2015年美赛A题优秀论文

ForofficeuseonlyT1________________T2________________T3________________T4________________TeamControlNumber35798ProblemChosenAForofficeuseonlyF1________________F2________________F3________________F4________________2015MathematicalContestinModeling(MCM)SummarySheet(Attachacopyofthispagetoyoursolutionpaper.)FarewelltoEbolaSummaryThecurrentoutbreakofEbolahascausedgreatharmtothepeopleinWestAfricasinceitbeganinDecember2013.Fortunately,theworldmedicalassociationhascreatednewmedicationtostopEbola.Inthispaper,wesetupmathematicmodelsintwopartsinordertocontrolandeveneradicatetheEbolavirusdisease.Ontheonehand,weestablishtwotransmissiondynamicalmodels,themedicinemodelandthemedicine-vaccinemodel,whicharebasedonthebasicmodelofinfectiousdisease.First,wedividepeopleintodifferenttypes.Then,webuildtheconversionrelationshipbetweendifferenttypesofpeople,onbasisofwhichwegettheiterativeequations.Atlast,weiteratetheequationstoobtainthepredictingresults.WefindthatthemedicinehaslargereffectonthecontrolofEbolavirusdiseasethanvaccine,becausethecontactrateisprettysmall.Therefore,itisurgenttodelivermedicinetotheinfecteddistricts.Besides,weobtaintheoptimalmaximalquantityofmedicineproducedeverydayis2000pieces.Ontheotherhand,wesetuptwooptimaldeliveryroutesformedicineandvaccineseparately.TheformerfocusesontheshortesttimeanditisoptimizedbytheimprovedDijkstraAlgorithm.ThelatterconcentratesontheleastdistanceanditisoptimizedbytherefinedSavingAlgorithm.Finally,weconcludethatthereare11trucksrequiredtotransportthemedicinefor20daysand7truckstransportingthevaccinefor30dayswhenthedailynumberofvaccinetransportedis0.3millionpieces.Additionally,weanalyzethestrengthsandweaknessesofourmodelsandwritealetterfortheworldmedicalassociationtoproposeoursuggestions.Team#35798Page2of27Content1Introduction.....................................................................................................................31.1AnalysisoftheProblem.............................................................................................31.2LiteratureReview.......................................................................................................32Assumptions.....................................................................................................................43TheTransmissionModel................................................................................................43.1TheBasicModelofEpidemicDynamics...................................................................43.2TheMedicineModel..................................................................................................63.2.1PartitionofPeople..................................................................................................63.2.2Assumptions.......................................................................................................63.2.3EstablishmentoftheModel................................................................................73.2.4ParameteroftheModel......................................................................................93.2.5ResultoftheModel..........................................................................................103.3TheMedicine-vaccineModel...................................................................................113.3.1Assumptions.....................................................................................................123.3.2EstablishmentoftheModel..............................................................................123.3.3ResultoftheModel..........................................................................................134TheDeliverySystems....................................................................................................174.1CollectionofData....................................................................................................174.2TheDeliverySystemsforMedicine.........................................................................184.2.1Assumptions.....................................................................................................184.2.2EstablishmentoftheDeliverysystems.............................................................184.2.3ResultoftheModel..........................................................................................194.3TheDeliverySystemsforVaccine........................................................................204.3.1Assumptions.....................................................................................................204.3.2EstablishmentoftheDeliverySystems............................................................204.3.3ResultoftheModel..........................................................................................225Conclusion......................................................................................................................236StrengthsandWeaknesses............................................................................................247ALe