中国手足口病发病率ARIMA、RBF及ARIMA-RBF组合模型拟合及预测效果比较

目的 比较求和自回归滑动平均混合模型（ARIMA）、径向基函数神经网络模型（RBF）和ARIMA-RBF组合模型对中国手足口病月发病率的拟合及预测效果，探讨预测手足口病发病率的优化模型。方法 收集2008年1月-2014年12月中国手足口病月发病率资料，基于2008年1月-2014年6月的78个数据分别建立ARIMA模型、RBF模型和ARIMA-RBF组合模型，采用2014年7-12月的6个数据进行外回代验证模型的外推预测效果，评价指标包括相对误差（RE）、平均相对误差（MRE）、均方误差（MSE），均方根误差（RMSE）和平均绝对误差（MAE）。结果 ARIMA模型拟合和预测的MRE、MSE、RMSE、MAE分别为14.006、4.689、2.165、0.916和13.565、4.416、2.101、0.577，RBF模型分别为9.031、1.559、1.249、0.508和8.964、1.504、1.226、0.503，ARIMA-RBF组合模型分别为6.397、1.357、1.165、0.416和6.655、1.485、1.218、0.433，ARIMA-RBF组合模型的拟合及预测曲线与原始值最接近。结论 ARIMA-RBF组合模型拟合及预测效果均优于ARIMA模型和RBF模型。

Comparison on predictive capacity and fitting efficiency of ARIMA,RBF and ARIMA-RBF combination model for incidence of hand-foot-mouth disease

Objective To compare predictive capacity and fitting efficiency of autoregressive integrated moving average model (ARIMA),radical basis function model (RBF),and ARIMA-RBF combined model for monthly incidence of hand-foot-mouth disease (HFMD) in China and to explore an optimized model.Methods Data on monthly incidence of HFMD from January 2008 to December 2014 in China were collected and ARIMA,RBF,and ARIMA-RBF combined models were established based on the data;then the data for the period from July to December 2014 were introduced back to the established models to evaluate their predictive capacity.The indexes of fitting efficiency of the models included relative error (RE),mean relative error (MRE),mean square error (MSE),root mean square error (RMSE),and mean absolute error (MAE).Results The MRE,MSE,RMSE,and MAE were 14.006,4.689,2.165,and 0.916 for ARIMA fitting model;13.565,4.416,2.101,and 0.577 for ARIMA predictive model;9.031,1.559,1.249,and 0.508 for RBF fitting model;8.964,1.504,1.226,and 0.503 for RBF predictive model;6.397,1.357,1.165,and 0.416 for ARIMA-RBF combined fitting model;and 6.655,1.485,1.218,and 0.433 for ARIMA-RBF combined predictive model,respectively.For the three established models,the fitting and predictive values of ARIMA-RBF combined model were closest to the original data.Conclusion The ARIMA-RBF combination model is superior to ARIMA model and RBF model in fitting and prediction of HFMD monthly incidence in China.