{"id":"https://openalex.org/W4294344037","doi":"https://doi.org/10.3390/axioms11090446","title":"A Fractional COVID-19 Model with Efficacy of Vaccination","display_name":"A Fractional COVID-19 Model with Efficacy of Vaccination","publication_year":2022,"publication_date":"2022-08-31","ids":{"openalex":"https://openalex.org/W4294344037","doi":"https://doi.org/10.3390/axioms11090446"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11090446","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11090446","pdf_url":"https://www.mdpi.com/2075-1680/11/9/446/pdf?version=1661941298","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/9/446/pdf?version=1661941298","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108819154","display_name":"M. Nandhini","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Nandhini","raw_affiliation_strings":["Department of Mathematics, Coimbatore Institute of Technology, Coimbatore 641014, Tamil Nadu, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Coimbatore Institute of Technology, Coimbatore 641014, Tamil Nadu, India","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081451440","display_name":"R. Lavanya","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R. Lavanya","raw_affiliation_strings":["Department of Mathematics, Coimbatore Institute of Technology, Coimbatore 641014, Tamil Nadu, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Coimbatore Institute of Technology, Coimbatore 641014, Tamil Nadu, India","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074558033","display_name":"Juan J. Nieto","orcid":"https://orcid.org/0000-0001-8202-6578"},"institutions":[{"id":"https://openalex.org/I200284239","display_name":"Universidade de Santiago de Compostela","ror":"https://ror.org/030eybx10","country_code":"ES","type":"education","lineage":["https://openalex.org/I200284239"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Juan J. Nieto","raw_affiliation_strings":["CITMAga, Departamento de Estat\u00edstica, An\u00e1lise Matem\u00e1tica e Optimizaci\u00f3n, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain"],"affiliations":[{"raw_affiliation_string":"CITMAga, Departamento de Estat\u00edstica, An\u00e1lise Matem\u00e1tica e Optimizaci\u00f3n, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain","institution_ids":["https://openalex.org/I200284239"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5074558033"],"corresponding_institution_ids":["https://openalex.org/I200284239"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.6849,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.64345367,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"11","issue":"9","first_page":"446","last_page":"446"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9994999766349792,"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":0.9994999766349792,"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/T10410","display_name":"COVID-19 epidemiological studies","score":0.9976000189781189,"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":0.9943000078201294,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.7371036410331726},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5809566974639893},{"id":"https://openalex.org/keywords/epidemic-model","display_name":"Epidemic model","score":0.5739092826843262},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5713856816291809},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.5327145457267761},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5282909870147705},{"id":"https://openalex.org/keywords/basic-reproduction-number","display_name":"Basic reproduction number","score":0.5261737108230591},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.5242153406143188},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.4759390354156494},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4642390012741089},{"id":"https://openalex.org/keywords/coronavirus-disease-2019","display_name":"Coronavirus disease 2019 (COVID-19)","score":0.4548533260822296},{"id":"https://openalex.org/keywords/vaccination","display_name":"Vaccination","score":0.44530150294303894},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4371243715286255},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.4257148206233978},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40861228108406067},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25884637236595154},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.2344549000263214},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22483697533607483},{"id":"https://openalex.org/keywords/disease","display_name":"Disease","score":0.21042481064796448},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.12137633562088013},{"id":"https://openalex.org/keywords/virology","display_name":"Virology","score":0.10363030433654785},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.08800530433654785},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.0815923810005188}],"concepts":[{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.7371036410331726},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5809566974639893},{"id":"https://openalex.org/C1627819","wikidata":"https://www.wikidata.org/wiki/Q2572354","display_name":"Epidemic model","level":3,"score":0.5739092826843262},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5713856816291809},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5327145457267761},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5282909870147705},{"id":"https://openalex.org/C204264503","wikidata":"https://www.wikidata.org/wiki/Q901464","display_name":"Basic reproduction number","level":3,"score":0.5261737108230591},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.5242153406143188},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.4759390354156494},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4642390012741089},{"id":"https://openalex.org/C3008058167","wikidata":"https://www.wikidata.org/wiki/Q84263196","display_name":"Coronavirus disease 2019 (COVID-19)","level":4,"score":0.4548533260822296},{"id":"https://openalex.org/C22070199","wikidata":"https://www.wikidata.org/wiki/Q192995","display_name":"Vaccination","level":2,"score":0.44530150294303894},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4371243715286255},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.4257148206233978},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40861228108406067},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25884637236595154},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.2344549000263214},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22483697533607483},{"id":"https://openalex.org/C2779134260","wikidata":"https://www.wikidata.org/wiki/Q12136","display_name":"Disease","level":2,"score":0.21042481064796448},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.12137633562088013},{"id":"https://openalex.org/C159047783","wikidata":"https://www.wikidata.org/wiki/Q7215","display_name":"Virology","level":1,"score":0.10363030433654785},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.08800530433654785},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0815923810005188},{"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/C142724271","wikidata":"https://www.wikidata.org/wiki/Q7208","display_name":"Pathology","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/C99454951","wikidata":"https://www.wikidata.org/wiki/Q932068","display_name":"Environmental health","level":1,"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/C524204448","wikidata":"https://www.wikidata.org/wiki/Q788926","display_name":"Infectious disease (medical specialty)","level":3,"score":0.0},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11090446","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11090446","pdf_url":"https://www.mdpi.com/2075-1680/11/9/446/pdf?version=1661941298","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:ce39220545344836b1a1db3b60b5c9bf","is_oa":true,"landing_page_url":"https://doaj.org/article/ce39220545344836b1a1db3b60b5c9bf","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 9, p 446 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/9/446/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11090446","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":"Axioms; Volume 11; Issue 9; Pages: 446","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11090446","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11090446","pdf_url":"https://www.mdpi.com/2075-1680/11/9/446/pdf?version=1661941298","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6399999856948853,"id":"https://metadata.un.org/sdg/3","display_name":"Good health and well-being"}],"awards":[{"id":"https://openalex.org/G1193235492","display_name":null,"funder_award_id":"PID2020-113275GB-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3111483846","display_name":null,"funder_award_id":"ED431C 2019/02","funder_id":"https://openalex.org/F4320326655","funder_display_name":"Xunta de Galicia"},{"id":"https://openalex.org/G6593419284","display_name":null,"funder_award_id":"ED431C 2019/02","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7416345212","display_name":null,"funder_award_id":"PID2020-113275GB-I00","funder_id":"https://openalex.org/F4320326655","funder_display_name":"Xunta de Galicia"}],"funders":[{"id":"https://openalex.org/F4320326655","display_name":"Xunta de Galicia","ror":"https://ror.org/0181xnw06"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4294344037.pdf","grobid_xml":"https://content.openalex.org/works/W4294344037.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W43498744","https://openalex.org/W1967539618","https://openalex.org/W2112680994","https://openalex.org/W2187932833","https://openalex.org/W2556784265","https://openalex.org/W2785557465","https://openalex.org/W3001118548","https://openalex.org/W3003668884","https://openalex.org/W3013566370","https://openalex.org/W3025578972","https://openalex.org/W3043090469","https://openalex.org/W3080438434","https://openalex.org/W3086487419","https://openalex.org/W3091856763","https://openalex.org/W3120648879","https://openalex.org/W3138233671","https://openalex.org/W3152943909","https://openalex.org/W3160256712","https://openalex.org/W3169901911","https://openalex.org/W3174920576","https://openalex.org/W3189224876","https://openalex.org/W3192171324","https://openalex.org/W3211110947","https://openalex.org/W3217719852","https://openalex.org/W4214652678","https://openalex.org/W4223534219","https://openalex.org/W4225254874","https://openalex.org/W6601779485","https://openalex.org/W6686907548","https://openalex.org/W6730176618","https://openalex.org/W6796908194"],"related_works":["https://openalex.org/W4320351350","https://openalex.org/W2230721379","https://openalex.org/W2376250553","https://openalex.org/W3138234900","https://openalex.org/W2356839139","https://openalex.org/W4388177052","https://openalex.org/W3095275161","https://openalex.org/W3113377908","https://openalex.org/W2032448025","https://openalex.org/W4293088316"],"abstract_inverted_index":{"This":[0,95],"paper":[1],"develops":[2],"a":[3],"fractional-order":[4],"model":[5,11,45],"of":[6,22,59,83,91,101],"COVID-19":[7,102],"with":[8],"vaccination.":[9],"The":[10],"is":[12,49,53],"well":[13],"designed":[14],"by":[15],"including":[16],"both":[17],"the":[18,28,34,43,57,60,72,76,81,84,92],"efficacy":[19],"and":[20,33,64],"inefficacy":[21],"vaccinations":[23],"in":[24],"humans.":[25],"Besides":[26],"calculating":[27],"reproduction":[29],"number,":[30],"equilibrium":[31,47],"points":[32,48],"feasibility":[35],"region":[36],"are":[37,68],"also":[38],"determined.":[39],"Stability":[40],"analysis":[41],"for":[42],"proposed":[44],"around":[46],"discussed.":[50],"Fixed-point":[51],"theory":[52],"employed":[54],"to":[55,70,79,104],"identify":[56],"singularity":[58],"solution.":[61,73],"Adomian":[62],"decomposition":[63],"Laplace":[65],"integral":[66],"transformation":[67],"combined":[69],"obtain":[71],"We":[74],"present":[75],"solutions":[77],"graphically":[78],"analyze":[80],"contributions":[82],"disease":[85],"dynamics":[86],"based":[87],"on":[88],"different":[89],"values":[90],"fractional":[93],"order.":[94],"study":[96],"seeks":[97],"an":[98],"in-depth":[99],"understanding":[100],"transmission":[103],"improve":[105],"health":[106],"outcomes.":[107]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2022-09-03T00:00:00"}