基于联合国数据预测中国未来人口年龄结构：Leslie 模型与 Matlab 代码

% 初始化数据 t = 2022:2050; % 年份 N = [1444216100, 1444216100, 1429067880, 1413794400, 1398675000, 1383450000, 1368230000, 1353040000, 1337850000, 1322610000, 1307400000, 1292270000, 1277100000, 1262000000, 1247000000, 1232000000, 1217000000, 1202000000, 1187000000, 1172000000, 1157000000, 1142000000, 1127000000, 1112000000, 1097000000, 1082000000, 1067000000, 1052000000, 1037000000, 1022000000, 1007000000, 991000000, 977000000, 963000000, 949000000, 935000000, 922000000, 908000000, 895000000, 881000000, 868000000, 855000000, 842000000, 829000000, 817000000, 804000000, 792000000, 779000000, 767000000, 755000000, 743000000]; % 人口数量 r = [1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6, 1.6]; % 生育率 d = [7.6, 7.7, 7.8, 7.8, 7.9, 7.9, 8, 8, 8.1, 8.1, 8.2, 8.2, 8.3, 8.3, 8.4, 8.4, 8.5, 8.5, 8.6, 8.6, 8.7, 8.7, 8.8, 8.8, 8.9, 8.9, 9, 9, 9.1, 9.1, 9.2, 9.2, 9.3, 9.3, 9.4, 9.4, 9.5, 9.5, 9.6, 9.6, 9.7, 9.7, 9.8, 9.8, 9.9, 9.9, 10, 10]; % 死亡率

% 建立Leslie模型 L = [0.5r(1) 0 0 0; d(1) 0.5r(2) 0 0; 0 d(2) 0.5r(3) 0; 0 0 d(3) 0.5r(4)]; % 矩阵L P = zeros(4, length(t)); % 初始化矩阵P P(:, 1) = [N(1); 0; 0; 0]; % 初始人口分布 for i = 2:length(t) P(:, i) = L * P(:, i-1); % 计算人口分布 end

% 绘制年龄结构图 figure; plot(t, P(1,:), t, P(2,:), t, P(3,:), t, P(4,:)); legend('0-20岁', '20-40岁', '40-60岁', '60-80岁'); xlabel('年份'); ylabel('人口数量'); title('中国年龄结构预测（2023年-2050年）');