GM(1,1)和趋势外推模型在我国艾滋病发病率预测中的应用

Prediction on the Incidence Rate of AIDS in China with Gray Model( 1,1 )and Trend Extrapolation Model

目的通过GM(1,1)和趋势外推模型在我国艾滋病发病率拟合中的应用,探讨适合我国艾滋病发病率的最优预测模型。方法采用GM(1,1)和趋势外推模型拟合2000-2011年发病规律,评价模型拟合精度;选择最优模型预测我国未来艾滋病的发病趋势,用2012年的数据评价模型预测精度。结果趋势外推模型中的二次曲线回归模型和GM(1,1)均可用于我国艾滋病发病率数据;但二次曲线回归模型的拟合精度优于GM(1,1),二次曲线回归模型和GM(1,1)的平均误差率分别为7.6%和28.6%,决定系数分别为0.990和0.800;采用二次曲线回归模型预测2012,2013和2014年,我国艾滋病发病率分别为1.68/10万,1.95/10万和2.24/10万,2012年的预测值与实际值相对预测误差为6.14%。结论趋势外推模型中的二次曲线回归模型更适合我国艾滋病发病率的预测,未来几年我国艾滋病的发病率仍将呈现上升趋势,需加强艾滋病的防控。

Objective We aimed to explore the best forecasting model of AIDS incidence rate in China by applying gray model（ 1,1） and trend extrapolation model. Methods Gray model（ 1,1） and trend extrapolation model w as used to fit AIDS incidence rate from 2000 to 2011 in China. The best model w as screened to predict AIDS incidence trend in the future after evaluating fitting precision of different models. The incidence data in 2012 w as used to evaluate prediction precision. Results Both quadratic curve regression model in trend extrapolation model and gray model（ 1,1） w ere suitable to the AIDS incidence data in China. But quadratic curve regression model yielded higher fitting precision. M ean error rate w as 7. 6% in quadratic curve regression model and 28. 6% in gray model（ 1,1）. Determination coefficient w as 0. 990 and 0. 800 betw een them. AIDS incidence rate in China from 2012 to 2014 w ould be 1. 68 /100 000,1. 95 /100 000 and 2. 24 /100 000 from quadratic curve regression model. The relative prediction error in 2012 w as 6. 14%. Conclusion Quadratic curve regression model in trend extrapolation model is a better method to predict AIDS incidence trend in China. The epidemic of AIDS in China w ill still rise,and prevention and control of AIDS should be strengthened.