数学建模 请解释一下leslie人口增长模型，不是很理解，最好带例子，谢谢

模型Ⅰ：建立了Logistic人口阻滞增长模型，利用附件2中数据，结合网上查找补充的数据，分别根据从1954年、1963年、1980年到2005年三组总人口数据建立模型，进行预测，把预测结果与附件1《国家人口发展战略研究报告》中提供的预测值进行分析比较。得出运用1980年到2005年的总人口数建立模型预测效果好，拟合的曲线的可决系数为0.9987。运用1980年到2005年总人口数据预测得到2010年、2020年、2033年我国的总人口数分别为13.55357亿、14.18440亿、14.70172亿。

模型Ⅱ：考虑到人口年龄结构对人口增长的影响，建立了按年龄分布的女性模型（Leslie模型）： 以附件2中提供的2001年的有关数据，构造Leslie矩阵，建立相应 Leslie模型；然后，根据中外专家给出的人口更替率1.8，构造Leslie矩阵，建立相应的 Leslie模型。

首先，分别预测2002年到2050年我国总人口数、劳动年龄人口数、老年人口数（见附录8），然后再用预测求得的数据分别对全国总人口数、劳动年龄人口数的发展情况进行分析，得出：我国总人口在2010年达到14.2609亿人，在2020年达到14.9513亿人，在2023年达到峰值14.985亿人；预测我国在短期内劳动力不缺，但须加强劳动力结构方面的调整。

其次，对人口老龄化问题、人口抚养比进行分析。得到我国老龄化在加速，预计本世纪40年代中后期形成老龄人口高峰平台，60岁以上老年人口达4.45亿人，比重达33.277%；65岁以上老年人口达3.51亿人，比重达25.53%；人口抚养呈现增加的趋势。

再次，讨论我国人口的控制，预测出将来我国育龄妇女人数与生育旺盛期育龄妇女人数，得到育龄妇女人数在短期内将达到高峰，随后又下降的趋势的结论。

最后，分别对模型Ⅰ与模型Ⅱ进行残差分析、优缺点评价与推广。

%WBS矩阵是按列存放了2005年城镇的女性比例，女性死亡率，农村女性比例，女性死亡率

WBS=[0.43,8.09,0.54,18.550.42,0.67,0.51,1.960.38,0.21,0.51,1.310.42,0.39,0.51,0.660.45,0.35,0.56,0.610.47,0.35,0.58,0.660.46,0.19,0.58,0.280.51,0.16,0.64,0.190.52,0.13,0.66,0.30.53,0.1,0.68,0.350.59,0.16,0.78,0.280.57,0.17,0.74,0.390.61,0.15,0.85,0.360.63,0.22,0.89,0.250.68,0.27,0.98,0.330.79,0.12,1.1,0.440.8,0.24,0.95,0.520.8,0.28,0.78,0.630.87,0.4,0.74,0.590.73,0.24,0.58,0.950.65,0.13,0.53,0.820.67,0.31,0.52,0.780.7,0.31,0.54,0.920.86,0.27,0.62,0.620.76,0.23,0.56,0.80.74,0.32,0.57,1.120.81,0.36,0.57,0.650.8,0.2,0.57,0.910.77,0.21,0.54,0.880.85,0.36,0.61,1.160.88,0.41,0.65,0.860.95,0.3,0.74,1.021,0.47,0.77,1.311.03,0.44,0.82,1.291.06,0.47,0.86,1.251.13,0.45,0.98,1.211.04,0.59,0.92,1.51.13,0.79,1.03,1.490.87,0.7,0.87,1.290.99,0.77,0.97,1.571.02,0.72,0.97,1.421.01,0.9,0.91,1.741.21,0.85,1.04,1.380.87,1.08,0.82,1.980.5,1.28,0.45,1.80.65,1.32,0.55,2.240.58,1.69,0.5,2.350.74,1.4,0.67,2.530.81,2.14,0.78,2.970.74,1.58,0.74,3.140.78,2.3,0.8,3.50.78,2.21,0.77,3.190.69,2.64,0.74,3.670.7,2.88,0.74,3.870.59,3.65,0.63,4.550.58,3.58,0.63,4.250.56,3.97,0.59,5.630.48,4.41,0.52,5.590.47,4.28,0.51,6.70.43,5.74,0.47,7.610.4,6.42,0.46,8.440.37,6.24,0.41,8.840.35,8,0.39,10.10.35,7.79,0.37,11.520.34,7.77,0.36,12.740.36,9.77,0.38,13.60.3,8.93,0.3,15.860.33,12.35,0.33,16.910.31,14.71,0.32,18.020.31,15.59,0.32,22.650.31,16.52,0.33,24.850.27,17.63,0.29,24.930.27,20.88,0.3,31.720.23,24.65,0.26,35.490.2,24.35,0.24,35.810.21,29.3,0.25,41.210.17,32.96,0.2,46.710.17,37.02,0.2,49.670.15,41.72,0.18,56.380.12,47.67,0.15,66.390.12,56.08,0.16,67.870.1,58.44,0.13,74.280.09,62.81,0.11,85.120.08,69.85,0.1,95.390.07,86.93,0.08,107.10.06,83.58,0.07,120.520.04,91.58,0.05,118.080.03,111.83,0.04,139.250.03,113.52,0.03,130.750.02,132.44,0.03,157.340.07,232.71,0.08,237.02]

%WR矩阵存放的是2005年城镇和农村女性总人口

WR=[3791447,4606484]

%WS矩阵按列存放城镇女性生育率，农村女性生育率

WS=[0.010.07

0.14 0.43

0.65 2.03

2.08 6.31

6.79 16.96

18.7344.18

31.4570.14

36.3476.53

52.0077.73

52.7473.13

46.3963.69

44.3754.54

39.5846.68

30.2141.40

25.3537.40

20.5332.17

16.8630.44

13.7523.78

10.7919.02

8.51 14.22

6.65 10.52

4.63 7.91

4.15 5.67

2.29 3.97

1.61 2.84

1.35 1.73

0.70 1.18

0.73 0.88

0.67 0.63

0.34 0.78

0.40 0.44

0.29 0.45

0.23 0.32

0.33 0.39

0.32 0.37 ]

WS(:,1)=1.7374*WS(:,1)

WS(:,2)=1.0889*WS(:,2)%分别对城镇农村的生育率修正

t=T-2005

%构造Leslie矩阵

leslie1=zeros(91,91)

leslie2=zeros(91,91)

leslie1(1,16:50)=WS(1:35,1)/1000

leslie2(1,16:50)=WS(1:35,2)/1000

for i=1:90

leslie1(i+1,i)=1-WBS(i,2)/1000

leslie2(i+1,i)=1-WBS(i,4)/1000

end

leslie1(91,91)=1-WBS(91,2)/1000

leslie2(91,91)=1-WBS(91,4)/1000

d10=WR(1)/0.49788*WBS(1:91,1)/100

d20=WR(2)/0.49168*WBS(1:91,3)/100

%求2005-T年的人口情况

a=100000000

for i=1:t

d1=leslie1*d10

d2=leslie2*d20

d=[d1,d2]

Z(i)=sum(sum(d))

Z(i)=Z(i)*2.18/0.013/a%化总人口以亿人为单位

%进行城镇化分析

d10=d(:,1)+sum(0.01*d,2)

d20=d(:,2)-sum(0.01*d,2)

%对未来人口分布的分析

laonian60(i,:)=sum(d(61:91,:))*2.18/0.013/a%60岁以上的老年人口

laonian65(i,:)=sum(d(66:91,:))*2.18/0.013/a%65岁以上的老年人口

l60b(i,:)=sum(laonian60(i,:))/Z(i)%60岁以上的老年人口占总人口的比例

l65b(i,:)=sum(laonian65(i,:))/Z(i)%65岁以上的老年人口占总人口的比例

yulin(i,:)=sum(d(16:50,:))*2.18/0.012/a%育龄妇女人口

f=sum(d,2)

fuyangbi(i,1)=(sum(f(1:15))+sum(f(66:91)))/sum(f(16:65))%人口抚养比

z(i,:)=sum(d)*2.18/0.012/a%城镇总人口、农村总人口

end

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