{"id":"https://openalex.org/W4411296260","doi":"https://doi.org/10.1142/s0218127425501226","title":"A Piecewise-Smooth Dynamic System with Two Thresholds and Its Application to Epidemic Control","display_name":"A Piecewise-Smooth Dynamic System with Two Thresholds and Its Application to Epidemic Control","publication_year":2025,"publication_date":"2025-06-12","ids":{"openalex":"https://openalex.org/W4411296260","doi":"https://doi.org/10.1142/s0218127425501226"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127425501226","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127425501226","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5110263656","display_name":"Haifeng Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haifeng Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an, Shaanxi 710049, P. R. China","School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an, Shaanxi 710049, P. R. China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, P. R. China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022540617","display_name":"Yanni Xiao","orcid":"https://orcid.org/0000-0003-0432-7628"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yanni Xiao","raw_affiliation_strings":["School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an, Shaanxi 710049, P. R. China","School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an, Shaanxi 710049, P. R. China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, P. R. China","institution_ids":["https://openalex.org/I87445476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5022540617"],"corresponding_institution_ids":["https://openalex.org/I87445476"],"apc_list":null,"apc_paid":null,"fwci":1.8295,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.84877182,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"35","issue":"10","first_page":null,"last_page":null},"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":0.9990000128746033,"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":0.9990000128746033,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10410","display_name":"COVID-19 epidemiological studies","score":0.921500027179718,"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/planar","display_name":"Planar","score":0.7824918031692505},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7586749792098999},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6887723207473755},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.6528952121734619},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5607600808143616},{"id":"https://openalex.org/keywords/parameter-space","display_name":"Parameter space","score":0.5424348711967468},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.531972348690033},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5224101543426514},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5082620978355408},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5061842799186707},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.4711184501647949},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.43146324157714844},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.4169093072414398},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37420159578323364},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.30090826749801636},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19987353682518005},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13137474656105042},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12473002076148987}],"concepts":[{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.7824918031692505},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7586749792098999},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6887723207473755},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.6528952121734619},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5607600808143616},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.5424348711967468},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.531972348690033},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5224101543426514},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5082620978355408},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5061842799186707},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.4711184501647949},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.43146324157714844},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.4169093072414398},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37420159578323364},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.30090826749801636},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19987353682518005},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13137474656105042},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12473002076148987},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127425501226","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127425501226","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/3","display_name":"Good health and well-being","score":0.8500000238418579}],"awards":[{"id":"https://openalex.org/G148668811","display_name":null,"funder_award_id":"12031010","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1963533398","https://openalex.org/W1997847487","https://openalex.org/W2003578553","https://openalex.org/W2004269351","https://openalex.org/W2020890117","https://openalex.org/W2055316229","https://openalex.org/W2055468478","https://openalex.org/W2061676200","https://openalex.org/W2065242464","https://openalex.org/W2069424479","https://openalex.org/W2083823140","https://openalex.org/W2091178112","https://openalex.org/W2302059450","https://openalex.org/W2420485525","https://openalex.org/W2515101212","https://openalex.org/W2819453093","https://openalex.org/W2884809825","https://openalex.org/W2946651630","https://openalex.org/W2966620931","https://openalex.org/W2997617322","https://openalex.org/W3034543452","https://openalex.org/W3035693076","https://openalex.org/W3044897934","https://openalex.org/W3047132168","https://openalex.org/W3152221430","https://openalex.org/W3172005488","https://openalex.org/W4213180705","https://openalex.org/W4230132907","https://openalex.org/W4237564398","https://openalex.org/W4255896881","https://openalex.org/W4293078920","https://openalex.org/W4392905712","https://openalex.org/W4392948284","https://openalex.org/W4402575587","https://openalex.org/W4410577823"],"related_works":["https://openalex.org/W587735977","https://openalex.org/W1978142926","https://openalex.org/W3157395178","https://openalex.org/W184455116","https://openalex.org/W2058473748","https://openalex.org/W963756281","https://openalex.org/W2371558776","https://openalex.org/W2045569473","https://openalex.org/W4226164715","https://openalex.org/W3096660584"],"abstract_inverted_index":{"A":[0],"general":[1],"type":[2],"of":[3,63,79,92,142,173,206,212],"piecewise-smooth":[4,126],"dynamic":[5],"system":[6,23,50,107,176],"with":[7,51,89,108,129],"two":[8,52,109,190],"thresholds":[9,53,110],"is":[10,137,200],"analyzed":[11],"in":[12,83],"this":[13,64,80],"work.":[14],"We":[15,161],"define":[16],"some":[17],"fundamental":[18],"notions":[19],"for":[20,35],"the":[21,33,36,47,61,75,84,90,93,101,104,112,119,133,140,164,170,174,183,189,194,204,210],"proposed":[22],"such":[24,67],"as":[25,68],"oscillating":[26,85],"space":[27,86],"and":[28,59,72,77,111,121,146],"real/virtual":[29],"equilibrium,":[30],"which":[31],"generalizes":[32],"counterparts":[34],"planar":[37,48,95,105,113],"Filippov":[38,96,114],"system.":[39,97,115],"Moreover,":[40],"we":[41,99,117],"show":[42],"that":[43,136,163],"under":[44,180],"certain":[45],"conditions":[46],"switched":[49,106],"generates":[54],"a":[55,125,148],"novel":[56],"limit":[57],"cycle,":[58],"analyze":[60],"properties":[62],"periodic":[65,81,185],"solution":[66,82,186],"existence,":[69],"stability,":[70],"amplitude":[71],"period.":[73],"Interestingly,":[74],"existence":[76],"stability":[78],"are":[87],"consistent":[88],"pseudo-equilibrium":[91],"corresponding":[94],"Hence,":[98],"establish":[100],"connection":[102],"between":[103],"Finally,":[116],"apply":[118],"modeling":[120],"analytical":[122],"approaches":[123],"to":[124,158,202],"epidemic":[127,165],"model":[128,166],"density-dependent":[130],"interventions,":[131],"describing":[132],"control":[134],"measure":[135,199],"triggered":[138],"when":[139,154],"number":[141,205],"infected":[143,207],"individuals":[144,208],"increases":[145],"reaches":[147],"critical":[149],"level":[150],"while":[151],"being":[152],"suspended":[153],"it":[155],"decreases":[156],"down":[157],"another":[159],"level.":[160],"prove":[162],"stabilizes":[167],"at":[168],"either":[169],"endemic":[171],"equilibrium":[172],"free":[175],"(the":[177],"one":[178],"not":[179],"control)":[181],"or":[182],"new":[184],"induced":[187],"by":[188],"thresholds,":[191],"depending":[192],"on":[193],"threshold":[195],"levels.":[196],"The":[197],"two-threshold":[198],"able":[201],"suppress":[203],"during":[209],"evolution":[211],"an":[213],"infectious":[214],"disease.":[215]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-04-03T22:45:19.894376","created_date":"2025-10-10T00:00:00"}