{"id":"https://openalex.org/W3173303060","doi":"https://doi.org/10.3390/sym13071120","title":"Novel Method to Analytically Obtain the Asymptotic Stable Equilibria States of Extended SIR-Type Epidemiological Models","display_name":"Novel Method to Analytically Obtain the Asymptotic Stable Equilibria States of Extended SIR-Type Epidemiological Models","publication_year":2021,"publication_date":"2021-06-23","ids":{"openalex":"https://openalex.org/W3173303060","doi":"https://doi.org/10.3390/sym13071120","mag":"3173303060"},"language":"en","primary_location":{"id":"doi:10.3390/sym13071120","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13071120","pdf_url":"https://www.mdpi.com/2073-8994/13/7/1120/pdf?version=1624613378","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/2073-8994/13/7/1120/pdf?version=1624613378","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041000511","display_name":"Teddy Lazebnik","orcid":"https://orcid.org/0000-0002-7851-8147"},"institutions":[{"id":"https://openalex.org/I52170813","display_name":"Ariel University","ror":"https://ror.org/03nz8qe97","country_code":"IL","type":"education","lineage":["https://openalex.org/I52170813"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Teddy Lazebnik","raw_affiliation_strings":["Department of Mathematics, Ariel University, Ariel 40700, Israel"],"raw_orcid":"https://orcid.org/0000-0002-7851-8147","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ariel University, Ariel 40700, Israel","institution_ids":["https://openalex.org/I52170813"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055152954","display_name":"Svetlana Bunimovich\u2010Mendrazitsky","orcid":"https://orcid.org/0000-0001-5280-3217"},"institutions":[{"id":"https://openalex.org/I52170813","display_name":"Ariel University","ror":"https://ror.org/03nz8qe97","country_code":"IL","type":"education","lineage":["https://openalex.org/I52170813"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Svetlana Bunimovich-Mendrazitsky","raw_affiliation_strings":["Department of Mathematics, Ariel University, Ariel 40700, Israel"],"raw_orcid":"https://orcid.org/0000-0001-5280-3217","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ariel University, Ariel 40700, Israel","institution_ids":["https://openalex.org/I52170813"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067012309","display_name":"Leonid Shaikhet","orcid":"https://orcid.org/0000-0001-7354-1383"},"institutions":[{"id":"https://openalex.org/I52170813","display_name":"Ariel University","ror":"https://ror.org/03nz8qe97","country_code":"IL","type":"education","lineage":["https://openalex.org/I52170813"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Leonid Shaikhet","raw_affiliation_strings":["Department of Mathematics, Ariel University, Ariel 40700, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ariel University, Ariel 40700, Israel","institution_ids":["https://openalex.org/I52170813"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5041000511"],"corresponding_institution_ids":["https://openalex.org/I52170813"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.369,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.80331412,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"13","issue":"7","first_page":"1120","last_page":"1120"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10410","display_name":"COVID-19 epidemiological studies","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9976999759674072,"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/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9605000019073486,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/epidemic-model","display_name":"Epidemic model","score":0.738083004951477},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.6585191488265991},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.61826491355896},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6060563325881958},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5861682295799255},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5521919131278992},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5288340449333191},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.49348127841949463},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.49051135778427124},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.47943586111068726},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.4335865378379822},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.34735679626464844},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.33858972787857056},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17500290274620056},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1255517601966858},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09888002276420593}],"concepts":[{"id":"https://openalex.org/C1627819","wikidata":"https://www.wikidata.org/wiki/Q2572354","display_name":"Epidemic model","level":3,"score":0.738083004951477},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.6585191488265991},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.61826491355896},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6060563325881958},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5861682295799255},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5521919131278992},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5288340449333191},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.49348127841949463},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.49051135778427124},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.47943586111068726},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.4335865378379822},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.34735679626464844},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.33858972787857056},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17500290274620056},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1255517601966858},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09888002276420593},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"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/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13071120","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13071120","pdf_url":"https://www.mdpi.com/2073-8994/13/7/1120/pdf?version=1624613378","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:6873eb3da612481e90384d78711fe418","is_oa":true,"landing_page_url":"https://doaj.org/article/6873eb3da612481e90384d78711fe418","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 13, Iss 7, p 1120 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/7/1120/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13071120","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/sym13071120","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13071120","pdf_url":"https://www.mdpi.com/2073-8994/13/7/1120/pdf?version=1624613378","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","score":0.8299999833106995,"display_name":"Good health and well-being"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3173303060.pdf","grobid_xml":"https://content.openalex.org/works/W3173303060.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W1499871105","https://openalex.org/W1537236879","https://openalex.org/W1980465669","https://openalex.org/W2011771253","https://openalex.org/W2056544360","https://openalex.org/W2071850519","https://openalex.org/W2078899217","https://openalex.org/W2084828843","https://openalex.org/W2094187171","https://openalex.org/W2119033269","https://openalex.org/W2144481813","https://openalex.org/W2148301044","https://openalex.org/W2151689585","https://openalex.org/W2155812848","https://openalex.org/W2250109196","https://openalex.org/W2321889608","https://openalex.org/W2476007957","https://openalex.org/W2515822818","https://openalex.org/W2622639018","https://openalex.org/W3015623674","https://openalex.org/W3016157888","https://openalex.org/W3016508742","https://openalex.org/W3022528597","https://openalex.org/W3028407576","https://openalex.org/W3046033700","https://openalex.org/W3102098446","https://openalex.org/W3103143917","https://openalex.org/W3127471580","https://openalex.org/W3146784223","https://openalex.org/W3165120713","https://openalex.org/W4244035502","https://openalex.org/W6630047673","https://openalex.org/W6682044371"],"related_works":["https://openalex.org/W3082668976","https://openalex.org/W2517973022","https://openalex.org/W1543121148","https://openalex.org/W1580703421","https://openalex.org/W2958348684","https://openalex.org/W2618518959","https://openalex.org/W2231364979","https://openalex.org/W4295745414","https://openalex.org/W4382202915","https://openalex.org/W2489516236"],"abstract_inverted_index":{"We":[0,19],"present":[1],"a":[2,41,68,72],"new":[3],"analytical":[4],"method":[5,22,63],"to":[6,56,66,101],"find":[7],"the":[8,15,24,76,79,90,102,105],"asymptotic":[9,85],"stable":[10,86],"equilibria":[11],"states":[12,88],"based":[13],"on":[14,23],"Markov":[16],"chain":[17],"technique.":[18],"reveal":[20],"this":[21],"Susceptible-Infectious-Recovered":[25],"(SIR)-type":[26],"epidemiological":[27],"model":[28,43,91],"that":[29],"we":[30],"developed":[31],"for":[32,92],"viral":[33],"diseases":[34],"with":[35],"long-term":[36],"immunity":[37],"memory.":[38],"This":[39],"is":[40,64],"large-scale":[42],"containing":[44],"15":[45],"nonlinear":[46],"ordinary":[47],"differential":[48],"equations":[49],"(ODEs),":[50],"and":[51,97],"classical":[52],"methods":[53],"have":[54],"failed":[55],"analytically":[57],"obtain":[58],"its":[59],"equilibria.":[60],"The":[61],"proposed":[62],"used":[65],"conduct":[67],"comprehensive":[69],"analysis":[70],"by":[71,82],"stochastic":[73],"representation":[74],"of":[75,78,89,95,104],"dynamics":[77],"model,":[80],"followed":[81],"finding":[83],"all":[84],"equilibrium":[87],"any":[93],"values":[94],"parameters":[96],"initial":[98],"conditions":[99],"thanks":[100],"symmetry":[103],"population":[106],"size":[107],"over":[108],"time.":[109]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}