数学建模 美赛 A题.docx

数学建模 美赛 A题.docx

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数学建模美赛A题

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2015MathematicalContestinModeling（MCM）SummarySheet

ModelingtheImpactofMedicationonEbola

EbolavirusdiseaseisspreadinginWestAfricancountries.AsthemedicationforEbolahasbeendeveloped,wemanagetoofferanoptimalplanforcontrollingthespreadofEbola.

Atfirst,weconsiderthesituationwithoutintervention.BasedonSEIRmodel,weformulateanepidemicmodel（SEIQFR）withtime-lagtosimulatethefuturesituationofEbola.ReferringtothedatafromtheWHOearlyperiod,wefittheunknownparameterswiththeleastsquaremethod.ImplementingourmodelwiththedataofSierraLeone,wegiveafuturepredictionofEbolaepidemicsituationwithRungeKuttamethod.Theresultsuggeststhatallcompartmentsbecomestableintheend,whichmeansanequilibriumpointisreached.

Asforinterventioninvolvedsituation,webuildanon-linerprogrammingmodeltogenerateadistributionplanofmedication.Basedonthefirstmodel,weaddinterventionofvaccine.AssistedwithmodifiedParticleSwarmOptimizationalgorithm,wereachtoasolutionleadingtofewerinfectedpopulationinSierraLeoneafter4dayswithasteadymanufacturespeedofvaccine.Wefindtheinfectedpeoplewilldecreaseby80,thereforeprovesthatvaccineisabletoeasetheepidemic.Then,wedevelopalinerprogrammingmodeltoprovideadeliverysystemwiththeleastcost.Accordingtotheresultsindistributionmodel,wegetthissolutionsystemforSierraLeone.

Oursensitivityanalysisconsidersinfluenceofotherfactors.Situationswithcontactratechangesaretested.Theresultssuggestthatthecontactratebetweeninfectedandsusceptiblepeoplehasthemostimpact.

OurSEIQFRmodelconsiderstheeffectoftime-lag,soitsuitsthefeaturesofEbolabetter.Themodelisflexibleininfectedcountries,aslongastheinitialdataofEbolacasesareavailable.

Content

I.Introduction1

1.1Background1

1.2Previouswork1

1.3Ourwork2

II.TheDescriptionoftheProblem2

2.1Howdowesimulatefutureepidemicsituation?

2

2.2Howdoweconsidertheinfluencesofmedicationdistribution?

2

2.3Howdoweanalyzeourresults?

2

III.Models3

3.1Notations3

3.2Assumptions3

3.3ImprovedSEIREpidemicModel4

3.3.1AscertainmentoftheParameters6

3.3.2SolutionandResult7

3.3.3AnalysisoftheResult9

3.4MedicationDistributionOptimizationModel9

3.4.1Ascertainmentofterminology10

3.4.2SolutionandResult11

3.4.3AnalysisoftheResult13

3.5MedicationDeliveryModel13

3.5.1SolutionandResult14

IV.SensitivityAnalysis15

4.1Influenceofβ15

4.1.1InfluenceofβI15

4.1.2InfluenceofβQ16

4.1.3InfluenceofβF17

4.1.4Analysisofresults17

4.2Timebeginintervention17

V.Conclusions18

5.1Conclusionsoftheproblem18

5.2Strengthsandweaknesses18

5.2.1Strengths18

5.2.2Weaknesses19

VI.FutureWork19

VII.References20

VIII.Memo21

I.Introduction

1.1Background

Ebolavirusdisease（EVD）,thediseasewithmostfatalityrate,spreadsbydirectcontactwith bodyfluids,suchas blood,ofaninfectedhumanorotheranimals.ThecurrentoutbreakinwestAfrica,（firstcasesnotifiedinMarch2014）,isthelargestandmostcomplexEbolaoutbreaksincetheEbolaviruswasfirstdiscoveredin1976.Ebolaisnotonlyfatal,butalsowithhighriskoftransmission.EventhebodyofEbolapatientsareinfectious,soimproperburialsmayalsocauseinfection.AnothercharacteristicofEbolaisthelatentperiod,whichpossiblyvariesfrom4to6daysbutcantopto29dayslong.Duringthelatentperiod,theinfectioushaslittlechanceoftransmissionandappearsnosymptom.

Recently,drugsaimingatcuringEbolapatientshasbeensuccessfullydeveloped.Asaworld-focusingvirus,Ebola’sspreadsituationhasbeenstudiedforaperiodoftime.Thenewmedicineisagreathelptocontroltheepidemicsituation.Thusatpresent,wecanassisttheEbolaeradicationprocessifoptimalplanisproposed,whichcanbereachedbybuildinganmathematicalsimulationmodeloftheepidemicsituation.Furthermore,relevantfactors,suchasthequantityofthemedicineneeded,possiblefeasibledeliverysystems,locationsofdelivery,speedofmanufacturingofthevaccineordrugandotherpossibleones,canalsobeaddressedonthebasisoftheformermodel.

Amongallinfectedcountries,Guinea,LiberiaandSierraLeonearethethreemostaffectedones.Andtherearestillnewlyoccurredcasesdaily.Soeverybeneficialmeasurementscounts.Aslongasthemethodisreasonableandscientific,theadoptionofwhichcanbeofgreatimpor