{"id":"https://openalex.org/W3197034357","doi":"https://doi.org/10.3390/axioms10030204","title":"How Containment Can Effectively Suppress the Outbreak of COVID-19: A Mathematical Modeling","display_name":"How Containment Can Effectively Suppress the Outbreak of COVID-19: A Mathematical Modeling","publication_year":2021,"publication_date":"2021-08-28","ids":{"openalex":"https://openalex.org/W3197034357","doi":"https://doi.org/10.3390/axioms10030204","mag":"3197034357"},"language":"en","primary_location":{"id":"doi:10.3390/axioms10030204","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10030204","pdf_url":"https://www.mdpi.com/2075-1680/10/3/204/pdf?version=1630563722","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/2075-1680/10/3/204/pdf?version=1630563722","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072378410","display_name":"Bootan Rahman","orcid":"https://orcid.org/0000-0002-6695-155X"},"institutions":[{"id":"https://openalex.org/I3151615967","display_name":"University of Kurdistan Hewler","ror":"https://ror.org/00268wk31","country_code":"IQ","type":"education","lineage":["https://openalex.org/I3151615967"]}],"countries":["IQ"],"is_corresponding":false,"raw_author_name":"Bootan Rahman","raw_affiliation_strings":["Mathematics Unit, School of Science and Engineering, University of Kurdistan Hewl\u00ear (UKH), Erbil 44001, Iraq"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Unit, School of Science and Engineering, University of Kurdistan Hewl\u00ear (UKH), Erbil 44001, Iraq","institution_ids":["https://openalex.org/I3151615967"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012006608","display_name":"Sarbaz H. A. Khoshnaw","orcid":"https://orcid.org/0000-0002-9176-8108"},"institutions":[{"id":"https://openalex.org/I3132703562","display_name":"University of Raparin","ror":"https://ror.org/00fs9wb06","country_code":"IQ","type":"education","lineage":["https://openalex.org/I3132703562"]}],"countries":["IQ"],"is_corresponding":false,"raw_author_name":"Sarbaz H. A. Khoshnaw","raw_affiliation_strings":["Department of Mathematics, University of Raparin, Ranya 46012, Iraq"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Raparin, Ranya 46012, Iraq","institution_ids":["https://openalex.org/I3132703562"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041557797","display_name":"Grace O. Agaba","orcid":"https://orcid.org/0000-0002-2198-9845"},"institutions":[{"id":"https://openalex.org/I187152970","display_name":"Benue State University","ror":"https://ror.org/04hfv3620","country_code":"NG","type":"education","lineage":["https://openalex.org/I187152970"]}],"countries":["NG"],"is_corresponding":false,"raw_author_name":"Grace O. Agaba","raw_affiliation_strings":["Department of Mathematics and Computer Science, Benue State University, Makurdi P.M.B. 102119, Nigeria"],"raw_orcid":"https://orcid.org/0000-0002-2198-9845","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Benue State University, Makurdi P.M.B. 102119, Nigeria","institution_ids":["https://openalex.org/I187152970"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087124112","display_name":"Fahad Al Basir","orcid":"https://orcid.org/0000-0003-3744-5524"},"institutions":[{"id":"https://openalex.org/I3131729800","display_name":"Kazi Nazrul University","ror":"https://ror.org/02qy8xv65","country_code":"IN","type":"education","lineage":["https://openalex.org/I3131729800"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Fahad Al Basir","raw_affiliation_strings":["Department of Mathematics, Asansol Girls\u2019 College, Asansol 713304, India","Department of Mathematics, Asansol Girls' College, Asansol 713304, India"],"raw_orcid":"https://orcid.org/0000-0003-3744-5524","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Asansol Girls\u2019 College, Asansol 713304, India","institution_ids":["https://openalex.org/I3131729800"]},{"raw_affiliation_string":"Department of Mathematics, Asansol Girls' College, Asansol 713304, India","institution_ids":["https://openalex.org/I3131729800"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5087124112"],"corresponding_institution_ids":["https://openalex.org/I3131729800"],"apc_list":{"value":2400,"currency":"CHF","value_usd":2896},"apc_paid":{"value":2400,"currency":"CHF","value_usd":2896},"fwci":0.5078,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.60668927,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"10","issue":"3","first_page":"204","last_page":"204"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10410","display_name":"COVID-19 epidemiological studies","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9955999851226807,"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/T10118","display_name":"SARS-CoV-2 and COVID-19 Research","score":0.9381999969482422,"subfield":{"id":"https://openalex.org/subfields/2725","display_name":"Infectious Diseases"},"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/normalization","display_name":"Normalization (sociology)","score":0.8769147396087646},{"id":"https://openalex.org/keywords/basic-reproduction-number","display_name":"Basic reproduction number","score":0.7440698146820068},{"id":"https://openalex.org/keywords/pandemic","display_name":"Pandemic","score":0.7013356685638428},{"id":"https://openalex.org/keywords/outbreak","display_name":"Outbreak","score":0.6931969523429871},{"id":"https://openalex.org/keywords/coronavirus-disease-2019","display_name":"Coronavirus disease 2019 (COVID-19)","score":0.6749606132507324},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.5204753875732422},{"id":"https://openalex.org/keywords/isolation","display_name":"Isolation (microbiology)","score":0.4737687408924103},{"id":"https://openalex.org/keywords/epidemic-model","display_name":"Epidemic model","score":0.47297871112823486},{"id":"https://openalex.org/keywords/containment","display_name":"Containment (computer programming)","score":0.4468925893306732},{"id":"https://openalex.org/keywords/severe-acute-respiratory-syndrome-coronavirus-2","display_name":"Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)","score":0.4270837903022766},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42317283153533936},{"id":"https://openalex.org/keywords/infectious-disease","display_name":"Infectious disease (medical specialty)","score":0.18537837266921997},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.17620432376861572},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.16634225845336914},{"id":"https://openalex.org/keywords/virology","display_name":"Virology","score":0.14404958486557007},{"id":"https://openalex.org/keywords/disease","display_name":"Disease","score":0.11532789468765259},{"id":"https://openalex.org/keywords/environmental-health","display_name":"Environmental health","score":0.10394507646560669},{"id":"https://openalex.org/keywords/bioinformatics","display_name":"Bioinformatics","score":0.09339344501495361}],"concepts":[{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.8769147396087646},{"id":"https://openalex.org/C204264503","wikidata":"https://www.wikidata.org/wiki/Q901464","display_name":"Basic reproduction number","level":3,"score":0.7440698146820068},{"id":"https://openalex.org/C89623803","wikidata":"https://www.wikidata.org/wiki/Q12184","display_name":"Pandemic","level":5,"score":0.7013356685638428},{"id":"https://openalex.org/C116675565","wikidata":"https://www.wikidata.org/wiki/Q3241045","display_name":"Outbreak","level":2,"score":0.6931969523429871},{"id":"https://openalex.org/C3008058167","wikidata":"https://www.wikidata.org/wiki/Q84263196","display_name":"Coronavirus disease 2019 (COVID-19)","level":4,"score":0.6749606132507324},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5204753875732422},{"id":"https://openalex.org/C2775941552","wikidata":"https://www.wikidata.org/wiki/Q25212305","display_name":"Isolation (microbiology)","level":2,"score":0.4737687408924103},{"id":"https://openalex.org/C1627819","wikidata":"https://www.wikidata.org/wiki/Q2572354","display_name":"Epidemic model","level":3,"score":0.47297871112823486},{"id":"https://openalex.org/C2777019822","wikidata":"https://www.wikidata.org/wiki/Q390066","display_name":"Containment (computer programming)","level":2,"score":0.4468925893306732},{"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":0.4270837903022766},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42317283153533936},{"id":"https://openalex.org/C524204448","wikidata":"https://www.wikidata.org/wiki/Q788926","display_name":"Infectious disease (medical specialty)","level":3,"score":0.18537837266921997},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.17620432376861572},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.16634225845336914},{"id":"https://openalex.org/C159047783","wikidata":"https://www.wikidata.org/wiki/Q7215","display_name":"Virology","level":1,"score":0.14404958486557007},{"id":"https://openalex.org/C2779134260","wikidata":"https://www.wikidata.org/wiki/Q12136","display_name":"Disease","level":2,"score":0.11532789468765259},{"id":"https://openalex.org/C99454951","wikidata":"https://www.wikidata.org/wiki/Q932068","display_name":"Environmental health","level":1,"score":0.10394507646560669},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.09339344501495361},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms10030204","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10030204","pdf_url":"https://www.mdpi.com/2075-1680/10/3/204/pdf?version=1630563722","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:f18ce781680f4072bbdf14d0c568219f","is_oa":true,"landing_page_url":"https://doaj.org/article/f18ce781680f4072bbdf14d0c568219f","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":"Axioms, Vol 10, Iss 3, p 204 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/10/3/204/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms10030204","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 10; Issue 3; Pages: 204","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms10030204","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10030204","pdf_url":"https://www.mdpi.com/2075-1680/10/3/204/pdf?version=1630563722","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":[{"id":"https://metadata.un.org/sdg/3","display_name":"Good health and well-being","score":0.8299999833106995}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3197034357.pdf","grobid_xml":"https://content.openalex.org/works/W3197034357.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W31877295","https://openalex.org/W94176095","https://openalex.org/W1538902679","https://openalex.org/W1598931416","https://openalex.org/W1967940959","https://openalex.org/W2112680994","https://openalex.org/W2168202968","https://openalex.org/W2725216843","https://openalex.org/W2896111000","https://openalex.org/W3003403425","https://openalex.org/W3006419733","https://openalex.org/W3007580879","https://openalex.org/W3008842543","https://openalex.org/W3010748696","https://openalex.org/W3011165726","https://openalex.org/W3013634385","https://openalex.org/W3014145608","https://openalex.org/W3014866318","https://openalex.org/W3015512447","https://openalex.org/W3019674250","https://openalex.org/W3024025841","https://openalex.org/W3024230195","https://openalex.org/W3025036455","https://openalex.org/W3025578972","https://openalex.org/W3025586072","https://openalex.org/W3030890021","https://openalex.org/W3031202235","https://openalex.org/W3033299997","https://openalex.org/W3033504345","https://openalex.org/W3035815753","https://openalex.org/W3037000545","https://openalex.org/W3039403300","https://openalex.org/W3091945164","https://openalex.org/W3101520573","https://openalex.org/W3110390059","https://openalex.org/W3112642064","https://openalex.org/W3113452046","https://openalex.org/W3121372095","https://openalex.org/W3123597583","https://openalex.org/W3164244978","https://openalex.org/W3174626066","https://openalex.org/W3176473356","https://openalex.org/W4247836593","https://openalex.org/W6774869222","https://openalex.org/W6780438130"],"related_works":["https://openalex.org/W2962891488","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/W3113377908","https://openalex.org/W2032448025","https://openalex.org/W4293088316"],"abstract_inverted_index":{"In":[0],"this":[1,138],"paper,":[2],"the":[3,8,17,34,61,64,70,80,83,87,98,115,122,129],"aim":[4],"is":[5,109],"to":[6,46],"capture":[7],"global":[9],"pandemic":[10],"of":[11,28,36,60,63,82,97,124],"COVID-19":[12,146],"with":[13],"parameters":[14,62],"that":[15,79],"consider":[16],"interactions":[18],"among":[19],"individuals":[20,39],"by":[21],"proposing":[22],"a":[23,29,95,110],"mathematical":[24],"model.":[25],"The":[26,90,134],"introduction":[27],"parsimonious":[30],"model":[31,66,88],"captures":[32],"both":[33,102],"isolation":[35],"symptomatic":[37,106],"infected":[38,107,125],"and":[40,51,73,104,127],"population":[41],"lockdown":[42,99,120],"practices":[43],"in":[44,113],"response":[45],"containment":[47],"policies.":[48],"Local":[49,57],"stability":[50],"basic":[52],"reproduction":[53],"numbers":[54],"are":[55,67,140],"analyzed.":[56],"sensitivity":[58],"indices":[59],"proposed":[65],"calculated,":[68],"using":[69],"non-normalization,":[71],"half-normalization,":[72],"full-normalization":[74],"techniques.":[75],"Numerical":[76],"investigations":[77],"show":[78],"dynamics":[81],"system":[84],"depend":[85],"on":[86],"parameters.":[89],"infection":[91],"transmission":[92],"rate":[93],"(as":[94],"function":[96],"parameter)":[100],"for":[101,143],"reported":[103],"unreported":[105],"peoples":[108],"significant":[111],"parameter":[112],"spreading":[114],"infection.":[116],"A":[117],"nationwide":[118],"public":[119],"decreases":[121],"number":[123],"cases":[126],"stops":[128],"pandemic\u2019s":[130],"peak":[131],"from":[132,137],"occurring.":[133],"results":[135],"obtained":[136],"study":[139],"beneficial":[141],"worldwide":[142],"developing":[144],"different":[145],"management":[147],"programs.":[148]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}