Leslie 模型预测中国 2023-2050 年人口年龄结构

本文使用 Leslie 模型，基于 2022 年中国人口数据，预测未来 28 年 (2023-2050 年) 的年龄结构变化。模型涵盖 0-80 岁年龄段，仅考虑生育率和死亡率，并提供 Matlab 代码示例。

模型设定

年龄组: 80 个年龄组，分别代表 0-79 岁
初始人口: 0 岁人口数为 1400 万
出生率: B = 0.6
死亡率: D 为一个包含 80 个元素的数组，分别代表每个年龄组的死亡率

Matlab 代码

%% Leslie模型预测中国人口年龄结构

% 设定初值
N = zeros(80,1); % 80个年龄组
N(1) = 14000000; % 0岁人口数
B = 0.6; % 出生率
D = [0.0015,0.0017,0.0019,0.0022,0.0027,0.0035,0.0046,0.0063,0.0084,0.0112,0.0149,0.0188,0.0230,0.0271,0.0311,0.0346,0.0374,0.0391,0.0400,0.0402,0.0397,0.0388,0.0376,0.0363,0.0351,0.0342,0.0337,0.0336,0.0337,0.0339,0.0341,0.0342,0.0342,0.0342,0.0342,0.0341,0.0339,0.0336,0.0332,0.0327,0.0321,0.0315,0.0310,0.0305,0.0301,0.0296,0.0291,0.0285,0.0278,0.0272,0.0267,0.0262,0.0258,0.0255,0.0252,0.0249,0.0248,0.0247,0.0247,0.0248,0.0250,0.0252,0.0255,0.0260,0.0266,0.0273,0.0282,0.0292,0.0303,0.0316,0.0330,0.0347,0.0366,0.0387,0.0411,0.0438,0.0469,0.0503,0.0542,0.0587,0.0638,0.0696,0.0762,0.0837,0.0921,0.1016,0.1122,0.1241,0.1376,0.1526,0.1694,0.1879,0.2084,0.2312,0.2563,0.2840,0.3146,0.3483,0.3855,0.4267,0.4725,0.5236,0.5807,0.6448,0.7168,0.7978,0.8889,0.9917,1.1080]; % 每个年龄组的死亡率

% 构建Leslie矩阵
L = diag(1-B.*D(1:79),-1);
L(1,:) = B;

% 预测未来人口年龄结构
for t = 1:28
    N(:,t+1) = L*N(:,t);
end

% 画图显示预测结果
age = 0:79;
figure;
plot(age,N(:,1),age,N(:,15),age,N(:,28));
legend('2022年','2037年','2050年');
xlabel('年龄');
ylabel('人口数');
title('中国人口年龄结构预测');

代码说明

N: 80 行 1 列的矩阵，代表每个年龄组的初始人口数
B: 出生率
D: 死亡率数组
L: Leslie 矩阵，用于计算人口变化
t: 时间步长，代表预测年份，从 1 开始，代表 2023 年
N(:,t+1): 代表第 t+1 年每个年龄组的人口数

预测结果

代码运行后，会绘制 2022 年、2037 年和 2050 年的年龄结构图，可直观地观察人口年龄结构的变化趋势。

注意: 这是一个简化的模型，只考虑了生育率和死亡率，没有考虑其他因素，如迁移、社会经济状况等。实际预测结果可能与实际情况有所偏差。

参考文献

Leslie, P. H. (1945). On the use of matrices in certain population mathematics. Biometrika, 33(3), 183-212.