{"id":"https://openalex.org/W4287921776","doi":"https://doi.org/10.1007/s12190-022-01766-3","title":"Threshold dynamics and optimal control of a dengue epidemic model with time delay and saturated incidence","display_name":"Threshold dynamics and optimal control of a dengue epidemic model with time delay and saturated incidence","publication_year":2022,"publication_date":"2022-07-26","ids":{"openalex":"https://openalex.org/W4287921776","doi":"https://doi.org/10.1007/s12190-022-01766-3"},"language":"en","primary_location":{"id":"doi:10.1007/s12190-022-01766-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s12190-022-01766-3","pdf_url":null,"source":{"id":"https://openalex.org/S199913245","display_name":"Journal of Applied Mathematics and Computing","issn_l":"1598-5865","issn":["1598-5865","1865-2085"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055704592","display_name":"Bian Wang","orcid":"https://orcid.org/0000-0001-8489-2744"},"institutions":[{"id":"https://openalex.org/I181877577","display_name":"Shanxi University","ror":"https://ror.org/03y3e3s17","country_code":"CN","type":"education","lineage":["https://openalex.org/I181877577"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bian Wang","raw_affiliation_strings":["Complex Systems Research Center, Shanxi University, Taiyuan, 030006, People\u2019s Republic of China","Complex Systems Research Center, Shanxi University, Taiyuan, 030006, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Complex Systems Research Center, Shanxi University, Taiyuan, 030006, People\u2019s Republic of China","institution_ids":["https://openalex.org/I181877577"]},{"raw_affiliation_string":"Complex Systems Research Center, Shanxi University, Taiyuan, 030006, People's Republic of China","institution_ids":["https://openalex.org/I181877577"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063147362","display_name":"Xiaohong Tian","orcid":"https://orcid.org/0000-0003-4468-0645"},"institutions":[{"id":"https://openalex.org/I181877577","display_name":"Shanxi University","ror":"https://ror.org/03y3e3s17","country_code":"CN","type":"education","lineage":["https://openalex.org/I181877577"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaohong Tian","raw_affiliation_strings":["Complex Systems Research Center, Shanxi University, Taiyuan, 030006, People\u2019s Republic of China","Complex Systems Research Center, Shanxi University, Taiyuan, 030006, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Complex Systems Research Center, Shanxi University, Taiyuan, 030006, People\u2019s Republic of China","institution_ids":["https://openalex.org/I181877577"]},{"raw_affiliation_string":"Complex Systems Research Center, Shanxi University, Taiyuan, 030006, People's Republic of China","institution_ids":["https://openalex.org/I181877577"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080981240","display_name":"Rui Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I181877577","display_name":"Shanxi University","ror":"https://ror.org/03y3e3s17","country_code":"CN","type":"education","lineage":["https://openalex.org/I181877577"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rui Xu","raw_affiliation_strings":["Complex Systems Research Center, Shanxi University, Taiyuan, 030006, People\u2019s Republic of China","Complex Systems Research Center, Shanxi University, Taiyuan, 030006, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Complex Systems Research Center, Shanxi University, Taiyuan, 030006, People\u2019s Republic of China","institution_ids":["https://openalex.org/I181877577"]},{"raw_affiliation_string":"Complex Systems Research Center, Shanxi University, Taiyuan, 030006, People's Republic of China","institution_ids":["https://openalex.org/I181877577"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029444437","display_name":"Chenwei Song","orcid":"https://orcid.org/0000-0002-0567-8748"},"institutions":[{"id":"https://openalex.org/I181877577","display_name":"Shanxi University","ror":"https://ror.org/03y3e3s17","country_code":"CN","type":"education","lineage":["https://openalex.org/I181877577"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chenwei Song","raw_affiliation_strings":["Complex Systems Research Center, Shanxi University, Taiyuan, 030006, People\u2019s Republic of China","Complex Systems Research Center, Shanxi University, Taiyuan, 030006, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Complex Systems Research Center, Shanxi University, Taiyuan, 030006, People\u2019s Republic of China","institution_ids":["https://openalex.org/I181877577"]},{"raw_affiliation_string":"Complex Systems Research Center, Shanxi University, Taiyuan, 030006, People's Republic of China","institution_ids":["https://openalex.org/I181877577"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5055704592"],"corresponding_institution_ids":["https://openalex.org/I181877577"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.7957,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.84340123,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"69","issue":"1","first_page":"871","last_page":"893"},"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/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9941999912261963,"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"}},{"id":"https://openalex.org/T10410","display_name":"COVID-19 epidemiological studies","score":0.9904000163078308,"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/mathematics","display_name":"Mathematics","score":0.7987581491470337},{"id":"https://openalex.org/keywords/basic-reproduction-number","display_name":"Basic reproduction number","score":0.7549753189086914},{"id":"https://openalex.org/keywords/stability-theory","display_name":"Stability theory","score":0.6833251714706421},{"id":"https://openalex.org/keywords/dengue-fever","display_name":"Dengue fever","score":0.6027751564979553},{"id":"https://openalex.org/keywords/epidemic-model","display_name":"Epidemic model","score":0.5854490399360657},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5589136481285095},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5122422575950623},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4867279827594757},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4852023422718048},{"id":"https://openalex.org/keywords/invariance-principle","display_name":"Invariance principle","score":0.4674210250377655},{"id":"https://openalex.org/keywords/maximum-principle","display_name":"Maximum principle","score":0.4669678509235382},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.3908313512802124},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.34961384534835815},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.29155099391937256},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.26889270544052124},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2088322639465332},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1120067834854126},{"id":"https://openalex.org/keywords/demography","display_name":"Demography","score":0.08363661170005798},{"id":"https://openalex.org/keywords/virology","display_name":"Virology","score":0.06376892328262329}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7987581491470337},{"id":"https://openalex.org/C204264503","wikidata":"https://www.wikidata.org/wiki/Q901464","display_name":"Basic reproduction number","level":3,"score":0.7549753189086914},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.6833251714706421},{"id":"https://openalex.org/C533803919","wikidata":"https://www.wikidata.org/wiki/Q30953","display_name":"Dengue fever","level":2,"score":0.6027751564979553},{"id":"https://openalex.org/C1627819","wikidata":"https://www.wikidata.org/wiki/Q2572354","display_name":"Epidemic model","level":3,"score":0.5854490399360657},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5589136481285095},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5122422575950623},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4867279827594757},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4852023422718048},{"id":"https://openalex.org/C156387681","wikidata":"https://www.wikidata.org/wiki/Q6059484","display_name":"Invariance principle","level":2,"score":0.4674210250377655},{"id":"https://openalex.org/C31010330","wikidata":"https://www.wikidata.org/wiki/Q1914255","display_name":"Maximum principle","level":3,"score":0.4669678509235382},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3908313512802124},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.34961384534835815},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29155099391937256},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.26889270544052124},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2088322639465332},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1120067834854126},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.08363661170005798},{"id":"https://openalex.org/C159047783","wikidata":"https://www.wikidata.org/wiki/Q7215","display_name":"Virology","level":1,"score":0.06376892328262329},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s12190-022-01766-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s12190-022-01766-3","pdf_url":null,"source":{"id":"https://openalex.org/S199913245","display_name":"Journal of Applied Mathematics and Computing","issn_l":"1598-5865","issn":["1598-5865","1865-2085"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7300000190734863,"display_name":"Good health and well-being","id":"https://metadata.un.org/sdg/3"}],"awards":[{"id":"https://openalex.org/G1030021811","display_name":null,"funder_award_id":"11871316","funder_id":"https://openalex.org/F4320315254","funder_display_name":"Innovative Research Group Project of the National Natural Science Foundation of China"},{"id":"https://openalex.org/G5258029177","display_name":null,"funder_award_id":"11801340","funder_id":"https://openalex.org/F4320315254","funder_display_name":"Innovative Research Group Project of the National Natural Science Foundation of China"},{"id":"https://openalex.org/G7004479228","display_name":null,"funder_award_id":"201801D221007","funder_id":"https://openalex.org/F4320322666","funder_display_name":"Natural Science Foundation of Shanxi Province"},{"id":"https://openalex.org/G811463108","display_name":null,"funder_award_id":"201801D121006","funder_id":"https://openalex.org/F4320322666","funder_display_name":"Natural Science Foundation of Shanxi Province"}],"funders":[{"id":"https://openalex.org/F4320315254","display_name":"Innovative Research Group Project of the National Natural Science Foundation of China","ror":null},{"id":"https://openalex.org/F4320322666","display_name":"Natural Science Foundation of Shanxi Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1894874618","https://openalex.org/W1967891459","https://openalex.org/W1991038590","https://openalex.org/W2011771253","https://openalex.org/W2021834060","https://openalex.org/W2027467474","https://openalex.org/W2032417357","https://openalex.org/W2033791313","https://openalex.org/W2037638145","https://openalex.org/W2059119472","https://openalex.org/W2069887487","https://openalex.org/W2075489080","https://openalex.org/W2075678942","https://openalex.org/W2077339070","https://openalex.org/W2083755715","https://openalex.org/W2112680994","https://openalex.org/W2113133070","https://openalex.org/W2114848791","https://openalex.org/W2132052962","https://openalex.org/W2152803686","https://openalex.org/W2158630456","https://openalex.org/W2335001735","https://openalex.org/W2522748901","https://openalex.org/W4211202937","https://openalex.org/W4302609762"],"related_works":["https://openalex.org/W4320351350","https://openalex.org/W2593471576","https://openalex.org/W4388177052","https://openalex.org/W2024035605","https://openalex.org/W2418891709","https://openalex.org/W2774469868","https://openalex.org/W3202281170","https://openalex.org/W1967741193","https://openalex.org/W4318818740","https://openalex.org/W2191940372"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}