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","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/T10288","display_name":"Fractional Differential Equations Solutions","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":0.9900000095367432,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9871000051498413,"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/variable","display_name":"Variable (mathematics)","score":0.673160195350647},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6630924344062805},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6502278447151184},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6400836706161499},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6274011731147766},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5902926325798035},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.48552370071411133},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4777756929397583},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.46415385603904724},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2303028106689453},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22137236595153809}],"concepts":[{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.673160195350647},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6630924344062805},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6502278447151184},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6400836706161499},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6274011731147766},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5902926325798035},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.48552370071411133},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4777756929397583},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.46415385603904724},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2303028106689453},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22137236595153809},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15040869","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040869","pdf_url":"https://www.mdpi.com/2073-8994/15/4/869/pdf?version=1680851995","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:9b8c6cf963394e3c80e8626e19006522","is_oa":false,"landing_page_url":"https://doaj.org/article/9b8c6cf963394e3c80e8626e19006522","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 4, p 869 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/4/869/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15040869","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15040869","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040869","pdf_url":"https://www.mdpi.com/2073-8994/15/4/869/pdf?version=1680851995","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4362669617.pdf","grobid_xml":"https://content.openalex.org/works/W4362669617.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W753712656","https://openalex.org/W2012163408","https://openalex.org/W2017663693","https://openalex.org/W2047140957","https://openalex.org/W2054312336","https://openalex.org/W2090252778","https://openalex.org/W2109958258","https://openalex.org/W2112680994","https://openalex.org/W2158629510","https://openalex.org/W2333047405","https://openalex.org/W2547631474","https://openalex.org/W2806926689","https://openalex.org/W2883589886","https://openalex.org/W2923505959","https://openalex.org/W2981732193","https://openalex.org/W3010137043","https://openalex.org/W3017809401","https://openalex.org/W3025509622","https://openalex.org/W3026872188","https://openalex.org/W3035895679","https://openalex.org/W3091880783","https://openalex.org/W3095034306","https://openalex.org/W3112138040","https://openalex.org/W3126042594","https://openalex.org/W3126540205","https://openalex.org/W3134966583","https://openalex.org/W3135021706","https://openalex.org/W3195631055","https://openalex.org/W3216329696","https://openalex.org/W4220652400","https://openalex.org/W4285009971","https://openalex.org/W4289313745","https://openalex.org/W4296041742","https://openalex.org/W4311955453","https://openalex.org/W6791058119"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W4301247218","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W2129818458","https://openalex.org/W4289551052","https://openalex.org/W2340777379","https://openalex.org/W4390756076","https://openalex.org/W2232781361"],"abstract_inverted_index":{"In":[0],"this":[1,176],"paper,":[2],"a":[3,20,101],"hybrid":[4,14,81],"variable-order":[5,15,25,31,82],"mathematical":[6],"model":[7,48,59,68,90,150,157],"for":[8,86],"multi-vaccination":[9],"COVID-19":[10],"is":[11,17,38,69,84,130,151],"analyzed.":[12],"The":[13,50,71,112],"derivative":[16],"defined":[18],"as":[19],"linear":[21],"combination":[22],"of":[23,27,56,65,79,108,117],"the":[24,30,46,57,63,66,77,80,89,109,118,124,135,148,156,159,162,166],"integral":[26],"Riemann\u2013Liouville":[28],"and":[29,54,114,140],"Caputo":[32],"derivative.":[33],"A":[34],"symmetry":[35],"parameter":[36],"\u03c3":[37],"presented":[39],"in":[40,158,175],"order":[41,126],"to":[42,133],"be":[43,95],"consistent":[44],"with":[45,76,100],"physical":[47],"problem.":[49,91],"existence,":[51],"uniqueness,":[52],"boundedness":[53],"positivity":[55],"proposed":[58,67,119,136,149,167],"are":[60,121,143,169],"given.":[61],"Moreover,":[62,123],"stability":[64,103,115],"discussed.":[70],"theta":[72],"finite":[73],"difference":[74],"method":[75,93,120,129,168],"discretization":[78],"operator":[83],"developed":[85],"solving":[87],"numerically":[88],"This":[92],"can":[94],"explicit":[96],"or":[97],"fully":[98],"implicit":[99],"large":[102],"region":[104],"depending":[105],"on":[106],"values":[107],"factor":[110],"\u0398.":[111],"convergence":[113],"analysis":[116],"proved.":[122],"fourth":[125],"generalized":[127],"Runge\u2013Kutta":[128],"also":[131,152],"used":[132],"study":[134],"model.":[137],"Comparative":[138],"studies":[139],"numerical":[141],"examples":[142],"presented.":[144],"We":[145],"found":[146],"that":[147],"more":[153,170],"general":[154],"than":[155,172],"previous":[160,173],"study;":[161],"results":[163],"obtained":[164],"by":[165],"stable":[171],"research":[174],"area.":[177]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-08-23T07:36:19.812096","created_date":"2025-10-10T00:00:00"}