{"id":"https://openalex.org/W4382983244","doi":"https://doi.org/10.3390/computation11070129","title":"Computation of the Exact Forms of Waves for a Set of Differential Equations Associated with the SEIR Model of Epidemics","display_name":"Computation of the Exact Forms of Waves for a Set of Differential Equations Associated with the SEIR Model of Epidemics","publication_year":2023,"publication_date":"2023-07-02","ids":{"openalex":"https://openalex.org/W4382983244","doi":"https://doi.org/10.3390/computation11070129"},"language":"en","primary_location":{"id":"doi:10.3390/computation11070129","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation11070129","pdf_url":"https://www.mdpi.com/2079-3197/11/7/129/pdf?version=1688388612","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"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":"Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2079-3197/11/7/129/pdf?version=1688388612","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009076375","display_name":"Nikolay K. Vitanov","orcid":"https://orcid.org/0000-0001-6209-547X"},"institutions":[{"id":"https://openalex.org/I24768866","display_name":"Bulgarian Academy of Sciences","ror":"https://ror.org/01x8hew03","country_code":"BG","type":"government","lineage":["https://openalex.org/I24768866"]},{"id":"https://openalex.org/I4210148896","display_name":"Institute of Mechanics","ror":"https://ror.org/03x78r446","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210148896"]}],"countries":["BG"],"is_corresponding":true,"raw_author_name":"Nikolay K. Vitanov","raw_affiliation_strings":["Climate, Atmosphere and Water Research Institute, Bulgarian Academy of Sciences, Blvd. Tzarigradsko Chaussee 66, 1784 Sofia, Bulgaria","Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria"],"affiliations":[{"raw_affiliation_string":"Climate, Atmosphere and Water Research Institute, Bulgarian Academy of Sciences, Blvd. Tzarigradsko Chaussee 66, 1784 Sofia, Bulgaria","institution_ids":["https://openalex.org/I24768866"]},{"raw_affiliation_string":"Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria","institution_ids":["https://openalex.org/I4210148896","https://openalex.org/I24768866"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060521011","display_name":"Zlatinka I. Dimitrova","orcid":"https://orcid.org/0000-0002-3390-5397"},"institutions":[{"id":"https://openalex.org/I24768866","display_name":"Bulgarian Academy of Sciences","ror":"https://ror.org/01x8hew03","country_code":"BG","type":"government","lineage":["https://openalex.org/I24768866"]},{"id":"https://openalex.org/I4210148896","display_name":"Institute of Mechanics","ror":"https://ror.org/03x78r446","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210148896"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"Zlatinka I. Dimitrova","raw_affiliation_strings":["Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria"],"affiliations":[{"raw_affiliation_string":"Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria","institution_ids":["https://openalex.org/I4210148896","https://openalex.org/I24768866"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5009076375"],"corresponding_institution_ids":["https://openalex.org/I24768866","https://openalex.org/I4210148896"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":5.2173,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.95862799,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"11","issue":"7","first_page":"129","last_page":"129"},"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":0.9995999932289124,"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":0.9995999932289124,"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":0.9972000122070312,"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":0.9868000149726868,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.6470216512680054},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.635475218296051},{"id":"https://openalex.org/keywords/epidemic-model","display_name":"Epidemic model","score":0.5868440270423889},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5643385648727417},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5546351075172424},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5418501496315002},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4938085973262787},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.48679277300834656},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.4823119640350342},{"id":"https://openalex.org/keywords/exact-differential-equation","display_name":"Exact differential equation","score":0.4550418257713318},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.45139381289482117},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33945077657699585},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20707109570503235},{"id":"https://openalex.org/keywords/method-of-characteristics","display_name":"Method of characteristics","score":0.20423629879951477},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17457735538482666},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.07595837116241455}],"concepts":[{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.6470216512680054},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.635475218296051},{"id":"https://openalex.org/C1627819","wikidata":"https://www.wikidata.org/wiki/Q2572354","display_name":"Epidemic model","level":3,"score":0.5868440270423889},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5643385648727417},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5546351075172424},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5418501496315002},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4938085973262787},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.48679277300834656},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.4823119640350342},{"id":"https://openalex.org/C185184677","wikidata":"https://www.wikidata.org/wiki/Q1366795","display_name":"Exact differential equation","level":4,"score":0.4550418257713318},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.45139381289482117},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33945077657699585},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20707109570503235},{"id":"https://openalex.org/C33163149","wikidata":"https://www.wikidata.org/wiki/Q1785085","display_name":"Method of characteristics","level":3,"score":0.20423629879951477},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17457735538482666},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07595837116241455},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"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/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/computation11070129","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation11070129","pdf_url":"https://www.mdpi.com/2079-3197/11/7/129/pdf?version=1688388612","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"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":"Computation","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:fb87823e00d04690b8d8eebe0e2d507c","is_oa":true,"landing_page_url":"https://doaj.org/article/fb87823e00d04690b8d8eebe0e2d507c","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":"Computation, Vol 11, Iss 7, p 129 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2079-3197/11/7/129/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/computation11070129","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":"Computation; Volume 11; Issue 7; Pages: 129","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/computation11070129","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation11070129","pdf_url":"https://www.mdpi.com/2079-3197/11/7/129/pdf?version=1688388612","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"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":"Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Good health and well-being","score":0.8700000047683716,"id":"https://metadata.un.org/sdg/3"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4382983244.pdf","grobid_xml":"https://content.openalex.org/works/W4382983244.grobid-xml"},"referenced_works_count":82,"referenced_works":["https://openalex.org/W257772133","https://openalex.org/W627727433","https://openalex.org/W1598422102","https://openalex.org/W1965880816","https://openalex.org/W1967111163","https://openalex.org/W1967407267","https://openalex.org/W1971169529","https://openalex.org/W1971812863","https://openalex.org/W1981961258","https://openalex.org/W1983142785","https://openalex.org/W1991038590","https://openalex.org/W1992677948","https://openalex.org/W1999646337","https://openalex.org/W2017558991","https://openalex.org/W2031615496","https://openalex.org/W2037538587","https://openalex.org/W2045384647","https://openalex.org/W2045767366","https://openalex.org/W2053580463","https://openalex.org/W2055356295","https://openalex.org/W2079776520","https://openalex.org/W2081267180","https://openalex.org/W2083332431","https://openalex.org/W2083960709","https://openalex.org/W2101530839","https://openalex.org/W2112861154","https://openalex.org/W2148301044","https://openalex.org/W2161728228","https://openalex.org/W2165151302","https://openalex.org/W2174063340","https://openalex.org/W2335001735","https://openalex.org/W2487175822","https://openalex.org/W2565432921","https://openalex.org/W2565615699","https://openalex.org/W2583580911","https://openalex.org/W2757842681","https://openalex.org/W2764025117","https://openalex.org/W2786999873","https://openalex.org/W2796652860","https://openalex.org/W2963503659","https://openalex.org/W2980308966","https://openalex.org/W3034658412","https://openalex.org/W3087667739","https://openalex.org/W3105737457","https://openalex.org/W3108720132","https://openalex.org/W3109882943","https://openalex.org/W3113975845","https://openalex.org/W3125061446","https://openalex.org/W3133735260","https://openalex.org/W3135168233","https://openalex.org/W3146869385","https://openalex.org/W3204515293","https://openalex.org/W3214107440","https://openalex.org/W3216097851","https://openalex.org/W4210872842","https://openalex.org/W4224304661","https://openalex.org/W4225603611","https://openalex.org/W4226119253","https://openalex.org/W4226296056","https://openalex.org/W4232650420","https://openalex.org/W4233746284","https://openalex.org/W4239975174","https://openalex.org/W4281484840","https://openalex.org/W4287147848","https://openalex.org/W4299429830","https://openalex.org/W4302138509","https://openalex.org/W4302331569","https://openalex.org/W4306742385","https://openalex.org/W4309026304","https://openalex.org/W4311611604","https://openalex.org/W4313328568","https://openalex.org/W4313890122","https://openalex.org/W4315786429","https://openalex.org/W4316466061","https://openalex.org/W4317502677","https://openalex.org/W4317810019","https://openalex.org/W4322771274","https://openalex.org/W6635549360","https://openalex.org/W6643077284","https://openalex.org/W6675450214","https://openalex.org/W6732955682","https://openalex.org/W6811146151"],"related_works":["https://openalex.org/W4302011354","https://openalex.org/W2168746866","https://openalex.org/W4318687821","https://openalex.org/W2020165868","https://openalex.org/W1516864479","https://openalex.org/W1981666348","https://openalex.org/W3142921075","https://openalex.org/W3150594254","https://openalex.org/W2103740921","https://openalex.org/W191904733"],"abstract_inverted_index":{"We":[0,28,57],"studied":[1],"obtaining":[2],"exact":[3,77,128,135,163],"solutions":[4,20,78,86,129,136,164],"to":[5,11,24,79,130,141,168,177],"a":[6,34,48,96],"set":[7,49,63],"of":[8,16,50,84,91,99,145,156,161,173],"equations":[9,52,60],"related":[10],"the":[12,30,62,65,80,89,102,111,143,149,153,157,162,171,174,178],"SEIR":[13,31,158],"(Susceptible-Exposed-Infectious-Recovered)":[14],"model":[15,25,32],"epidemic":[17,26,92,179],"spread.":[18],"These":[19],"may":[21],"be":[22],"used":[23],"waves.":[27,180],"transformed":[29],"into":[33],"differential":[35,51,132],"equation":[36,43],"that":[37,94,120],"contained":[38,54],"an":[39,123],"exponential":[40],"nonlinearity.":[41],"This":[42],"was":[44],"then":[45],"approximated":[46],"by":[47],"which":[53],"polynomial":[55],"nonlinearities.":[56],"solved":[58],"several":[59],"from":[61],"using":[64],"Simple":[66],"Equations":[67],"Method":[68],"(SEsM).":[69],"In":[70,152],"doing":[71],"so,":[72],"we":[73],"obtained":[74,137],"many":[75],"new":[76],"corresponding":[81],"equations.":[82,133],"Several":[83],"these":[85],"can":[87,138,165],"describe":[88],"evolution":[90,144,172],"waves":[93,105],"affect":[95],"small":[97],"percentage":[98],"individuals":[100],"in":[101,110,114,148],"population.":[103],"Such":[104],"have":[106],"frequently":[107],"been":[108],"observed":[109],"COVID-19":[112],"pandemic":[113],"recent":[115],"years.":[116],"The":[117,134],"discussion":[118],"shows":[119],"SEsM":[121],"is":[122],"effective":[124],"methodology":[125],"for":[126],"computing":[127],"nonlinear":[131],"help":[139,166],"us":[140,167],"understand":[142,170],"various":[146],"processes":[147],"modeled":[150],"systems.":[151],"specific":[154],"case":[155],"model,":[159],"some":[160],"better":[169],"quantities":[175],"connected":[176]},"counts_by_year":[{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
