夏令营A题英文版.docx
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夏令营A题英文版.docx
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夏令营A题英文版
PopulationAndMedicalNeedsForecastofShenzhen
ZimiaoXu
DanYang
XiaomengXie
SouthwestUniversityforNationalities
Chengdu,China
Advisor:
YaxiChen
Summary
Abstract:
Populationandmedicalproblems,relatedtonationalinterestandpeople’slivelihoodisthebigproblem.Forecastingthemreasonablyandaccuratelyisofgreatimportant.Shenzhen,populationflowsofwhichisbigisthefastestgrowingcitiesineconomicdevelopmentinChina.Therefore,forecastingpopulationandmedicalneedsofShenzhenissignificant.
Forthefirstquestion,wemainlyinvestigatedShenzhen’sdemographictrendsandbedspaceindemandforecast,byusinggraymodelmethod.Firstofall,wecollectthestatisticsofShenzhenpopulationstructurein2001-2010,andusegraymodelandregressionanalysistosimulatethechangerule,andthenwepredictthetrendsofShenzhenpopulationstructureinthefollowingdecade.Then,wepredictthenumberofbedsperthousandpopulationinthenextdecadethroughthenumberofbedsperthousandpopulationofthepreviousyearsinShenzhen,andgetthequantityofbedsindemandinthenextdecadebymultiplyingthenumberofbedsperthousandpopulationbythepopulation.
Forthesecondquestion,wefirstdividedifferenttypesofhospitalsclassifiedintothreetypicaltypesoforganizations,andthenusetheprobabilitymodeltosurveyinfantilepneumonia,hypertensionandacuteappendicitisthesethreebedspacedemandformedicaltreatmentofthediseaseindifferenttypesofmedicalinstitutions.
Theresultsshowthatthetrendforecastandactualresultsisconsistent,butthereisacertaingapinspecificvalue.Thisindicatesthatthebasicmathematicalmodeldiscussedinthispapergrasptheinherentlawsofpopulationstructureandbedsindemand,havesomepredictivevalue.
Keywords:
graymodel,regressionanalysis,populationprojections,bedsneeds
1.Background
ItisknowntousallthatShenzhenisoneofthemostrapidlydevelopedcity.TheremarkablecharacteristicsofShenzhenarethatthefloatingpopulationandtheyoungoccupythemost.Theyoungisseldomattackedbydiseasebecauseoftheirstrongbodies.Therefore,althoughthepercapitamedicalfacilitiesofShenzhenislowerthantheaveragelevelofsimilarcityinthecountry,itcanstillmeetthemedicalneedsoftheexistingpopulation.However,withthepassingoftimeandtheadjustmentofthepolicy,thepopulationoftheoldofShenzhenwillgraduallyincrease,theindustrialchangesinthewillalsoaffectthenumberofmigrantworkers.AllofthesemayleadtothedifferenceofthemedicalneedsofShenzhenbetweenthefutureandnow.
Themedicaldemandisrelatedtopopulationstructure,economicdevelopmentandsoon.Thereasonableforecastcanhelpthemedicalfacilitiesmatchthefuturemedicaldemands,whichistheimportantconditiontoguaranteethesustainableeconomicdevelopmentinShenzhen.Therefore,weestablishedamathematicsmodelforShenzhen,inordertopredictthegrowthofpopulationandmedicalneeds.Weshouldsolvethefollowingproblems:
(1).Topredictthedemandofmedicalbedsinthecityanddistricts.
(2).Thedemandofmedicalbedswhenattackedbyheartdisease.hypertensionorgastriccancerindifferenttypesofmedicalinstitutions.
2.Analysis
2.1.标题
Inordertomakepredictionsmoreaccurately,weanalyzetheresidentpopulationvariationofnearlyadecadeinShenzhen,andforecastthedevelopmenttrendofShenzhenpopulationandstructureofthenextdecade.Thenwepredictthenumberofmedicalbedsindemand.Buttherealityiscomplex,sotobetterpredictthedemandformedicalbedsinthenextfewyearsismoredifficult.Inadditiontoanalyzethemanyfactorsthataffectthequantityofmedicalbedsindemandaccurately,moreapplicabledatasimulationmethodandselectthepredictionmodelusedtopredicttheperformanceofanunknownsystemisalsoinneed.Inactualpredictionprocess,wehavechosenagraysystemmodel,andmainlyuse"graymodelGM(1,1)topredictthefutureofShenzhendecadepopulationtrend,andcollectthedataofthedistrictthisstagebedspacedemand,theuseofinterpolationintendsShenzhenanddistrictmedicalbedsoncombinedoverthenextdecade.
2.2Forquestiontwo,Shenzhen’sdifferenttypesofmedicalstructuresclassifieddividedroughlydividedintothreecategoriesofA,B,C.Forthepurposesofthisdiscussion,weselectinfantilepneumonia,hypertensionandacuteappendicitis,thesethreemorerepresentativediseasetoanalyze.Theprobabilisticmodelusedintheanalysisprocesstopredictthethreediseasessolving,andwegetthesolutionofthethreediseases,abouttheirbedsindemandinthedifferenttypesofmedicalstructuresbycollectingandanalyzingthedataof2011bedsinneed.
3.Assumptionsandsymbols
3.1ModelAssumptions
(1)AssumingtheScheduletoaccuratedata.
(2)Assumingourresearchprocessisnotinfluencedbyoutsidefactors.
(3)Weregardedhouseholdpopulationastheresidentpopulationandnon-householdpopulationastheresidentpopulation.
(4)Assumingnomajorpolicychangedandunexpectedeventshappenedintheforecastyears.
3.2Symbols
SymbolsAssumptions
Thereferencesequenceofgraymodel
Thesequenceofgraymodelafterbeingaccumulatedonetime
Themeansequenceofgraymodel
Thepredictionerrorofgraymodel
and
Distributionofthemeanvalueofnormaldistribution
4.ModelandSolving
4.1Modelingandsolutiontoproblem1
4.1.1PredictingthepopulationofShenzheninthetenyears---Graymodel
4.1.1.1Analysisandprocessingdata
Firstly,wedrewascatterdiagramwhichshowsthepopulationchangesinShenzhenfrom2001to2010accordingtothedataofappendix:
Fig1Thefigureshowsthatthepopulationhasanincreasingtrendanditsgrowthrateisbasicallystablein2001-2010.
4.1.1.2Modeling
Weregardedthedataoftenyearsastheresearchobjectwhenintheprocessofmodelbuilding.
Order
(1)
Firstofall,makinganaccumulationtothedataforaprogression(AGO)
(2)
and,
.
Second,makeouttheseriesofmean
So
.
establishthedifferentialequations
(3)
Thewhiteningequationis
(4)
Order
,
accordingtoleastsquaremethod,weknowtheleastof
is
.,
Sosolvingtheequation(4)have:
Accordingtothedataprovidedwiththeschedule1andschedule2,wefittedtheresidentandnon-residentpopulationthroughtheMATLABprogramandthenwegotthemapofthedevelopmenttrendofthepopulation.Asshowninfig2.
Fig2
Note:
Thecurveinfigure2isfittingcurveandthatcircledareactualdatainnearlytenyears.
Fromthechart,wecancometoaconclusionthatthepopulationofShenzhenhasatrendofgrowth.Becausetherearealotofyoungpeopleatthepresentstage,itwillincreasethedemandforbeds.
Weuseresidualmethodtotestthemodel.
4.1.1.3ModelTest
If
,itisconsideredthatitmeetsgeneralrequirements;if
itisconsideredthatitmeetshigherrequirements.Inthecalculation,theresidualsofthemodelarebetween[-0.0642,0.0699],whichachievedthehigherrequirements,sothepredictionresultsarereliable.Thedatashowninthetablebelow:
Years
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
Res.
-0.05
-0.06
-0.05
-0.03
0.01
0.02
0.03
0.03
0.02
0.00
4.1.2ForecastthedemandofmedicalbedinShenzhenanditsareas
4.1.2.1ThenumberofbedforperthousandpopulationinShenzhen
AfterconsultingFamilyPlanningCommissionofhealthstatisticsyearbook,wedrawatablewhichpresentthebedchangesofShenzhenfrom1979to2010.
Fig3
Accordingtothechangesofpattern,itiseasytofindthatitcontainsthesinefunctionandexponentialfunction,soweusethefollowingfunctiontosimulatetheabovegraph,
f=x
(1)-x
(2)*exp(-(t-x(3)).^2*x(4))+sin(x(5)*t+x(6)).*x(7).*t.
thenwesimulationbyMATLABprogramandgotthefollowinggraph:
Fig4
Theblackcurvesdirectlyrepresentthefittingresultsandtheredoneisfittingcurveafterdeviationcorrection.
Wechosethepartofthedataafter1975andfitfortheoveralltrendandthendrawcurve.Accordingtothedeviationbetweentheoriginaldataandfitting,wegotthedeviationvalue,then,fittedvalueminusdeviationcorrectionvalueisobtainedandthenagainfitting.ThenumberofbedsperthousandpopulationpredictionobtainedinShenzhencityfrom2011to2020asshowninthefollowingtable:
Fig5
4.1.2.2ThemedicalpredictionofthetotalareaofShenzhen
Weusethedatain4.1.1.1and4.1.1.2andthefollowingformulatopredictthenumberofmedicalbed.Theformulais:
Shenzhengeneralmedicalbeds=(populationofShenzhen/1000)perthousandpopulationbeds
Fig6
4.1.3ShenzhenCityDistrictmedicaldemandforecasting
WegotademanddatabyreferringtotheShenzhencityhealthandFamilyPlanningCommission
Thehospitalbedsofthedistrictgovernment
year
Luohu
Futian
Nanshan
Yantian
Baoan
Longgan
2002
470
637
891
170
2670
1727
2003
422
781
1145
250
3060
1857
2004
423
771
1122
205
3450
1991
2005
483
761
1372
277
3800
2045
2006
462
771
1392
277
4070
2107
2007
453
791
1430
277
4170
2263
2008
510
811
1648
305
4590
2391
2009
568
886
1672
310
4370
2272
2010
584
906
1686
365
4659
2630
Fig7
Wealsousethegraymethod.ForecastingthebeddemandinShenzhendistrictfrom2011to2020accordingtothedemandfrom2002to2010.Theresultisinaccordancewiththeactualsituation.Thespecificdataasshowninthefollowingtable:
Bedspredictionduring2011-2020
year
Luohu
Futian
Nanshan
Yantian
Baoan
Longgan
2011
602
900
1865
368
5057
2656
201
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