2015年建模美赛(A题)O奖论文

ForofficeuseonlyT1________________T2________________T3________________T4________________TeamControlNumber32150ProblemChosenAForofficeuseonlyF1________________F2________________F3________________F4________________2015MathematicalContestinModeling(MCM/ICM)SummarySheetHowtoEradicateEbola?ThebreakoutofEbolain2014triggeredglobalpanic.HowtocontrolanderadicateEbolahasbecomeauniversalconcerneversince.Firstly,webuildupanepidemicmodelSEIHCR(CT)whichtakesthespecialfeaturesofEbolaintoconsideration.Thesearetreatmentfromhospital,infectiouscorpsesandintensifiedcontacttracing.ThismodelisdevelopedfromthetraditionalSEIRmodel.Themodel’sresults(Fig.4,5,6),whoseparametersaredecidedusingcomputersimulation,matchperfectlywiththedatareportedbyWHO,suggestingthevalidityofourimprovedmodel.Secondly,pharmaceuticalinterventionisstudiedthoroughly.ThetotalquantityofthemedicineneededisbasedonthecumulativenumberofindividualsCUM(Fig.7).ResultscalculatedfromtheWHOstatisticsandfromtheSEIHCR(CT)modelshowonlyminordiscrepancy,furtherindicatingthefeasibilityofourmodel.Indesigningthedeliverysystem,weapplytheweightedFuzzy-cMeansClusteringAlgorithmandselect6locations(Fig.10,Table.2)thatshouldserveasthedeliverycentersforothercities.Weoptimizethedeliverylocationsbyeachcity’slocationandneededmedicine.Thepercentageeachlocationsharesisalsofiguredouttofacilitatefutureallocation(Table.3,4).Theaveragespeedofmanufacturingshouldbenolessthan106.2unitdoseperdayandanincreaseinthemanufacturingspeedandtheefficacyofmedicinewillreinforcetheinterventioneffect.Thirdly,othercriticalfactorsbesidesthosediscussedearlyinthemodel,safertreatmentofcorpses,andearlieridentification/isolationalsoprovetoberelevant.Byvaryingthevalueofparameters,wecanprojectthefutureCUM.Results(Fig.12,13)showthattheseinterventionswillhelpreduceCUMtoalowerplateauatafasterspeed.WethenanalyzethefactorsforcontrollingandthetimeoferadicationofEbola.Forexample,whentherateoftheinfectiousbeingisolatedis33%-40%,thediseasecanbesuccessfullycontrolled(Table.5).Whentheintroductiontimefortreatmentdecreasesfrom210to145days,theeradicationofEbolaarrivesover200daysearlier.Finally,weselectthreeparameters:thetransmissionrate,theincubationperiodandthefatalityrateforsensitivityanalysis.Keywords:Ebola,epidemicmodel,cumulativecases,ClusteringAlgorithmContents1.Introduction........................................................................................................11.1.ProblemBackground.........................................................................11.2.PreviousResearch..............................................................................21.3.OurWork............................................................................................22.GeneralAssumptions.........................................................................................33.NotationsandSymbolDescription....................................................................43.1.Notations............................................................................................43.2.SymbolDescription...........................................................................44.SpreadofEbola..................................................................................................54.1.TraditionalEpidemicModel..............................................................54.1.1.TheSEIRModel..........................................................................54.1.2.OutbreakData..............................................................................64.1.3.ResultsoftheSEIRModel..........................................................74.2.ImprovedModel.................................................................................84.2.1.TheSEIHCR(CT)Model...........................................................84.2.2.ChoosingParameters.................................................................102.1.1.ResultsoftheSEIHCR(CT)Model..........................................115.PharmaceuticalIntervention............................................................................135.1.TotalQuantityoftheMedicine........................................................135.1.1.ResultsfromWHOStatistics.....................................................135.1.2.ResultsfromtheSEIHCR(CT)Model.....................................155.2.DeliverySystem...............................................................................155.2.1.LocationsofDelivery................................................................165.2.2.AmountofDelivery...................................................................195.3.SpeedofManufacturing...................................................................205.4.MedicineEfficacy............................................................................216.OtherImportantInterventions..........................................................................216.1.SaferTreatmentofCorpses..............................................................216.2.IntensifiedContactTracingandEarl