人口年龄结构模型建模和预测

上海交通大学硕士学位论文人口年龄结构模型建模和预测姓名：虞丽萍申请学位级别：硕士专业：控制理论与控制工程指导教师：袁景淇200701012015MODELINGANDFORECASTINGTHEAGESTRUCTUREOFPOPULATIONABSTRACTThepopulationsystemisadynamicalsystem.Thetrendofapopulationwillaffectthedevelopmentofthesocietyanditseconomy.Theagestructureisoneofthemostimportantindexesinpopulationresearch.Theforecastofagestructureplaysanimportantroleinmakingpopulationpolicies.Adiscretemodelofpopulationdevelopmentwasappliedinthispaper.Fertilitymodel,mortalitymodelandimmigrationmodelwerealsoestablishedtoforecastthefertility,mortality,immigrationpopulationandtheagestructure.Comparedwithtraditionalfunctions,boththecompositefertilitymodelwhichisbasedonrandomdistributionfunctionsandthesegmentedmortalitymodelimprovedthemodels’accuracy.HistoricalChinesepopulationstatisticswereusedtoprovethevalidityofthemodelsreferredinthispaper.TheagestructureofShanghaiin2015wasforecastedanddisplayedinatree-likegraph.Theshapeofthepopulationtreereflectsthehealthconditionofitsagestructure.Byanalyzingthedevelopmenttrendoftheagestructure,wecanfindpopulationproblemsandprovidescientificevidenceforgovernmenttocontrolthepopulation.KEYWORDS:DiscretePopulationDevelopmentEquations,Fertility,Mortality,Immigration,PopulationForecast,AgeStructurePopulationTree1·······································································································52·······································································································63······················································································84················································································115··············································································126BP·······································································167(CFR)(TFR)············································1882000···················249···························2710····························································28112004········································32122015·······································32132003·········35142003·········36152001··················4116················································································4217a································································································4418b·······························································································4419c································································································45202004··························46212004··························47222000·················································55232004·············································································58242004······························5825··············································································64262015·········································································651LognormalPoisson·······················222······················································253GM1,1··························································3142003··························································3451989···································3961994···································3971998···································3982001···································409GNP·································································4310················································5311····································································5512············································································56132004············································································5914······················································5915················································································64162015··························································65),(trpµϕNβhglkLognormalpkPoissonckfqkrt1r2rabuABαβµσc–82–20072262007226–83–2007226–1–1.1–2–1.2–3–2.11210003100015-4915-494TFR56–4–781009100015-495101.002.1111211–5–11990Fig.1Populationpyramid132–6–21990Fig.2Agestructuretreeofpopulation2.23–7–122203(a)(b)–8–(c)3Fig.3Treetypesofpopulationstructure12.3–9–[1][2]GM(1,1)[3][4]7080[5]2.3.1–10–∫====+−=∂∂+∂∂21),(),(),()()()()()(),0()(),(),(),(),(),(),(0rrdrtrptrktrhtttNtttprptrptrgtrptrttrprtrpβϕµϕµ······························································(2.1)),(trprtrNtrp∂∂=/),(),(),(trNtrr),(trµtr)(tϕt)(tNt)(tβ),(trh),(trk),(trgt21,rr1r=152r=49),(trp)(tβ)(tϕ4–11–4Fig.4Controlchartofpopulationdevelopmentequations2.3.2[6]nn0tr)(txr(t+1)(r+1))(trµ)(tgr(t+1)(r+1))())(1()(tgttxrrr+−×µ0)(0tx5–12–5)()()()()()()1(tGtxtBttxtHtx++=+β)())(1()1(000tttxΨ−=+µ∑==Ψ21)()()()()(rriiiitxthtkttβTmtxtxtxtx))(),(),(()(110−……=mTmtgtgtgtG))(),(),(()(10……=–13–−−−=0)(100)(10000)(10000)(21ttttHmµµµΟΛΛΛ=00000000000000)()(00)(21ΛΛΛΜΜΜΜΜΜΛΛΛΛΛΛtbtbtBrr·········································(2.2)21000),()())(1))((1()(rrithtktttbiii…=−−=µµ)(tbiti2.42.4.1)()1(tbXatX+=