滨州学院学报第39卷[2]ARENASAJ,GONZALEZ-PARRAG,DELAESPRIELLAN.Nonlineardynamicsofanewsea-sonalepidemiologicalmodelwithage-structureandnonlinearincidencerate[J]・Computationalandappliedmathematics)2021,40(2)：1—27.[3]LIXZ,YANGJ,MARTCHEVAM・Agestructuredepidemicmodeling[M].Berne：SpringerNature,2020.[4]CAIY,KANGY,BANERJEEM,etal.AstochasticSIRSepidemicmodelwithinfectiousforceunderinterventionstrategies[J].Journalofdifferentialequations>2015,259(12)：7463-7502.[5]KUMARA.Mathematicalanalysisofadelayedepidemicmodelwithnonlinearincidenceandtreatmentrates[J].Journalofengineeringmathematics,2019,115(1):1—20.[6]DELASENM,ALONSO-QUESADAS,IBEASA.OnthestabilityofanSEIRepidemicmodelwithdistributedtime-delayandageneralclassoffeedbackvaccinationrulesEJZI・Appliedmathematicsandcomputation,2015,270：953-976.[7]WANGW.GlobalbehaviorofanSEIRSepidemicmodelwithtimedelays]〕].Appliedmathematicsletters,2002,15(4)-423-42&[8]AKIMENKOV・Anage-structuredSIRepidemicmodelwithfixedincubationperiodofinfection[J]・Computers&mathematicswithapplications,2017,73(7)：1485-1504.[9]HASSARDBD,KAZARINOFFND,WANYH,etal.TheoryandapplicationsofHopfbifurca-tion[J],SIAMreview?1982,24(4)：498-499.Age-structuredSIQRSEpidemicModelwithTimeDelayWANGXin-yu(SchoolofMathematicsandPhysics,LanzhouJiaotongUniversityLanzhou730070,China)Abstract:Inordertofurtheranalyzethecharacteristicsofepidemictransmissionandbettercontrolthedevelopmentoftheepidemic,aSIQRSepidemicmodelwithverticaltransmissionandtimedelayisestablished.TheexistenceanduniquenessofthetravelingwavesolutionofthesystemareprovedbyusingtheexplicitrecursivealgorithmcombinedwiththecharacteristiclinemethodandRouthHurwitzcriterion,andthenthestabilityoftheequilibriumpointofthesystemisanalyzedinordertofindouttheinfluenceofdelayonHopfbifurcation.Itisprovedthatcontrollingtimedelayisbeneficialtoeliminatetheepidemic.Keywords:age-structure；stability；time-delay；transmissiondynamics(责任编辑：贾晶晶)本刊声明本刊已许可《中国学术期刊（光盘版）》电子杂志社有限公司、北京万方数据股份有限公司（万方数据电子出版社）、重庆维普资讯有限公司、超星期刊域出版平台等在其各自的系列数据库产品中以数字化方式复制、汇编、发行及在信息网络传播本刊全文。作者著作权使用费和稿酬（即包括印刷版、光盘版和网络版等各种使用方式的报酬）一并支付。如作者对本声明持有异议，请在投稿时说明。•46•
