{"id":"https://openalex.org/W4323570297","doi":"https://doi.org/10.1142/s0218127423500190","title":"Stability and Hopf Bifurcation Analysis of an HIV Infection Model in the Evolution of Drug Resistance","display_name":"Stability and Hopf Bifurcation Analysis of an HIV Infection Model in the Evolution of Drug Resistance","publication_year":2023,"publication_date":"2023-02-01","ids":{"openalex":"https://openalex.org/W4323570297","doi":"https://doi.org/10.1142/s0218127423500190"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127423500190","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s0218127423500190","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/A5035883117","display_name":"Rui Xu","orcid":"https://orcid.org/0000-0001-6367-7631"},"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":"Rui Xu","raw_affiliation_strings":["Complex Systems Research Center, Shanxi University, Taiyuan 030006, P. R. China"],"raw_orcid":"https://orcid.org/0000-0001-6367-7631","affiliations":[{"raw_affiliation_string":"Complex Systems Research Center, Shanxi University, Taiyuan 030006, P. R. China","institution_ids":["https://openalex.org/I181877577"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103251101","display_name":"Yan Yang","orcid":"https://orcid.org/0009-0002-4042-0109"},"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":"Yan Yang","raw_affiliation_strings":["Complex Systems Research Center, Shanxi University, Taiyuan 030006, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Complex Systems Research Center, Shanxi University, Taiyuan 030006, P. R. China","institution_ids":["https://openalex.org/I181877577"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5035883117"],"corresponding_institution_ids":["https://openalex.org/I181877577"],"apc_list":null,"apc_paid":null,"fwci":0.2582,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.56065409,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"33","issue":"02","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":0.9997000098228455,"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":0.9997000098228455,"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/T10112","display_name":"HIV Research and Treatment","score":0.9919000267982483,"subfield":{"id":"https://openalex.org/subfields/2406","display_name":"Virology"},"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/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9916999936103821,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/ctl*","display_name":"CTL*","score":0.9757239818572998},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.7974830269813538},{"id":"https://openalex.org/keywords/cytotoxic-t-cell","display_name":"Cytotoxic T cell","score":0.6271389722824097},{"id":"https://openalex.org/keywords/effector","display_name":"Effector","score":0.5290961265563965},{"id":"https://openalex.org/keywords/virology","display_name":"Virology","score":0.5037474036216736},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.4848938584327698},{"id":"https://openalex.org/keywords/basic-reproduction-number","display_name":"Basic reproduction number","score":0.469896525144577},{"id":"https://openalex.org/keywords/immune-system","display_name":"Immune system","score":0.4698411822319031},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.469698429107666},{"id":"https://openalex.org/keywords/human-immunodeficiency-virus","display_name":"Human immunodeficiency virus (HIV)","score":0.4446483850479126},{"id":"https://openalex.org/keywords/drug","display_name":"Drug","score":0.43028995394706726},{"id":"https://openalex.org/keywords/drug-resistance","display_name":"Drug resistance","score":0.42079877853393555},{"id":"https://openalex.org/keywords/immunology","display_name":"Immunology","score":0.3240162432193756},{"id":"https://openalex.org/keywords/cd8","display_name":"CD8","score":0.301933228969574},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.1981540024280548},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.18655601143836975},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16608479619026184},{"id":"https://openalex.org/keywords/genetics","display_name":"Genetics","score":0.13541170954704285},{"id":"https://openalex.org/keywords/in-vitro","display_name":"In vitro","score":0.10411211848258972},{"id":"https://openalex.org/keywords/pharmacology","display_name":"Pharmacology","score":0.07515823841094971}],"concepts":[{"id":"https://openalex.org/C147969180","wikidata":"https://www.wikidata.org/wiki/Q5014579","display_name":"CTL*","level":4,"score":0.9757239818572998},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.7974830269813538},{"id":"https://openalex.org/C154317977","wikidata":"https://www.wikidata.org/wiki/Q376266","display_name":"Cytotoxic T cell","level":3,"score":0.6271389722824097},{"id":"https://openalex.org/C51785407","wikidata":"https://www.wikidata.org/wiki/Q2627568","display_name":"Effector","level":2,"score":0.5290961265563965},{"id":"https://openalex.org/C159047783","wikidata":"https://www.wikidata.org/wiki/Q7215","display_name":"Virology","level":1,"score":0.5037474036216736},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.4848938584327698},{"id":"https://openalex.org/C204264503","wikidata":"https://www.wikidata.org/wiki/Q901464","display_name":"Basic reproduction number","level":3,"score":0.469896525144577},{"id":"https://openalex.org/C8891405","wikidata":"https://www.wikidata.org/wiki/Q1059","display_name":"Immune system","level":2,"score":0.4698411822319031},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.469698429107666},{"id":"https://openalex.org/C3013748606","wikidata":"https://www.wikidata.org/wiki/Q15787","display_name":"Human immunodeficiency virus (HIV)","level":2,"score":0.4446483850479126},{"id":"https://openalex.org/C2780035454","wikidata":"https://www.wikidata.org/wiki/Q8386","display_name":"Drug","level":2,"score":0.43028995394706726},{"id":"https://openalex.org/C114851261","wikidata":"https://www.wikidata.org/wiki/Q12147416","display_name":"Drug resistance","level":2,"score":0.42079877853393555},{"id":"https://openalex.org/C203014093","wikidata":"https://www.wikidata.org/wiki/Q101929","display_name":"Immunology","level":1,"score":0.3240162432193756},{"id":"https://openalex.org/C167672396","wikidata":"https://www.wikidata.org/wiki/Q417800","display_name":"CD8","level":3,"score":0.301933228969574},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.1981540024280548},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.18655601143836975},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16608479619026184},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.13541170954704285},{"id":"https://openalex.org/C202751555","wikidata":"https://www.wikidata.org/wiki/Q221681","display_name":"In vitro","level":2,"score":0.10411211848258972},{"id":"https://openalex.org/C98274493","wikidata":"https://www.wikidata.org/wiki/Q128406","display_name":"Pharmacology","level":1,"score":0.07515823841094971},{"id":"https://openalex.org/C99454951","wikidata":"https://www.wikidata.org/wiki/Q932068","display_name":"Environmental health","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"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":1,"locations":[{"id":"doi:10.1142/s0218127423500190","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s0218127423500190","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":[{"score":0.8600000143051147,"id":"https://metadata.un.org/sdg/3","display_name":"Good health and well-being"}],"awards":[{"id":"https://openalex.org/G423030170","display_name":"\u57fa\u4e8e\u6e38\u79bb\u75c5\u6bd2\u548c\u7ec6\u80de-\u7ec6\u80de\u4f20\u64ad\u7684HIV\u514d\u75ab-\u6d41\u884c\u75c5\u5b66\u5d4c\u5957\u52a8\u529b\u5b66\u7684\u5efa\u6a21\u4e0e\u7814\u7a76","funder_award_id":"11871316","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1851248039","https://openalex.org/W1975002344","https://openalex.org/W1980587508","https://openalex.org/W1981054952","https://openalex.org/W1987514016","https://openalex.org/W2009710695","https://openalex.org/W2010266827","https://openalex.org/W2036642613","https://openalex.org/W2057003218","https://openalex.org/W2060701294","https://openalex.org/W2062152384","https://openalex.org/W2081879691","https://openalex.org/W2092181965","https://openalex.org/W2106514943","https://openalex.org/W2112680994","https://openalex.org/W2137222057","https://openalex.org/W2146089461","https://openalex.org/W2196026454","https://openalex.org/W2335001735","https://openalex.org/W2481048563","https://openalex.org/W2792882465","https://openalex.org/W4293244147"],"related_works":["https://openalex.org/W1549922507","https://openalex.org/W1605884721","https://openalex.org/W2102262438","https://openalex.org/W2027917976","https://openalex.org/W2032919665","https://openalex.org/W1864390991","https://openalex.org/W2414401084","https://openalex.org/W1985728487","https://openalex.org/W4239554058","https://openalex.org/W1584466340"],"abstract_inverted_index":{"In":[0,76],"the":[1,53,56,108,126,145,150],"course":[2],"of":[3,27,110],"reverse":[4],"transcription,":[5],"drug-sensitive":[6,85],"strain":[7,104],"can":[8,32],"mutate":[9],"to":[10,18,64],"a":[11],"drug-resistant":[12,87],"one.":[13],"Cell-to-cell":[14],"transmission":[15],"is":[16,58,114],"proved":[17],"be":[19,33],"more":[20,142],"efficient":[21],"than":[22],"virus-to-cell":[23],"infection.":[24],"The":[25,98,120],"population":[26],"Cytotoxic":[28],"T":[29],"Lymphocytes":[30],"(CTLs)":[31],"divided":[34],"into":[35,68],"CTL":[36,39,42,60,69,129],"precursors":[37,43,61],"and":[38,66,86,91,95,107,153],"effectors.":[40],"Naive":[41],"are":[44,105],"those":[45],"that":[46],"never":[47],"have":[48,73],"contacted":[49],"antigen,":[50],"circulating":[51],"around":[52],"body.":[54],"Once":[55],"host":[57],"infected,":[59],"(CTLp)":[62],"begin":[63],"proliferate":[65],"differentiate":[67],"effectors":[70],"(CTLe),":[71],"which":[72],"antiviral":[74],"activity.":[75],"this":[77],"paper,":[78],"we":[79,140],"study":[80],"an":[81],"HIV":[82],"model":[83],"with":[84,128],"mixed":[88],"strains,":[89],"CTLp":[90],"CTLe,":[92],"both":[93],"viral":[94],"cellular":[96],"infections.":[97],"basic":[99],"reproduction":[100],"ratios":[101],"for":[102],"each":[103,111],"derived":[106],"stability":[109],"feasible":[112],"equilibrium":[113,127],"analyzed":[115],"by":[116],"using":[117,136],"Routh\u2013Hurwitz":[118],"criteria.":[119],"periodic":[121],"solutions":[122],"may":[123],"occur":[124],"near":[125],"immune":[130],"response":[131],"via":[132],"Hopf":[133],"bifurcation.":[134],"By":[135],"normal":[137],"form":[138],"theory,":[139],"find":[141],"information":[143],"about":[144],"limit":[146],"cycles,":[147],"such":[148],"as":[149],"amplitude,":[151],"phase":[152],"stability.":[154]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
