{"id":"https://openalex.org/W3024451092","doi":"https://doi.org/10.3390/sym12060990","title":"A Mathematical Model for the COVID-19 Outbreak and Its Applications","display_name":"A Mathematical Model for the COVID-19 Outbreak and Its Applications","publication_year":2020,"publication_date":"2020-06-10","ids":{"openalex":"https://openalex.org/W3024451092","doi":"https://doi.org/10.3390/sym12060990","mag":"3024451092"},"language":"en","primary_location":{"id":"doi:10.3390/sym12060990","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12060990","pdf_url":"https://www.mdpi.com/2073-8994/12/6/990/pdf?version=1591770212","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/2073-8994/12/6/990/pdf?version=1591770212","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051428126","display_name":"Roman Cherniha","orcid":"https://orcid.org/0000-0002-1733-5240"},"institutions":[{"id":"https://openalex.org/I149851306","display_name":"National Academy of Sciences of Ukraine","ror":"https://ror.org/00je4t102","country_code":"UA","type":"government","lineage":["https://openalex.org/I149851306"]},{"id":"https://openalex.org/I190444043","display_name":"Institute of Mathematics","ror":"https://ror.org/04q3mp532","country_code":"UA","type":"facility","lineage":["https://openalex.org/I149851306","https://openalex.org/I190444043"]}],"countries":["UA"],"is_corresponding":true,"raw_author_name":"Roman Cherniha","raw_affiliation_strings":["Institute of Mathematics, National Academy of Sciences of Ukraine, 3, Tereshchenkivs\u2019ka Street, 01004 Kyiv, Ukraine","Institute of Mathematics, National Academy of Sciences of Ukraine, 3, Tereshchenkivs'ka Street, 01004 Kyiv, Ukraine"],"raw_orcid":"https://orcid.org/0000-0002-1733-5240","affiliations":[{"raw_affiliation_string":"Institute of Mathematics, National Academy of Sciences of Ukraine, 3, Tereshchenkivs\u2019ka Street, 01004 Kyiv, Ukraine","institution_ids":["https://openalex.org/I190444043","https://openalex.org/I149851306"]},{"raw_affiliation_string":"Institute of Mathematics, National Academy of Sciences of Ukraine, 3, Tereshchenkivs'ka Street, 01004 Kyiv, Ukraine","institution_ids":["https://openalex.org/I190444043","https://openalex.org/I149851306"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053144999","display_name":"Vasyl\u2019 Davydovych","orcid":"https://orcid.org/0000-0001-5004-4608"},"institutions":[{"id":"https://openalex.org/I149851306","display_name":"National Academy of Sciences of Ukraine","ror":"https://ror.org/00je4t102","country_code":"UA","type":"government","lineage":["https://openalex.org/I149851306"]},{"id":"https://openalex.org/I190444043","display_name":"Institute of Mathematics","ror":"https://ror.org/04q3mp532","country_code":"UA","type":"facility","lineage":["https://openalex.org/I149851306","https://openalex.org/I190444043"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Vasyl\u2019 Davydovych","raw_affiliation_strings":["Institute of Mathematics, National Academy of Sciences of Ukraine, 3, Tereshchenkivs\u2019ka Street, 01004 Kyiv, Ukraine","Institute of Mathematics, National Academy of Sciences of Ukraine, 3, Tereshchenkivs'ka Street, 01004 Kyiv, Ukraine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, National Academy of Sciences of Ukraine, 3, Tereshchenkivs\u2019ka Street, 01004 Kyiv, Ukraine","institution_ids":["https://openalex.org/I190444043","https://openalex.org/I149851306"]},{"raw_affiliation_string":"Institute of Mathematics, National Academy of Sciences of Ukraine, 3, Tereshchenkivs'ka Street, 01004 Kyiv, Ukraine","institution_ids":["https://openalex.org/I190444043","https://openalex.org/I149851306"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5051428126"],"corresponding_institution_ids":["https://openalex.org/I149851306","https://openalex.org/I190444043"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.1926,"has_fulltext":true,"cited_by_count":44,"citation_normalized_percentile":{"value":0.85061356,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"12","issue":"6","first_page":"990","last_page":"990"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10410","display_name":"COVID-19 epidemiological studies","score":0.9991000294685364,"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/T10410","display_name":"COVID-19 epidemiological studies","score":0.9991000294685364,"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":0.9610999822616577,"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/coronavirus-disease-2019","display_name":"Coronavirus disease 2019 (COVID-19)","score":0.7182251214981079},{"id":"https://openalex.org/keywords/outbreak","display_name":"Outbreak","score":0.6432043313980103},{"id":"https://openalex.org/keywords/pandemic","display_name":"Pandemic","score":0.5321651697158813},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5245882868766785},{"id":"https://openalex.org/keywords/2019-20-coronavirus-outbreak","display_name":"2019-20 coronavirus outbreak","score":0.5016937255859375},{"id":"https://openalex.org/keywords/severe-acute-respiratory-syndrome-coronavirus-2","display_name":"Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)","score":0.4897940158843994},{"id":"https://openalex.org/keywords/mathematical-model","display_name":"Mathematical model","score":0.48582980036735535},{"id":"https://openalex.org/keywords/coronavirus","display_name":"Coronavirus","score":0.4654897451400757},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.46499764919281006},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.44257697463035583},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3836144804954529},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38188546895980835},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.34002214670181274},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3218924403190613},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.27707433700561523},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15948811173439026},{"id":"https://openalex.org/keywords/virology","display_name":"Virology","score":0.15477031469345093},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1174258291721344}],"concepts":[{"id":"https://openalex.org/C3008058167","wikidata":"https://www.wikidata.org/wiki/Q84263196","display_name":"Coronavirus disease 2019 (COVID-19)","level":4,"score":0.7182251214981079},{"id":"https://openalex.org/C116675565","wikidata":"https://www.wikidata.org/wiki/Q3241045","display_name":"Outbreak","level":2,"score":0.6432043313980103},{"id":"https://openalex.org/C89623803","wikidata":"https://www.wikidata.org/wiki/Q12184","display_name":"Pandemic","level":5,"score":0.5321651697158813},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5245882868766785},{"id":"https://openalex.org/C3006700255","wikidata":"https://www.wikidata.org/wiki/Q81068910","display_name":"2019-20 coronavirus outbreak","level":3,"score":0.5016937255859375},{"id":"https://openalex.org/C3007834351","wikidata":"https://www.wikidata.org/wiki/Q82069695","display_name":"Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)","level":5,"score":0.4897940158843994},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.48582980036735535},{"id":"https://openalex.org/C2777648638","wikidata":"https://www.wikidata.org/wiki/Q57751738","display_name":"Coronavirus","level":5,"score":0.4654897451400757},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.46499764919281006},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.44257697463035583},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3836144804954529},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38188546895980835},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.34002214670181274},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3218924403190613},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.27707433700561523},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15948811173439026},{"id":"https://openalex.org/C159047783","wikidata":"https://www.wikidata.org/wiki/Q7215","display_name":"Virology","level":1,"score":0.15477031469345093},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1174258291721344},{"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C2779134260","wikidata":"https://www.wikidata.org/wiki/Q12136","display_name":"Disease","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym12060990","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12060990","pdf_url":"https://www.mdpi.com/2073-8994/12/6/990/pdf?version=1591770212","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:198ac5e349674525b73c8d6f0c604279","is_oa":true,"landing_page_url":"https://doaj.org/article/198ac5e349674525b73c8d6f0c604279","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 12, Iss 6, p 990 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/6/990/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym12060990","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/sym12060990","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12060990","pdf_url":"https://www.mdpi.com/2073-8994/12/6/990/pdf?version=1591770212","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":[{"id":"https://metadata.un.org/sdg/3","display_name":"Good health and well-being","score":0.8500000238418579}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3024451092.pdf","grobid_xml":"https://content.openalex.org/works/W3024451092.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W154646596","https://openalex.org/W1849590887","https://openalex.org/W1989315300","https://openalex.org/W2002944058","https://openalex.org/W2079949023","https://openalex.org/W2093517417","https://openalex.org/W2148301044","https://openalex.org/W2166022262","https://openalex.org/W3007602081","https://openalex.org/W3009221227","https://openalex.org/W3012864042","https://openalex.org/W3013634385","https://openalex.org/W3013696685","https://openalex.org/W3020140277","https://openalex.org/W3024451092","https://openalex.org/W3121025217","https://openalex.org/W4247272566","https://openalex.org/W4250716583","https://openalex.org/W4251048656","https://openalex.org/W4255777804","https://openalex.org/W4292156591","https://openalex.org/W4302331569","https://openalex.org/W6682044371","https://openalex.org/W6775463879"],"related_works":["https://openalex.org/W2373635223","https://openalex.org/W2412355096","https://openalex.org/W1990012352","https://openalex.org/W2431766951","https://openalex.org/W4385969441","https://openalex.org/W127458931","https://openalex.org/W2362266265","https://openalex.org/W2557977292","https://openalex.org/W4405746056","https://openalex.org/W2043671984"],"abstract_inverted_index":{"A":[0],"mathematical":[1],"model":[2,23,44,95],"based":[3],"on":[4],"nonlinear":[5],"ordinary":[6],"differential":[7],"equations":[8],"is":[9,76],"proposed":[10],"for":[11],"quantitative":[12],"description":[13],"of":[14,17,42,68,72,93],"the":[15,18,35,43,46,52,60,69,73,83,94],"outbreak":[16],"novel":[19],"coronavirus":[20],"pandemic.":[21],"The":[22,32],"possesses":[24],"remarkable":[25],"properties,":[26],"such":[27],"as":[28,29,98],"full":[30],"integrability.":[31],"comparison":[33],"with":[34,59],"public":[36],"data":[37,62,85],"shows":[38],"that":[39],"exact":[40],"solutions":[41],"(with":[45],"correctly":[47],"specified":[48],"parameters)":[49],"lead":[50],"to":[51],"results,":[53],"which":[54],"are":[55,80,96],"in":[56,63,86],"good":[57],"agreement":[58],"measured":[61,84],"China":[64],"and":[65,78,89],"Austria.":[66],"Prediction":[67],"total":[70],"number":[71],"COVID-19":[74],"cases":[75],"discussed":[77],"examples":[79],"presented":[81],"using":[82],"Austria,":[87],"France,":[88],"Poland.":[90],"Some":[91],"generalizations":[92],"suggested":[97],"well.":[99]},"counts_by_year":[{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":15},{"year":2020,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}