预览加载中，请您耐心等待几秒...

一类带有脉冲免疫TB模型的稳定性分析(英文).docx

预览
1/2
2/2

在线预览结束，喜欢就下载吧，查找使用更方便

下载提示 文本预览

如果您无法下载资料，请参考说明：

1、部分资料下载需要金币，请确保您的账户上有足够的金币

2、已购买过的文档，再次下载不重复扣费

3、资料包下载后请先用软件解压，在使用对应软件打开

一类带有脉冲免疫TB模型的稳定性分析(英文) StabilityAnalysisofaPulseImmuneTBModel Tuberculosis(TB)isaseriousinfectiousdiseasethataffectsmillionsofpeopleeveryyear.Sincetheadventofantibiotics,thetreatmentofTBhasbecomeeasier.However,theemergenceofdrug-resistantstrainsofthediseasehascomplicatedthesituation,leadingtothedevelopmentofnewtreatmentstrategies.Inrecentyears,mathematicalmodelinghasbeenusedtostudythedynamicsofTBinfectionandtodevelopnewtreatmentprotocols. Inthispaper,wepresentapulseimmuneTBmodelthatincorporatestheeffectsofimmuneboostingtreatments.Themodelisrepresentedbyasystemofdifferentialequationsthatcapturetheinteractionsbetweenthesusceptible,latent,andactiveTBpopulations,aswellastheimmuneresponsetothedisease.WethenperformastabilityanalysisofthemodeltoinvestigatethedynamicsofTBinfectionunderdifferenttreatmentregimes. ThestabilityofthemodelisdeterminedbyanalyzingtheeigenvaluesoftheJacobianmatrix,whichrepresentsthelinearizedsystemofequationsaroundthedisease-freeequilibriumpoint.UsingtheRouth-Hurwitzcriterion,weshowthatthedisease-freeequilibriumpointisgloballyasymptoticallystableforarangeofparametervalues.ThisimpliesthattheTBepidemiccanbecontrolledbypreventingthetransmissionofthedisease. Wethenconsidertheeffectsofpulseimmuneboostingtreatmentsonthedynamicsofthemodel.Thesetreatmentssimulatetheadministrationofdrugsthatboosttheimmuneresponsetothedisease.Weshowthatthestabilityofthemodeldependsonthefrequencyandstrengthofthepulsetreatments,aswellasonthetimingofthepulses.Specifically,wefindthattherearecriticalvaluesofthepulsefrequencyandstrengthbelowwhichthedisease-freeequilibriumpointbecomesunstable,leadingtotheemergenceofendemicTB.Furthermore,weshowthatthetimingofthepulsescanhaveasignificanteffectonthestabilityofthemodel,withearlyorlatepulsesleadingtodestabilizationofthesystem. OurresultssuggestthatpulseimmuneboostingtreatmentscanbeaneffectivetoolforcontrollingTBoutbreaks,butcautionmustbetakenindesigningthetreatmentprotocols.Thefrequencyandstrengthofthepulsesmustbecarefullycontrolledtoavo