{"id":"https://openalex.org/W2964769529","doi":"https://doi.org/10.1155/2019/1097201","title":"Dynamic Analysis of a Fractional\u2010Order Model for Hepatitis B Virus with Holling II Functional Response","display_name":"Dynamic Analysis of a Fractional\u2010Order Model for Hepatitis B Virus with Holling II Functional Response","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2964769529","doi":"https://doi.org/10.1155/2019/1097201","mag":"2964769529"},"language":"en","primary_location":{"id":"doi:10.1155/2019/1097201","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/1097201","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/1097201.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/2019/1097201.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032880028","display_name":"Ruiqing Shi","orcid":"https://orcid.org/0000-0002-7012-7651"},"institutions":[{"id":"https://openalex.org/I4210139885","display_name":"Shanxi Normal University","ror":null,"country_code":"CN","type":null,"lineage":["https://openalex.org/I4210139885"]},{"id":"https://openalex.org/I94310126","display_name":"Shanxi Normal University","ror":"https://ror.org/03zd3ta61","country_code":"CN","type":"education","lineage":["https://openalex.org/I94310126"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ruiqing Shi","raw_affiliation_strings":["School of Mathematics and Computer Science, Shanxi Normal University, Linfen , China","School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science, Shanxi Normal University, Linfen , China","institution_ids":["https://openalex.org/I4210139885"]},{"raw_affiliation_string":"School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, China","institution_ids":["https://openalex.org/I94310126"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078894334","display_name":"Ting\u2010Jang Lu","orcid":"https://orcid.org/0000-0002-3956-8272"},"institutions":[{"id":"https://openalex.org/I4210139885","display_name":"Shanxi Normal University","ror":null,"country_code":"CN","type":null,"lineage":["https://openalex.org/I4210139885"]},{"id":"https://openalex.org/I94310126","display_name":"Shanxi Normal University","ror":"https://ror.org/03zd3ta61","country_code":"CN","type":"education","lineage":["https://openalex.org/I94310126"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ting Lu","raw_affiliation_strings":["School of Mathematics and Computer Science, Shanxi Normal University, Linfen , China","School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science, Shanxi Normal University, Linfen , China","institution_ids":["https://openalex.org/I4210139885"]},{"raw_affiliation_string":"School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, China","institution_ids":["https://openalex.org/I94310126"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102004003","display_name":"Cuihong Wang","orcid":"https://orcid.org/0000-0002-8676-6722"},"institutions":[{"id":"https://openalex.org/I4210139885","display_name":"Shanxi Normal University","ror":null,"country_code":"CN","type":null,"lineage":["https://openalex.org/I4210139885"]},{"id":"https://openalex.org/I94310126","display_name":"Shanxi Normal University","ror":"https://ror.org/03zd3ta61","country_code":"CN","type":"education","lineage":["https://openalex.org/I94310126"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Cuihong Wang","raw_affiliation_strings":["School of Mathematics and Computer Science, Shanxi Normal University, Linfen , China","School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science, Shanxi Normal University, Linfen , China","institution_ids":["https://openalex.org/I4210139885"]},{"raw_affiliation_string":"School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, China","institution_ids":["https://openalex.org/I94310126"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5032880028"],"corresponding_institution_ids":["https://openalex.org/I4210139885","https://openalex.org/I94310126"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":2.3756,"has_fulltext":true,"cited_by_count":28,"citation_normalized_percentile":{"value":0.88707692,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"2019","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9987000226974487,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9987000226974487,"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":0.9983000159263611,"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/T10151","display_name":"Hepatitis C virus research","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/2721","display_name":"Hepatology"},"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/functional-response","display_name":"Functional response","score":0.8049443364143372},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5610349178314209},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5498015880584717},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4862453043460846},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.11464554071426392},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.06234106421470642}],"concepts":[{"id":"https://openalex.org/C110201527","wikidata":"https://www.wikidata.org/wiki/Q5508845","display_name":"Functional response","level":4,"score":0.8049443364143372},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5610349178314209},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5498015880584717},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4862453043460846},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.11464554071426392},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.06234106421470642},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C96857902","wikidata":"https://www.wikidata.org/wiki/Q2138108","display_name":"Predator","level":3,"score":0.0},{"id":"https://openalex.org/C188382862","wikidata":"https://www.wikidata.org/wiki/Q170430","display_name":"Predation","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2019/1097201","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/1097201","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/1097201.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:1097201","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2019/1097201.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:d8f9dd80125e42f3be74aea507334112","is_oa":true,"landing_page_url":"https://doaj.org/article/d8f9dd80125e42f3be74aea507334112","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 2019 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2019/1097201","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/1097201","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/1097201.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":[{"display_name":"Good health and well-being","score":0.7699999809265137,"id":"https://metadata.un.org/sdg/3"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2964769529.pdf","grobid_xml":"https://content.openalex.org/works/W2964769529.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W980151242","https://openalex.org/W1217212134","https://openalex.org/W1974721186","https://openalex.org/W1980587508","https://openalex.org/W1988269521","https://openalex.org/W1990198162","https://openalex.org/W1991592276","https://openalex.org/W1994527567","https://openalex.org/W2002304265","https://openalex.org/W2005190756","https://openalex.org/W2031966433","https://openalex.org/W2036442409","https://openalex.org/W2043519223","https://openalex.org/W2055339872","https://openalex.org/W2057414857","https://openalex.org/W2064059889","https://openalex.org/W2112680994","https://openalex.org/W2157098396","https://openalex.org/W2168003330","https://openalex.org/W2204270911","https://openalex.org/W2237461300","https://openalex.org/W2259227674","https://openalex.org/W2389878665","https://openalex.org/W2410602295","https://openalex.org/W2510943529","https://openalex.org/W2520377028","https://openalex.org/W2562779659","https://openalex.org/W2736160477","https://openalex.org/W2751624414","https://openalex.org/W2767477371","https://openalex.org/W2843225982","https://openalex.org/W2888548938","https://openalex.org/W2920879259","https://openalex.org/W2949260457","https://openalex.org/W2954126033","https://openalex.org/W4388364567"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2129001831","https://openalex.org/W2277768163","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4400697040","https://openalex.org/W4234536609","https://openalex.org/W2067110756","https://openalex.org/W2365962591","https://openalex.org/W2013670049"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3,64],"fractional\u2010order":[4],"model":[5],"is":[6,67],"constructed":[7],"to":[8,58],"describe":[9],"the":[10,18,28,33,37,45,60],"transmission":[11],"of":[12,22,39,47],"Hepatitis":[13],"B":[14],"Virus":[15],"(HBV).":[16],"Firstly,":[17],"existence":[19,38],"and":[20,32],"uniqueness":[21],"positive":[23],"solutions":[24],"are":[25,42,49,56],"proved.":[26],"Secondly,":[27],"basic":[29],"reproduction":[30],"number":[31],"sufficient":[34],"conditions":[35],"for":[36],"two":[40],"equilibriums":[41,48],"obtained.":[43],"Thirdly,":[44],"stability":[46],"analyzed.":[50],"After":[51],"that,":[52],"some":[53],"numerical":[54],"simulations":[55],"performed":[57],"verify":[59],"theoretical":[61],"prediction.":[62],"Finally,":[63],"brief":[65],"discussion":[66],"presented.":[68]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
