{"id":"https://openalex.org/W4408844655","doi":"https://doi.org/10.1142/s021812742550066x","title":"Modeling and Analysis for a Delayed Cytokine-Enhanced Viral Infection Model","display_name":"Modeling and Analysis for a Delayed Cytokine-Enhanced Viral Infection Model","publication_year":2025,"publication_date":"2025-03-25","ids":{"openalex":"https://openalex.org/W4408844655","doi":"https://doi.org/10.1142/s021812742550066x"},"language":"en","primary_location":{"id":"doi:10.1142/s021812742550066x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812742550066x","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/A5030374259","display_name":"Jinhu Xu","orcid":"https://orcid.org/0000-0003-1995-7913"},"institutions":[{"id":"https://openalex.org/I4210115513","display_name":"Xi\u2019an University","ror":"https://ror.org/01zzmf129","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210115513"]},{"id":"https://openalex.org/I4210131919","display_name":"Xi'an University of Technology","ror":"https://ror.org/038avdt50","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210131919"]},{"id":"https://openalex.org/I51622183","display_name":"Shaanxi University of Science and Technology","ror":"https://ror.org/034t3zs45","country_code":"CN","type":"education","lineage":["https://openalex.org/I51622183"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jinhu Xu","raw_affiliation_strings":["School of Sciences, Xi\u2019an University of Technology, Xi\u2019an, Shaanxi 710048, P.\u00a0R.\u00a0China","School of Sciences, Xi\u2019an University of Technology, Xi\u2019an, Shaanxi 710048, P. R. China"],"raw_orcid":"https://orcid.org/0000-0003-1995-7913","affiliations":[{"raw_affiliation_string":"School of Sciences, Xi\u2019an University of Technology, Xi\u2019an, Shaanxi 710048, P.\u00a0R.\u00a0China","institution_ids":["https://openalex.org/I4210131919","https://openalex.org/I51622183","https://openalex.org/I4210115513"]},{"raw_affiliation_string":"School of Sciences, Xi\u2019an University of Technology, Xi\u2019an, Shaanxi 710048, P. R. China","institution_ids":["https://openalex.org/I4210131919"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Xueru Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210115513","display_name":"Xi\u2019an University","ror":"https://ror.org/01zzmf129","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210115513"]},{"id":"https://openalex.org/I4210131919","display_name":"Xi'an University of Technology","ror":"https://ror.org/038avdt50","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210131919"]},{"id":"https://openalex.org/I51622183","display_name":"Shaanxi University of Science and Technology","ror":"https://ror.org/034t3zs45","country_code":"CN","type":"education","lineage":["https://openalex.org/I51622183"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xueru Liu","raw_affiliation_strings":["School of Sciences, Xi\u2019an University of Technology, Xi\u2019an, Shaanxi 710048, P.\u00a0R.\u00a0China","School of Sciences, Xi\u2019an University of Technology, Xi\u2019an, Shaanxi 710048, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Sciences, Xi\u2019an University of Technology, Xi\u2019an, Shaanxi 710048, P.\u00a0R.\u00a0China","institution_ids":["https://openalex.org/I4210131919","https://openalex.org/I51622183","https://openalex.org/I4210115513"]},{"raw_affiliation_string":"School of Sciences, Xi\u2019an University of Technology, Xi\u2019an, Shaanxi 710048, P. R. China","institution_ids":["https://openalex.org/I4210131919"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102965617","display_name":"Suxia Zhang","orcid":"https://orcid.org/0000-0002-1790-7958"},"institutions":[{"id":"https://openalex.org/I4210115513","display_name":"Xi\u2019an University","ror":"https://ror.org/01zzmf129","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210115513"]},{"id":"https://openalex.org/I4210131919","display_name":"Xi'an University of Technology","ror":"https://ror.org/038avdt50","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210131919"]},{"id":"https://openalex.org/I51622183","display_name":"Shaanxi University of Science and Technology","ror":"https://ror.org/034t3zs45","country_code":"CN","type":"education","lineage":["https://openalex.org/I51622183"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Suxia Zhang","raw_affiliation_strings":["School of Sciences, Xi\u2019an University of Technology, Xi\u2019an, Shaanxi 710048, P.\u00a0R.\u00a0China","School of Sciences, Xi\u2019an University of Technology, Xi\u2019an, Shaanxi 710048, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-1790-7958","affiliations":[{"raw_affiliation_string":"School of Sciences, Xi\u2019an University of Technology, Xi\u2019an, Shaanxi 710048, P.\u00a0R.\u00a0China","institution_ids":["https://openalex.org/I4210131919","https://openalex.org/I51622183","https://openalex.org/I4210115513"]},{"raw_affiliation_string":"School of Sciences, Xi\u2019an University of Technology, Xi\u2019an, Shaanxi 710048, P. R. China","institution_ids":["https://openalex.org/I4210131919"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107306360","display_name":"Aili Wang","orcid":"https://orcid.org/0000-0003-3372-899X"},"institutions":[{"id":"https://openalex.org/I4210115513","display_name":"Xi\u2019an University","ror":"https://ror.org/01zzmf129","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210115513"]},{"id":"https://openalex.org/I4210131919","display_name":"Xi'an University of Technology","ror":"https://ror.org/038avdt50","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210131919"]},{"id":"https://openalex.org/I51622183","display_name":"Shaanxi University of Science and Technology","ror":"https://ror.org/034t3zs45","country_code":"CN","type":"education","lineage":["https://openalex.org/I51622183"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Aili Wang","raw_affiliation_strings":["School of Sciences, Xi\u2019an University of Technology, Xi\u2019an, Shaanxi 710048, P.\u00a0R.\u00a0China","School of Sciences, Xi\u2019an University of Technology, Xi\u2019an, Shaanxi 710048, P. R. China"],"raw_orcid":"https://orcid.org/0000-0003-3372-899X","affiliations":[{"raw_affiliation_string":"School of Sciences, Xi\u2019an University of Technology, Xi\u2019an, Shaanxi 710048, P.\u00a0R.\u00a0China","institution_ids":["https://openalex.org/I4210131919","https://openalex.org/I51622183","https://openalex.org/I4210115513"]},{"raw_affiliation_string":"School of Sciences, Xi\u2019an University of Technology, Xi\u2019an, Shaanxi 710048, P. R. China","institution_ids":["https://openalex.org/I4210131919"]}]},{"author_position":"last","author":{"id":null,"display_name":"Mengli Hao","orcid":"https://orcid.org/0000-0002-7430-6868"},"institutions":[{"id":"https://openalex.org/I4210115513","display_name":"Xi\u2019an University","ror":"https://ror.org/01zzmf129","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210115513"]},{"id":"https://openalex.org/I4210131919","display_name":"Xi'an University of Technology","ror":"https://ror.org/038avdt50","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210131919"]},{"id":"https://openalex.org/I51622183","display_name":"Shaanxi University of Science and Technology","ror":"https://ror.org/034t3zs45","country_code":"CN","type":"education","lineage":["https://openalex.org/I51622183"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mengli Hao","raw_affiliation_strings":["School of Sciences, Xi\u2019an University of Technology, Xi\u2019an, Shaanxi 710048, P.\u00a0R.\u00a0China","School of Sciences, Xi\u2019an University of Technology, Xi\u2019an, Shaanxi 710048, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-7430-6868","affiliations":[{"raw_affiliation_string":"School of Sciences, Xi\u2019an University of Technology, Xi\u2019an, Shaanxi 710048, P.\u00a0R.\u00a0China","institution_ids":["https://openalex.org/I4210131919","https://openalex.org/I51622183","https://openalex.org/I4210115513"]},{"raw_affiliation_string":"School of Sciences, Xi\u2019an University of Technology, Xi\u2019an, Shaanxi 710048, P. R. China","institution_ids":["https://openalex.org/I4210131919"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5030374259"],"corresponding_institution_ids":["https://openalex.org/I4210115513","https://openalex.org/I4210131919","https://openalex.org/I51622183"],"apc_list":null,"apc_paid":null,"fwci":2.1031,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.83336034,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"35","issue":"06","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11495","display_name":"Animal Virus Infections Studies","score":0.9207000136375427,"subfield":{"id":"https://openalex.org/subfields/1103","display_name":"Animal Science and Zoology"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T11495","display_name":"Animal Virus Infections Studies","score":0.9207000136375427,"subfield":{"id":"https://openalex.org/subfields/1103","display_name":"Animal Science and Zoology"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cytokine","display_name":"Cytokine","score":0.5652375817298889},{"id":"https://openalex.org/keywords/viral-infection","display_name":"Viral infection","score":0.5318548083305359},{"id":"https://openalex.org/keywords/virology","display_name":"Virology","score":0.48391443490982056},{"id":"https://openalex.org/keywords/immunology","display_name":"Immunology","score":0.41075006127357483},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.399605929851532},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.3386704623699188},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.328666627407074},{"id":"https://openalex.org/keywords/virus","display_name":"Virus","score":0.23455798625946045}],"concepts":[{"id":"https://openalex.org/C2778690821","wikidata":"https://www.wikidata.org/wiki/Q212354","display_name":"Cytokine","level":2,"score":0.5652375817298889},{"id":"https://openalex.org/C2994541485","wikidata":"https://www.wikidata.org/wiki/Q1928978","display_name":"Viral infection","level":3,"score":0.5318548083305359},{"id":"https://openalex.org/C159047783","wikidata":"https://www.wikidata.org/wiki/Q7215","display_name":"Virology","level":1,"score":0.48391443490982056},{"id":"https://openalex.org/C203014093","wikidata":"https://www.wikidata.org/wiki/Q101929","display_name":"Immunology","level":1,"score":0.41075006127357483},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.399605929851532},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.3386704623699188},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.328666627407074},{"id":"https://openalex.org/C2522874641","wikidata":"https://www.wikidata.org/wiki/Q808","display_name":"Virus","level":2,"score":0.23455798625946045}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021812742550066x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812742550066x","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":[],"awards":[{"id":"https://openalex.org/G158655710","display_name":null,"funder_award_id":"12271431","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1683288925","display_name":null,"funder_award_id":"11701445","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":40,"referenced_works":["https://openalex.org/W1967016316","https://openalex.org/W1980587508","https://openalex.org/W1986426368","https://openalex.org/W1992572795","https://openalex.org/W2009710695","https://openalex.org/W2041572706","https://openalex.org/W2063032390","https://openalex.org/W2071448055","https://openalex.org/W2091174536","https://openalex.org/W2105265365","https://openalex.org/W2112680994","https://openalex.org/W2114497207","https://openalex.org/W2153180469","https://openalex.org/W2205248131","https://openalex.org/W2401150906","https://openalex.org/W2493294075","https://openalex.org/W2777812259","https://openalex.org/W2794171901","https://openalex.org/W2888057265","https://openalex.org/W2972361566","https://openalex.org/W2991465736","https://openalex.org/W3014242104","https://openalex.org/W3036651695","https://openalex.org/W3111531784","https://openalex.org/W3131336024","https://openalex.org/W3156325092","https://openalex.org/W3160574451","https://openalex.org/W4220985010","https://openalex.org/W4225788872","https://openalex.org/W4299164051","https://openalex.org/W4323519779","https://openalex.org/W4361026444","https://openalex.org/W4367396634","https://openalex.org/W4386011902","https://openalex.org/W4387977843","https://openalex.org/W4388364567","https://openalex.org/W4389975478","https://openalex.org/W4391785468","https://openalex.org/W4396597969","https://openalex.org/W4400413137"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,61,145],"propose":[4],"a":[5,12,15],"delayed":[6],"viral":[7,84,156,180],"infection":[8,47,157,181],"model":[9],"to":[10,92],"incorporate":[11],"logistic":[13,115,129],"proliferation,":[14],"cell":[16,150,173],"pyroptosis":[17,151,174],"effect":[18,152],"and":[19,31,35,46,65,99,118,159],"the":[20,27,33,36,58,63,66,83,94,104,114,124,128,134,138,141,149,155,160,170,179],"three":[21],"intracellular":[22],"time":[23,59,107,119],"delays.":[24,108],"We":[25,79],"present":[26],"basic":[28],"reproduction":[29],"number":[30],"investigate":[32,62],"existence":[34,64],"global":[37],"stability":[38,95],"of":[39,57,68,106,140,172],"equilibria:":[40],"infection-free":[41],"equilibrium":[42,48],"[Formula:":[43,49,72],"see":[44,50,73],"text]":[45,74],"text],":[51],"respectively.":[52],"By":[53],"considering":[54],"different":[55],"combinations":[56],"delays,":[60],"properties":[67],"Hopf":[69,142],"bifurcation":[70],"from":[71],"when":[75],"it":[76],"is":[77,175],"unstable.":[78],"also":[80],"numerically":[81],"explore":[82],"dynamics":[85],"beyond":[86],"stability.":[87],"Bifurcation":[88],"diagrams":[89],"are":[90,121],"used":[91],"show":[93,146],"switches,":[96],"multiperiod":[97],"solutions":[98],"irregular":[100],"sustained":[101],"oscillations":[102],"with":[103],"variation":[105],"The":[109],"results":[110],"reveal":[111],"that":[112,147,164],"both":[113],"proliferation":[116,130],"term":[117,131],"delays":[120],"responsible":[122],"for":[123,137,168,177],"rich":[125],"dynamics,":[126],"but":[127],"may":[132,153],"be":[133],"main":[135],"factor":[136],"occurrence":[139],"bifurcation.":[143],"Moreover,":[144],"ignoring":[148],"underevaluate":[154],"risk":[158],"sensitivity":[161],"analysis":[162],"implies":[163],"taking":[165],"effective":[166],"strategies":[167],"reducing":[169],"impact":[171],"beneficial":[176],"decreasing":[178],"risk.":[182]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}