数学模型在人口预测中的应用——以江苏省为例

APPLICATION OF MATHEMATICAL MODELS IN PREDICATION OF THE POPULATION——TAKING JIANGSU PROVINCE AS AN EXAMPLE

人口规模是城市规划和土地利用总体规划中一项重要的控制性指标。人口规模是否合理，不仅影响到未来地区经济和社会发展，而且会影响到地区生态环境可持续发展。因此准确地预测未来人口的发展趋势，制定合理的人口规划和人口布局方案具有重大的理论意义和现实意义。运用马尔萨斯人口模型、Logistic增长模型和线性回归分析方法。利用《江苏统计年鉴》人口数据对江苏省2005～2020年的人口发展规模做出预测。预测结果显示。3种模型均取得了较好的模拟效果，但马尔萨斯人口模型和Logistic增长模型的模拟精度比线性回归更理想。在模型的验证过程中。前两者的平均相对误差较小。分别为0．35％和0．12％，而线性回归为2．25％，故采用两种非线性预测值的平均值作为预测结果。结果为2010年达到7695．19万人。2020年达到7919．20万人。

The scale of population is considered as an important control index of urban planning and the land use planning. The rationality of the scale of population can affect not only development of economy and society, but also sustainable development of ecological environment. So it has great theory meaning and realistic meaning to exactly predict development trend of population and establish rational population layout. The paper dealt with Malthusian models,Logistic models and linear regression and used the data of Jiangsu Statistical Yearbook to predict gross population in Jiangsu Province in 2005～2020. Results show that three models fit well. But Malthusian models and Logistic models are better than linear regression accordi 0.12 in two million to residue errors which residue errors in two non-linear models are smaller and close, 0. 35%and than 2.25%in linear regression in validating models. So the authors select the mean of prediction non-linear models as prediction results. Prediction results show gross population reaches to 76.95 in 2010, 79.19 million in 2020.