应用灰色预测模型GM(1,1)对结核病发病率进行预测

Application of residual grey model(1,1) to the prediction of tuberculosis prevalence

目的:探讨灰色预测模型GM(1,1)在时间序列资料中的应用;建立结核病登记发病率的预测模型。方法:利用重庆市结核病防治所于1993-2003年登记的结核病发病率资料建立灰色预测模型即残差GM(1,1)模型,并对2004年结核病登记发病率进行预测。结果:残差GM(1,1)模型为:■(1)(k+1)=89.5776e0.0392k-85.0913+δ(k-1)1.6435e-0.3068k,1993-2003年预测值的相对误差均小于0.05,关联度>0.6,小误差概率P>0.8;2004年结核病登记发病率预测为5.2942/10万,相对误差为0.0461,修正后的相对误差为0.0121。结论:残差GM(1,1)模型拟合效果结果较为理想,是一种短期内预测精度较高的预测模型。

Objective：To discuss the application of residual Grey Model （1,1） in the time series data to set up the prediction model for Tuberculosis prevalence.Methods ：Grey Model （1,1）was set up by using the material on Tuberculosis prevalence collected by Tuberculosis Prevention and Treatment Institute of Chongqing city from 1993 to 2003,and then used to predict the Tuberculosis prevalence of 2004.Results ：The residual Grey Model（1,1）is ^X^（1）（k＋1）=89.5776e^0.0392k-85.0913-δ（k-1）1.6435e^0.3068k, the relative error values of predictive value for 1993 to 2003 were all less than 0.05,and the degree of grey incidence was bigger than 0.6,and the little error probability was bigger than 0.8;The predictive prevalence value in 2004 was 5.2942 per 100 thousands,the relative error was 0.0461 and the modified one was O.O121.Conclusion：The residual grey model （1,1） had a good fitness and can be used to predict tuberculosis prevalence with high prediction precision in short-term time series.