2015年美赛A题论文

ForofficeuseonlyT1________________T2________________T3________________T4________________TeamControlNumber36448ProblemChosenAForofficeuseonlyF1________________F2________________F3________________F4________________2015MathematicalContestinModeling(MCM)SummarySheetAbstractThispaperaimstoestablishamodeltodistributedrugtothevariousaffectedareasrationallyandefficiently.Ourmodelincludesthefollowingfactors.Spreadofthevirus:WeselectsomedataaboutthenumberofinfectionsintheareaofWestAfrica.Wecalculatethesumofthenumbersofinfections,forecasttotalnumberofinfectionsinthecomingsixweeksviatheanalysisofTimeSeriesModels.Thequantityofthemedicineneededandspeedofmanufacturingofthedrug:Weaccesstorelevantinformationandcomparethedemandtothesupplyforthedrugatatthisstage,Wecanconcludethatdrugisinshortsupplyatthisstage.Selectionofthedistributioncenters:WetakeETCasthedeliverydestinations.Wetaketheairportasthedistributioncenter.Accordingtothecurrentnumberofinfectionsandthepredictednumberofinfectionsinthecomingsixweeks,weclassifyETCsintothreecategories:Alevel,BlevelandClevel.ThenweestablishGoalProgrammingModeltoselectthemostappropriate8airportsasdistributioncenters(resultisshowninTable4)basedonthelevelofETCanddistancesbetweentheairportsandETCs.Drugdistributionmechanism:AccordingtolevelsandnumberofETCwhichiswithinthedistributioncirclesandthespeedofmanufacturingofthedrug,wecanselecttheappropriatedistributioncentersandthetotalquantityofdrugdistributedtovariousairports.ThequantityofdrugwhichshouldbedeliveredtovariousETCsisdeterminedbytheleveloftheETC.Finally,ETCdistributethedrugtonearbyepidemicareas.Thedrugdistributionmechanismiseconomicalandefficientwithsuchoptimization.TheresultisshowninTable4.Innovationsofourmodel:1.WepredictthenumberofinfectionsoverthenextsixweeksbytheARIMAmodel.Thuswecancalculatetheamountofdrugofvariousepidemicareasinadvanceandeffectively.InthiswaywecanmakepreparationforFollow-uptreatment.2.WedistributethedrugbythelevelofETCtomakethebestuseoftheshortagedrug.3.Wereducethecostofdeliveryunderthepremiseoftakingtheleasttimetodistributedrugs.Team#36448Page1of13BackgroundTheEbolaviruscausesanacute,seriousillnesswhichisoftenfatalifuntreated.ThecurrentoutbreakinwestAfrica,(firstcasesnotifiedinMarch2014),isthelargestandmostcomplexEbolaoutbreaksincetheEbolaviruswasfirstdiscoveredin1976.Therehavebeenmorecasesanddeathsinthisoutbreakthanallotherscombined.AccordingtothereportfromtheWorldHealthOrganization,inWestAfrica,casesnumberofinfectionincountriessuchasLiberia,SierraLeoneandGuinea,themostthreeseverecountriestherewiththeplagueofEbolahemorrhagicfever,reachmorethantwentythousand(includingsuspectedcases),aboveonemilliondeathsincluded,meaningthatthemortalityishigherthan50%.Andaftercomparisonbetweencountries,theinfectedcases,diagnosedorsuspected,anddeathsinGuinea,Liberia,SierraLeone,Mali,UnitedStatesaswellastheotherthreecountrieswhichhavefinishedthisepidemic,includingNigeria,SenegalandSpain,areevenmore.ThenumbersofinfectedcasesanddeathsinWestAfricahavereachedarecordhigh,andthesituationisstillinastateofdeterioration.Guinea,SierraLeoneandLiberiahaveveryweakhealthsystems,lackinghumanandinfrastructuralresources,havingonlyrecentlyemergedfromlongperiodsofconflictandinstability.OnAugust8,Thedirector-generaloftheWorldHealthOrganizationannouncedthatthisepidemicisapublichealthemergencywithinternationalconcern.Severalaidagenciesandinternationalorganizations,includingtheUSCentersforDiseaseandPrevention(CDC),theEuropeanCommissionandtheEconomicCommunityofWestAfricanStatesandotherunitsaretryingtoextenuateinvestmentinhumandisease.[]NowAmericanexpertshavedevelopedaneffectivedrugtreatmentwhichcanpreventdiseaseandcurediseasenottooserious.Sonowitisnecessarytodeliverthedrugtoallinfectedareasreasonablyandefficientlyafterconsiderationoftheinfectionandtrafficconditionsinallregions,tomitigatethecurrentepidemicpressureanderadicateEbolaviruseventually,thusreducethelossestoaminimum.ProblemDescriptionAccordingtotheWorldMedicalAssociation'sreport,thereisnewdrugthatcanpreventthespreadofEbolaandcurethediseaseisnotseriouspatientsnow.Wecombinespreadofthevirus,quantityofrequiredmedicine,feasibledeliverysystems,locationsofdeliveryandspeedofmanufacturingofthevaccineordrugtoestablishaviablemodeltooptimizetheeradicationofEbola,oratleastitscurrentstrain.Also,a1-2pagenon-technicallettershouldbepreparedfortheworldmedicalassociationtouseintheirannouncement.Team#36448Page2of13TerminologyandDefinitionTable1.Modelparameters.ZtThenaturallogarithmofthenumberofpatientsperweekBBackwardshiftoperatoratRandominterferenceNiThenumberofpatientswithithWeek（i=1,2,3……34）αAlevelETCdemandcoefficient（Highestlevel）βBlevelETCdemandcoefficientγClevelETCdemandcoefficient（Lowestlevel）μVaccineordrugdemandintensitymNumberofAlevelETCinthedistributioncirclenNumberofBlevelETCinthedistributioncirclekNumberofClevelETCinthedistributioncirclexDrugproductioninperweekWiQuantityofdrugwhichisdistributedtoairportLThesummationsofdistancesfromvariousETCswhichareintheintersectionofvariousdistributioncircl