{"id":"https://openalex.org/W3022975273","doi":"https://doi.org/10.1155/2020/8596371","title":"Asymptotic Dynamics of a Stochastic SIR Epidemic System Affected by Mixed Nonlinear Incidence Rates","display_name":"Asymptotic Dynamics of a Stochastic SIR Epidemic System Affected by Mixed Nonlinear Incidence Rates","publication_year":2020,"publication_date":"2020-05-08","ids":{"openalex":"https://openalex.org/W3022975273","doi":"https://doi.org/10.1155/2020/8596371","mag":"3022975273"},"language":"en","primary_location":{"id":"doi:10.1155/2020/8596371","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2020/8596371","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/8596371.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2020/8596371.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110675407","display_name":"Ping Han","orcid":null},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ping Han","raw_affiliation_strings":["College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China","institution_ids":["https://openalex.org/I80143920"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087674147","display_name":"Zhengbo Chang","orcid":null},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhengbo Chang","raw_affiliation_strings":["College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China","institution_ids":["https://openalex.org/I80143920"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019874854","display_name":"Xinzhu Meng","orcid":"https://orcid.org/0000-0002-6553-9686"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xinzhu Meng","raw_affiliation_strings":["College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China","institution_ids":["https://openalex.org/I80143920"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5019874854"],"corresponding_institution_ids":["https://openalex.org/I80143920"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.7212,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.74069447,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2020","issue":null,"first_page":"1","last_page":"17"},"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":0.9998999834060669,"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":0.9998999834060669,"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/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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9749000072479248,"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/uniqueness","display_name":"Uniqueness","score":0.719039261341095},{"id":"https://openalex.org/keywords/stationary-distribution","display_name":"Stationary distribution","score":0.7043372988700867},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6506468057632446},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.5994805693626404},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5991132259368896},{"id":"https://openalex.org/keywords/epidemic-model","display_name":"Epidemic model","score":0.5979882478713989},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5551455616950989},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.5486071109771729},{"id":"https://openalex.org/keywords/extinction","display_name":"Extinction (optical mineralogy)","score":0.5406967401504517},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.47892364859580994},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.4589390158653259},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4302114248275757},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26069700717926025},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14461550116539001},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.13759028911590576},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1353760063648224},{"id":"https://openalex.org/keywords/demography","display_name":"Demography","score":0.07935428619384766}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.719039261341095},{"id":"https://openalex.org/C98951983","wikidata":"https://www.wikidata.org/wiki/Q7604341","display_name":"Stationary distribution","level":3,"score":0.7043372988700867},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6506468057632446},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.5994805693626404},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5991132259368896},{"id":"https://openalex.org/C1627819","wikidata":"https://www.wikidata.org/wiki/Q2572354","display_name":"Epidemic model","level":3,"score":0.5979882478713989},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5551455616950989},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.5486071109771729},{"id":"https://openalex.org/C101991246","wikidata":"https://www.wikidata.org/wiki/Q5422078","display_name":"Extinction (optical mineralogy)","level":2,"score":0.5406967401504517},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.47892364859580994},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.4589390158653259},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4302114248275757},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26069700717926025},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14461550116539001},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.13759028911590576},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1353760063648224},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.07935428619384766},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2020/8596371","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2020/8596371","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/8596371.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:8596371","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2020/8596371.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:ad73424997be42fc81060fad00700c07","is_oa":true,"landing_page_url":"https://doaj.org/article/ad73424997be42fc81060fad00700c07","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2020 (2020)","raw_type":"article"},{"id":"pmh:oai:hindawi.com:10.1155/2020/8596371","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/8596371","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"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":"","raw_type":"Research Article"}],"best_oa_location":{"id":"doi:10.1155/2020/8596371","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2020/8596371","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/8596371.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8700000047683716,"display_name":"Good health and well-being","id":"https://metadata.un.org/sdg/3"}],"awards":[{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2103659285","display_name":null,"funder_award_id":"ZR2019MA003","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G2696157397","display_name":null,"funder_award_id":"ZR201","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3497226477","display_name":null,"funder_award_id":"ZR2019","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G4020255992","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7827202963","display_name":null,"funder_award_id":"ZR2019MA003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3022975273.pdf","grobid_xml":"https://content.openalex.org/works/W3022975273.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W1460986822","https://openalex.org/W1972079349","https://openalex.org/W2002882243","https://openalex.org/W2010497553","https://openalex.org/W2015391697","https://openalex.org/W2017558991","https://openalex.org/W2051203270","https://openalex.org/W2076579387","https://openalex.org/W2077943267","https://openalex.org/W2078987314","https://openalex.org/W2124508608","https://openalex.org/W2175057542","https://openalex.org/W2255245649","https://openalex.org/W2329452640","https://openalex.org/W2472217300","https://openalex.org/W2767477371","https://openalex.org/W2773322315","https://openalex.org/W2800640381","https://openalex.org/W2808484841","https://openalex.org/W2808735225","https://openalex.org/W2892958929","https://openalex.org/W2901575059","https://openalex.org/W2905267520","https://openalex.org/W2909016487","https://openalex.org/W2909094219","https://openalex.org/W2913393012","https://openalex.org/W2915859360","https://openalex.org/W2920889573","https://openalex.org/W2921804423","https://openalex.org/W2924845864","https://openalex.org/W2932986619","https://openalex.org/W2937630855","https://openalex.org/W2940950468","https://openalex.org/W2942886942","https://openalex.org/W2945331674","https://openalex.org/W2949448993","https://openalex.org/W2955871719","https://openalex.org/W2969076740","https://openalex.org/W2971953615","https://openalex.org/W2974359300","https://openalex.org/W3009706270","https://openalex.org/W3013297774","https://openalex.org/W3121807557","https://openalex.org/W4250459335"],"related_works":["https://openalex.org/W3195354540","https://openalex.org/W2743254765","https://openalex.org/W3004150910","https://openalex.org/W3198844958","https://openalex.org/W3168020330","https://openalex.org/W2942382916","https://openalex.org/W3191115266","https://openalex.org/W2025476050","https://openalex.org/W4281560024","https://openalex.org/W2889375222"],"abstract_inverted_index":{"This":[0],"paper":[1],"considers":[2],"a":[3,37],"stochastic":[4,29,48],"SIR":[5],"epidemic":[6],"system":[7,49],"affected":[8],"by":[9],"mixed":[10],"nonlinear":[11],"incidence":[12],"rates.":[13],"Using":[14],"Markov":[15],"semigroup":[16],"theory":[17],"and":[18,40,75],"the":[19,24,28,34,47,58,70,77,87],"Fokker\u2013Planck":[20],"equation,":[21],"we":[22,44,90],"explore":[23],"asymptotic":[25],"dynamics":[26],"of":[27,36,79],"system.":[30],"We":[31],"first":[32],"investigate":[33],"existence":[35],"positive":[38],"solution":[39],"its":[41],"uniqueness.":[42],"Furthermore,":[43],"prove":[45],"that":[46,69],"has":[50],"an":[51],"asymptotically":[52],"stable":[53],"stationary":[54],"distribution.":[55],"In":[56],"addition,":[57],"sufficient":[59],"conditions":[60],"for":[61],"disease":[62],"extinction":[63],"are":[64],"also":[65],"obtained,":[66],"which":[67],"imply":[68],"white":[71],"noise":[72],"can":[73],"suppress":[74],"control":[76],"spread":[78],"infectious":[80],"diseases.":[81],"Finally,":[82],"in":[83],"order":[84],"to":[85],"illustrate":[86],"analytical":[88],"results,":[89],"give":[91],"some":[92],"numerical":[93],"simulations.":[94]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}
