{"id":"https://openalex.org/W2960545788","doi":"https://doi.org/10.1142/s0218127419500913","title":"Stability and Hopf Bifurcation of a Delayed Prey\u2013Predator Model with Disease in the Predator","display_name":"Stability and Hopf Bifurcation of a Delayed Prey\u2013Predator Model with Disease in the Predator","publication_year":2019,"publication_date":"2019-06-30","ids":{"openalex":"https://openalex.org/W2960545788","doi":"https://doi.org/10.1142/s0218127419500913","mag":"2960545788"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127419500913","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127419500913","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/A5024358389","display_name":"Chuangxia Huang","orcid":"https://orcid.org/0000-0002-0732-226X"},"institutions":[{"id":"https://openalex.org/I56934997","display_name":"Changsha University of Science and Technology","ror":"https://ror.org/03yph8055","country_code":"CN","type":"education","lineage":["https://openalex.org/I56934997"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chuangxia Huang","raw_affiliation_strings":["School of Mathematics and Statistics, Changsha University of Science and Technology, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha 410114, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Changsha University of Science and Technology, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha 410114, P. R. China","institution_ids":["https://openalex.org/I56934997"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100749493","display_name":"Hua Zhang","orcid":"https://orcid.org/0000-0002-8397-4315"},"institutions":[{"id":"https://openalex.org/I56934997","display_name":"Changsha University of Science and Technology","ror":"https://ror.org/03yph8055","country_code":"CN","type":"education","lineage":["https://openalex.org/I56934997"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hua Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Changsha University of Science and Technology, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha 410114, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Changsha University of Science and Technology, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha 410114, P. R. China","institution_ids":["https://openalex.org/I56934997"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017808266","display_name":"Jinde Cao","orcid":"https://orcid.org/0000-0003-3133-7119"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jinde Cao","raw_affiliation_strings":["School of Mathematics, Southeast University, Nanjing 210096, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Southeast University, Nanjing 210096, P. R. China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103254550","display_name":"Haijun Hu","orcid":"https://orcid.org/0000-0002-6517-0540"},"institutions":[{"id":"https://openalex.org/I56934997","display_name":"Changsha University of Science and Technology","ror":"https://ror.org/03yph8055","country_code":"CN","type":"education","lineage":["https://openalex.org/I56934997"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haijun Hu","raw_affiliation_strings":["School of Mathematics and Statistics, Changsha University of Science and Technology, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha 410114, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Changsha University of Science and Technology, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha 410114, P. R. China","institution_ids":["https://openalex.org/I56934997"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5017808266"],"corresponding_institution_ids":["https://openalex.org/I76569877"],"apc_list":null,"apc_paid":null,"fwci":27.9734,"has_fulltext":false,"cited_by_count":152,"citation_normalized_percentile":{"value":0.99805156,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"29","issue":"07","first_page":"1950091","last_page":"1950091"},"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":1.0,"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":1.0,"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":0.9983999729156494,"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/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.9484999775886536,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.7891192436218262},{"id":"https://openalex.org/keywords/predator","display_name":"Predator","score":0.768903374671936},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.6710844039916992},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6022770404815674},{"id":"https://openalex.org/keywords/predation","display_name":"Predation","score":0.596347987651825},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.561459481716156},{"id":"https://openalex.org/keywords/functional-response","display_name":"Functional response","score":0.513200044631958},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.5104516744613647},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.506423830986023},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4745129942893982},{"id":"https://openalex.org/keywords/bifurcation-theory","display_name":"Bifurcation theory","score":0.4572065472602844},{"id":"https://openalex.org/keywords/saddle-node-bifurcation","display_name":"Saddle-node bifurcation","score":0.4509992003440857},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3989679515361786},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.3184528946876526},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.24340805411338806},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2233523726463318},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.11465483903884888},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11451047658920288},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11270216107368469},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09837713837623596},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.08466580510139465},{"id":"https://openalex.org/keywords/demography","display_name":"Demography","score":0.056092530488967896}],"concepts":[{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.7891192436218262},{"id":"https://openalex.org/C96857902","wikidata":"https://www.wikidata.org/wiki/Q2138108","display_name":"Predator","level":3,"score":0.768903374671936},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.6710844039916992},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6022770404815674},{"id":"https://openalex.org/C188382862","wikidata":"https://www.wikidata.org/wiki/Q170430","display_name":"Predation","level":2,"score":0.596347987651825},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.561459481716156},{"id":"https://openalex.org/C110201527","wikidata":"https://www.wikidata.org/wiki/Q5508845","display_name":"Functional response","level":4,"score":0.513200044631958},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5104516744613647},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.506423830986023},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4745129942893982},{"id":"https://openalex.org/C85075877","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Bifurcation theory","level":4,"score":0.4572065472602844},{"id":"https://openalex.org/C101225446","wikidata":"https://www.wikidata.org/wiki/Q740190","display_name":"Saddle-node bifurcation","level":4,"score":0.4509992003440857},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3989679515361786},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.3184528946876526},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.24340805411338806},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2233523726463318},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.11465483903884888},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11451047658920288},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11270216107368469},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09837713837623596},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.08466580510139465},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.056092530488967896},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"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/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127419500913","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127419500913","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":0.7400000095367432,"display_name":"Good health and well-being","id":"https://metadata.un.org/sdg/3"}],"awards":[{"id":"https://openalex.org/G1778948287","display_name":null,"funder_award_id":"71471020","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8051261019","display_name":null,"funder_award_id":"51839002","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":50,"referenced_works":["https://openalex.org/W39295172","https://openalex.org/W145452558","https://openalex.org/W576454838","https://openalex.org/W1063798334","https://openalex.org/W1531715726","https://openalex.org/W1985255261","https://openalex.org/W1986548439","https://openalex.org/W1989861394","https://openalex.org/W1991371351","https://openalex.org/W1993350087","https://openalex.org/W1997208785","https://openalex.org/W1998251843","https://openalex.org/W2007190506","https://openalex.org/W2009948646","https://openalex.org/W2011225381","https://openalex.org/W2011674454","https://openalex.org/W2027665073","https://openalex.org/W2029259603","https://openalex.org/W2033180586","https://openalex.org/W2034167224","https://openalex.org/W2038548575","https://openalex.org/W2052189521","https://openalex.org/W2054937635","https://openalex.org/W2055938377","https://openalex.org/W2056869658","https://openalex.org/W2057632611","https://openalex.org/W2057902575","https://openalex.org/W2059350553","https://openalex.org/W2059579326","https://openalex.org/W2061050995","https://openalex.org/W2064233192","https://openalex.org/W2070097517","https://openalex.org/W2071923791","https://openalex.org/W2084500991","https://openalex.org/W2091563444","https://openalex.org/W2121634156","https://openalex.org/W2164261207","https://openalex.org/W2165654051","https://openalex.org/W2192092280","https://openalex.org/W2209062859","https://openalex.org/W2253515180","https://openalex.org/W2401616512","https://openalex.org/W2562779659","https://openalex.org/W2609576084","https://openalex.org/W2807442327","https://openalex.org/W2885436354","https://openalex.org/W2897043363","https://openalex.org/W2901366191","https://openalex.org/W2903253632","https://openalex.org/W2908985861"],"related_works":["https://openalex.org/W2363682937","https://openalex.org/W3012287595","https://openalex.org/W2905043181","https://openalex.org/W3184324514","https://openalex.org/W4311297143","https://openalex.org/W2070512385","https://openalex.org/W2036212567","https://openalex.org/W1126432747","https://openalex.org/W2960545788","https://openalex.org/W2091792699"],"abstract_inverted_index":{"Dealing":[0],"with":[1,48],"the":[2,12,27,32,49,52,57,71,75,84,88,91,100,106,119,135,139,149,154,158,167],"epidemiological":[3,45],"prey\u2013predator":[4,34,46],"is":[5,54,126],"very":[6],"important":[7],"for":[8],"us":[9],"to":[10,78,165],"understand":[11],"dynamical":[13],"characteristics":[14],"of":[15,64,93,98,102,153,171],"population":[16],"models.":[17],"The":[18,96],"existing":[19],"literature":[20],"has":[21],"shown":[22],"that":[23,51,128],"disease":[24,53],"introduction":[25],"into":[26],"predator":[28,58,73,86],"group":[29],"can":[30],"destabilize":[31],"established":[33],"communities.":[35],"In":[36],"this":[37],"paper,":[38],"we":[39],"establish":[40],"a":[41,129],"new":[42],"delayed":[43],"SIS":[44],"model":[47],"assumptions":[50],"transmitted":[55],"among":[56],"species":[59],"only":[60],"and":[61,83,108,151,169],"different":[62,67],"type":[63],"predators":[65],"have":[66],"functional":[68,81],"responses,":[69],"viz.":[70],"infected":[72],"consumes":[74,87],"prey":[76,89],"according":[77],"Holling":[79],"type-II":[80],"response":[82],"susceptible":[85],"following":[90],"law":[92],"mass":[94],"action.":[95],"positivity":[97],"solutions,":[99],"existence":[101],"various":[103],"equilibrium":[104,112,136,160],"points,":[105],"stability":[107,152],"bifurcation":[109,123,131,156],"at":[110,116],"those":[111],"points":[113,137],"are":[114,163],"investigated":[115],"length.":[117],"Using":[118],"incubation":[120],"period":[121],"as":[122],"parameter,":[124],"it":[125],"observed":[127],"Hopf":[130,155],"may":[132],"occur":[133],"around":[134,157],"when":[138],"parameter":[140],"passes":[141],"through":[142],"some":[143],"critical":[144],"values.":[145],"We":[146],"also":[147],"discuss":[148],"direction":[150],"interior":[159],"point.":[161],"Simulations":[162],"arranged":[164],"show":[166],"correctness":[168],"effectiveness":[170],"these":[172],"theoretical":[173],"results.":[174]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":17},{"year":2020,"cited_by_count":71},{"year":2019,"cited_by_count":24}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
