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具有分布时滞的病毒感染模型动力学性质研究(英文).docx

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具有分布时滞的病毒感染模型动力学性质研究(英文) Title:Dynamicalpropertiesofavirusinfectionmodelwithdistributedtimedelay Abstract: Inthispaper,westudythedynamicalpropertiesofavirusinfectionmodelwithdistributedtimedelay.Themodelrepresentstheinteractionbetweeninfectedanduninfectedpopulationsandincludesbothverticalandhorizontaltransmissionofthevirus.WeanalyzethestabilityofthemodelbyusingthecharacteristicequationandinvestigatetheexistenceofHopfbifurcationandstabilityofperiodicsolutions.Wealsostudytheeffectofthedelaydistributiononthedynamicsofthemodel.Ourresultsindicatethatdistributedtimedelaycansignificantlyimpactthestabilityofthesystemandgiverisetoarangeofcomplexdynamicalbehaviors,includingHopfbifurcation,stableperiodicoscillations,andchaoticbehavior. Introduction: Virusesareoneofthemostwidespreadandinfluentialpathogensinhumanandanimalpopulations.Thetransmissionofvirusesisaffectedbymultiplefactors,includingtheinteractionbetweeninfectedanduninfectedpopulations,modeoftransmission,andincubationperiod.Timedelayisanotherimportantfactorthatcansignificantlyaffectthedynamicsofviralepidemics.Theeffectoftimedelayonvirustransmissionhasbeenstudiedinmanydifferentcontexts,includingepidemicmodels,delaydifferentialequations,andstochasticmodels. Inthispaper,weproposeavirusinfectionmodelthatincludesadistributedtimedelay.ThemodelextendsthestandardSIR(Susceptible-Infected-Recovered)modeltoincludebothverticalandhorizontaltransmissionofthevirus.Weinvestigatethedynamicalpropertiesofthemodelandtheeffectsofthedelaydistributiononthestabilityofthesystem. Model: Thevirusinfectionmodelwithdistributedtimedelayisgivenbythefollowingsetofequations: dS/dt=b(1-S)-qSV-δS(t)∫_0^∞f(τ)I(t-τ)dτ dV/dt=pV-qSV(t)-αV(t)∫_0^∞g(τ)I(t-τ)dτ dI/dt=qSV(t)+αV(t)∫_0^∞g(τ)I(t-τ)dτ-γI whereS(t),V(t),andI(t)representtheproportionofsusceptible,verticallyinfected,andhorizontallyinfectedindividualsattimet,respectively.Theparameterbisthenaturalbirthrate,δisthedeathrate,andpistheproportionofverticallyinfectedindividuals.qisthetransmissionrate,αisthera