文档介绍：中北大学学位论文摘要本文主要研究三类具有脉冲效应的传染瘸模型的渐近性态,主要内容如下: 第二章研究了一类具脉冲出生和标准发生率的SIR传染病模型的动力学性态。利用频闪映射。得到了模型的无病周期解。借助Floquet定理,证明了无病周期解的局部稳定性, 且给出了疾病持续与否的阈值"。当”<1时,无病周期解全局渐近稳定性,意味着疾病在种群中消亡。另一方面,当口>1时,疾病在种群中一致持续。定理的论证过程主要依据比较原理和脉冲微分不等式。第三章中利用动力系统和脉冲微分方程基本理论,分析了一类具有垂直传染和脉冲接种的SIR传染病模型,给出了该模型的基本再生数,证明了无瘸周期解的全局稳定性。并利用分支定理证明了正周期解的存在性。第四章建立了具有脉冲预防接种的SlQR传染病模型,利用脉冲微分方程基本理论,对该模型的动力学性态进行了分析:给出了该模型的基本再生数彤,证明了无病周期解的存在性及全局稳定性,并且讨论了当彤>l时疾病的一致持续性。通过计算机数值模拟,验证了结论的正确性。关键词:无病周期解,阈值,基本再生数,稳定性,一致持续性,正周翦I解第1页中北大学学位论文 ABSTRACT This dissertation intended tomake research on theasymptotic behavior ofthree clJlssesofepidemic models with impulsive effects. epidemic model withbirthpulses andstandard incidence isconsid- thediscretedynamical system determined by thestroboscopic map,we obtain the exact infeetion-freeperiodic solution ofthe mean8 oftheFloquet theory,we considerthe localstabflity ofthe infection-freeper/odic threshold口is iden- alsohave shown thatinfection-freeperiodic solution isgloballyasymptotically stableifthethreshold口is the otherhand,when q isgreater than one, technique mainly depends On impulsive differential inequality parison principle. InChapter 3,we establish an SIR epidemic model with verticaltransmission andira- means ofdynamical system andthebasictheoriesofimpulsive dif- ferentialequation,we give outthe basicreproduction number corresponding tothemodel. globalstability ofan infection-freeperiodic the exis- tence of anontrivialperiodic solution isconsideredby using bifurcation theory. InChapter 4,by means ofbasic theories ofimpulsive differentialequation,we analyze anSIQR epidemic modelwithimpulsive basicreproductive number ofthe model R’ prove theexistence and globalstability oftheinfection-freeperiodic consider theUlmOm persistence ofthe diseasewhen R+> numerical simulation isalsopresented in