PureMathematics理论数学,2023,13(9),2465-2477PublishedOnlineSeptember2023inHans.https://www.hanspub.org/journal/pmhttps://doi.org/10.12677/pm.2023.139253文章引用:史旭元,高红亮.具有年龄结构的SVIQR传染病模型的稳定性分析[J].理论数学,2023,13(9):2465-2477.DOI:10.12677/pm.2023.139253具有年龄结构的SVIQR传染病模型的稳定性分析史旭元，高红亮*兰州交通大学，数理学院，甘肃兰州收稿日期：2023年7月26日；录用日期：2023年8月28日；发布日期：2023年9月4日摘要讨论一类具有疫苗接种和隔离的年龄结构SVIQR传染病模型，得出基本再生数R0的表达式。证明了当R0<1时，无病平衡点全局渐近稳定；当R0>1时，无病平衡点不稳定；此时系统存在地方病平衡点，并且证明了地方病平衡点是唯一的并且局部渐进稳定。最终得出，隔离是消除传染病的有效方式，如果不能进一步降低传播率，那么就需要最大限度地提高疫苗接种率。关键词年龄结构，疫苗接种，隔离，基本再生数，稳定性StabilityAnalysisofSVIQRInfectiousDiseaseModelwithAgeStructureXuyuanShi,HongliangGao*CollegeofMathematicsandPhysics,LanzhouJiaotongUniversity,LanzhouGansuReceived:Jul.26th,2023;accepted:Aug.28th,2023;published:Sep.4th,2023AbstractAclassofage-structuredSVIQRinfectiousdiseasemodelswithvaccinationandisolatio-nwasdiscussed.TheexpressionsofbasicregenerationnumberR0werederived.ItwasprovedthatwhenR0<1,thedisease-freeequilibriumpointwasgloballyasymptoticallystable;whenR0>1,thedis-ease-freeequilibriumpointwasunstable.Andthereexistsendemicequilibriumstate,anditwasprovedthatendemicequilibriumpointwasuniqueandlocallyasymptoticallystable.Ultimately,isolationwasaneffectivewaytoeliminateinfectiousdiseases;iftransmissionratescannotbere-ducedinfuture,thenvaccinationratesneedtobemaximized.*通讯作者。史旭元，高红亮DOI:10.12677/pm.2023.1392532466理论数学KeywordsAgeStructure,Vaccination,Isolation,BasicRegenerationNumber,StabilityCopyright©2023byauthor(s)andHansPublishersInc.ThisworkislicensedundertheCreativeCommonsAttributionInternationalLicense(CCBY4.0).http://creativecommons.org/licenses/by/4.0/1.引言传染病是人类历史上极易造成重大伤亡的疾病，近年来，艾滋病、肺结核、麻疹等疾病从未淡出...
