Gompertz模型在人口增长预测问题中的应用  

Application of Gompertz model in population prediction

作　　者：阎慧臻[1] 

机构地区：[1]大连工业大学信息科学与工程学院,辽宁大连116034

出　　处：《大连工业大学学报》2015年第2期150-152,共3页Journal of Dalian Polytechnic University

基　　金：辽宁省教育厅科技研究项目(2009A075)

摘　　要：Gompertz模型是常用的动物种群生长模型,可用于描述种群的生长发育规律。利用分离变量的方法求出了Gompertz模型的解析解,利用MATLAB软件描绘了Gompertz模型解析解的图形。基于Gompertz模型,运用最小二乘法,对1985—2012年中国人口数据进行非线性拟合,建立了中国人口增长的近似公式,运用此公式估算了中国历年人口数量,并对中国2020、2030和2050年的人口数量进行了预测。估算的中国人口数量与实际统计结果吻合情况良好。Gompertz model is a commonly used model for biological population growth, which can describe the laws of population growth. In this paper, the analytical solution of Gompertz model is obtained with the method of separating variables, and the figure of analytical solution is acquired with the help of MATLAB. Then an approximate formula is established by doing a non-linear fitting to the actual populations of China from 1985 to 2012 with Gompertz model and the least square method, and the populations of China are predicted by using this approximate formula. The results showed that the calculations were in conformity with the statistical data in principle. At last, the populations of China in 2020, 2030 and 2050 can be predicted by using the approximate formula.

关 键 词：Gompertz模型 人口数量 预测 

分 类 号：O29[理学—应用数学] Q141[理学—数学]