{"id":"https://openalex.org/W4404246953","doi":"https://doi.org/10.3934/nhm.2024054","title":"Dynamic analysis and optimal control of leptospirosis based on Caputo fractional derivative","display_name":"Dynamic analysis and optimal control of leptospirosis based on Caputo fractional derivative","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4404246953","doi":"https://doi.org/10.3934/nhm.2024054"},"language":"en","primary_location":{"id":"doi:10.3934/nhm.2024054","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2024054","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/nhm.2024054","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018656583","display_name":"Ling Zhang","orcid":"https://orcid.org/0000-0001-8174-9176"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ling Zhang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028345539","display_name":"Xuewen Tan","orcid":"https://orcid.org/0000-0002-4710-2325"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xuewen Tan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100768805","display_name":"Jia Li","orcid":"https://orcid.org/0000-0002-3148-6897"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jia Li","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100761647","display_name":"Fan Yang","orcid":"https://orcid.org/0000-0003-4831-2241"},"institutions":[{"id":"https://openalex.org/I145897649","display_name":"Minzu University of China","ror":"https://ror.org/0044e2g62","country_code":"CN","type":"education","lineage":["https://openalex.org/I145897649"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fan Yang","raw_affiliation_strings":["School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650031, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650031, China","institution_ids":["https://openalex.org/I145897649"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5018656583"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0821,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.77586654,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"19","issue":"3","first_page":"1262","last_page":"1285"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12223","display_name":"Leptospirosis research and findings","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2405","display_name":"Parasitology"},"field":{"id":"https://openalex.org/fields/24","display_name":"Immunology and Microbiology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T12223","display_name":"Leptospirosis research and findings","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2405","display_name":"Parasitology"},"field":{"id":"https://openalex.org/fields/24","display_name":"Immunology and Microbiology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12047","display_name":"Viral Infections and Vectors","score":0.9544000029563904,"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/fractional-calculus","display_name":"Fractional calculus","score":0.6535154581069946},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.520578920841217},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5050244927406311},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41732481122016907},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35940849781036377},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3297562599182129},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3261035680770874},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.12817305326461792}],"concepts":[{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6535154581069946},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.520578920841217},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5050244927406311},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41732481122016907},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35940849781036377},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3297562599182129},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3261035680770874},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.12817305326461792},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3934/nhm.2024054","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2024054","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c7db7171ad7549b2affb32828bef00ed","is_oa":true,"landing_page_url":"https://doaj.org/article/c7db7171ad7549b2affb32828bef00ed","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Networks and Heterogeneous Media, Vol 19, Iss 3, Pp 1262-1285 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/nhm.2024054","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2024054","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W75505851","https://openalex.org/W1678356000","https://openalex.org/W1948094720","https://openalex.org/W1963581131","https://openalex.org/W1978349032","https://openalex.org/W1988790447","https://openalex.org/W2054312336","https://openalex.org/W2056132907","https://openalex.org/W2057414857","https://openalex.org/W2063917507","https://openalex.org/W2088303893","https://openalex.org/W2110454331","https://openalex.org/W2113143936","https://openalex.org/W2116341502","https://openalex.org/W2119821739","https://openalex.org/W2135293965","https://openalex.org/W2153513200","https://openalex.org/W2263853988","https://openalex.org/W2285079527","https://openalex.org/W2510356152","https://openalex.org/W2516268940","https://openalex.org/W2810040590","https://openalex.org/W2900672594","https://openalex.org/W2911964244","https://openalex.org/W2912934387","https://openalex.org/W2914046124","https://openalex.org/W2967296229","https://openalex.org/W2997628747","https://openalex.org/W3003765007","https://openalex.org/W3004732066","https://openalex.org/W3041852941","https://openalex.org/W3045020061","https://openalex.org/W3080748243","https://openalex.org/W3201938985","https://openalex.org/W3202069269","https://openalex.org/W4205928213","https://openalex.org/W4221000792","https://openalex.org/W4283272137","https://openalex.org/W4287447672","https://openalex.org/W4295732991","https://openalex.org/W4362471053","https://openalex.org/W4386323057"],"related_works":["https://openalex.org/W2082446734","https://openalex.org/W4313560640","https://openalex.org/W2253351617","https://openalex.org/W4246784705","https://openalex.org/W3121927021","https://openalex.org/W4390948881","https://openalex.org/W2089892488","https://openalex.org/W2416906960","https://openalex.org/W2050580331","https://openalex.org/W3049300385"],"abstract_inverted_index":{"&lt;p&gt;Caputo":[0],"fractional":[1,5,12,64,187],"derivative":[2,19,42,65],"solves":[3],"the":[4,22,26,34,37,40,44,47,51,62,69,78,86,90,99,105,118,136,142,145,149,171,182,190,213,219,223,230,235,240],"initial":[6],"value":[7,38,45],"problem":[8],"in":[9,21],"Riemann-Liouville":[10],"(R-L)":[11],"calculus.":[13],"The":[14,197,209],"definition":[15,27],"of":[16,28,36,39,46,72,89,98,111,114,120,144,156,185,222,237],"a":[17,56,81,153,161],"Caputo-type":[18],"is":[20],"same":[23],"form":[24],"as":[25,93,129],"an":[29],"integral":[30,41],"differential":[31],"equation,":[32],"including":[33],"restriction":[35],"to":[43,67,75,104,138,148,169,234],"unknown":[48],"function":[49],"at":[50],"endpoint":[52],"$":[53],"t":[54],"=":[55],"$.":[57],"Therefore,":[58,229],"this":[59],"paper":[60],"introduced":[61,168],"Caputo":[63],"(CFD)":[66],"establish":[68],"transmission":[70,220],"model":[71,79,155],"leptospirosis.":[73],"First,":[74],"ensure":[76],"that":[77,212],"had":[80],"particular":[82],"significance,":[83],"we":[84,124],"proved":[85],"dynamic":[87],"properties":[88],"model,":[91],"such":[92,128],"nonnegative,":[94],"boundedness,":[95],"and":[96,108,116,134,140,160,203,207,239],"stability":[97],"equilibrium":[100],"point.":[101],"Second,":[102],"according":[103],"existence":[106],"mode":[107],"genetic":[109],"characteristics":[110],"pathogenic":[112],"bacteria":[113],"leptospirosis,":[115],"from":[117],"perspective":[119],"score":[121],"optimal":[122],"control,":[123],"put":[125],"forward":[126],"measures":[127],"wearing":[130],"protective":[131],"clothing,":[132],"hospitalization,":[133],"cleaning":[135],"environment":[137],"prevent":[139],"control":[141,151,154,172,177,215],"spread":[143],"disease.":[146],"According":[147],"proposed":[150],"measures,":[152],"leptospirosis":[157,238],"was":[158,167],"established,":[159],"forward-backward":[162],"scanning":[163],"algorithm":[164],"(FB":[165],"algorithm)":[166],"optimize":[170],"function.":[173],"Three":[174],"different":[175,186],"disease":[176,224],"strategies":[178],"were":[179,205],"proposed.":[180],"Finally,":[181],"numerical":[183],"simulation":[184],"orders":[188],"used":[189],"fde12":[191],"(based":[192],"on":[193],"Adams\u2013Bashforth\u2013Moulton":[194],"scheme)":[195],"solver.":[196],"three":[198],"optimized":[199,214],"strategies,":[200],"A,":[201],"B,":[202],"C,":[204],"compared":[206],"analyzed.":[208],"results":[210],"showed":[211],"strategy":[216],"could":[217],"shorten":[218],"time":[221],"by":[225],"about":[226],"80":[227],"days.":[228],"above":[231],"methods":[232],"contributed":[233],"study":[236],"World":[241],"Health":[242],"Organization.&lt;/p&gt;":[243]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2025-12-27T23:08:20.325037","created_date":"2025-10-10T00:00:00"}
