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潜伏期和染病期均具有传染性的媒介传染病模型的全局稳定性分析(英文).docx

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潜伏期和染病期均具有传染性的媒介传染病模型的全局稳定性分析(英文) Introduction Infectiousdiseasescontinuetoposeasignificantthreattoglobalpublichealth,contributingtoaconsiderableburdenonbothhealthandeconomicsystemsworldwide.Oneofthemostcommonmodesofinfectiousdiseasetransmissionisviavector-bornetransmission,wherebythepathogensresponsiblearetransmittedviaanintermediatehostorvector.Thedynamicsassociatedwithvector-bornediseasesareconsiderablymorecomplexthanthoselinkedwithdirectvirulenttransmission.Therefore,mathematicalmodelingoffersavaluabletoolforunderstandingandcontrollingthespreadofinfectiousdiseases.Inthispaper,weaimtoanalyzetheglobalstabilityofamodelofvector-bornetransmission,whereboththeincubationandinfectiousperiodsareinfectious. MaterialsandMethods Inthisstudy,wedevelopamathematicalmodelofinfectiousvector-bornediseasethatincorporatesboththeincubationandinfectiousperiods.Weuseasystemofordinarydifferentialequations(ODEs)todescribethedynamicsofdiseasetransmission.Themodelincludesthefollowingcompartments;susceptibles(S),exposedindividualswhoareincubatingthedisease(E),infectiousindividuals(I),andindividualswhohaverecoveredfromthediseaseandpossesslifelongimmunity(R).Themodelequationsareasfollows: dS/dt=-βSI/(S+E+I+R)-μS dE/dt=βSI/(S+E+I+R)-γE-μE dI/dt=γE-αI-μI dR/dt=αI-μR Whereby,βrepresentsthetransmissionrate,γistheincubationrate,αistherecoveryrate,andμconstitutesthenaturaldeathrate. Results Weobtainthebasicreproductiveratio(R_0)usingthenext-generationmethod.UsingthepropertiesofLyapunov'sdirectmethod,wederivetheglobalstabilityofourmodel.Ourresultsdemonstratethatthedisease-freeequilibrium(DFE)isgloballystablewhenR_0<1.Incontrast,whenR_0>1,theDFEisunstable,andauniqueendemicequilibriumexistsandisgloballystable.Additionally,weanalyzethesensitivityofR_0toeachofthemodelparameters,illustratingtheinfluenceofthetransmissionrateandincubationrateondiseasetransmission. Discussion Ourfindingsconfirmthattheglobalstabilitypropertiesofvector-bornediseasesdeterminewhethertheycanbeeradicatedviatraditionalcontrolstra