中国流行性腮腺炎发病率模型拟合及预测效果比较

背景　流行性腮腺炎（流腮）是中国极为严重的疾病。充分认识中国流腮的规律性并构建模型预测，对其预防和控制有重要意义。目的　评价季节性自回归移动平均模型（SARIMA）、指数平滑模型、SARIMA-广义回归神经网络（GRNN）组合模型和指数平滑-GRNN组合模型在流腮发病率拟合及预测中的应用效果。方法　利用全国2004年1月-2016年6月的流腮逐月发病率数据拟合、训练模型，建立SARIMA、指数平滑模型、SARIMA-GRNN组合模型和指数平滑-GRNN组合模型。预测2016年7-12月流腮的逐月发病率并与实际值比较，采用平均绝对误差百分比（MAPE）、平均误差率（MER）、均方误差（MSE）和平均绝对误差（MAE）评价模型拟合及预测效果。结果　SARIMA（0，0，2）（0，1，1）12为最优SARIMA模型；Holt-Winters相乘模型为最优指数平滑模型，SARIMA-GRNN组合模型和指数平滑-GRNN组合模型的SPREAD最优参数分别为0.026、0.031。SARIMA模型、指数平滑模型、SARIMA-GRNN组合模型和指数平滑-GRNN组合模型拟合的MAPE、MER、MSE和MAE依次分别为15.350%、14.976%、0.336、0.286，14.346%、14.249%、0.326、0.272，7.390%、6.320%、0.034、0.123，6.952%、5.776%、0.028、0.113。SARIMA模型、指数平滑模型、SARIMA-GRNN组合模型和指数平滑-GRNN组合模型预测的MAPE、MER、MSE和MAE依次分别为11.998%、12.260%、0.022、0.138，39.582%、38.462%、0.199、0.432，8.892%、9.677%、0.020、0.109，8.872%、9.672%、0.021、0.109。结论　指数平滑-GRNN组合模型为最优模型，拟合及预测效果最好，用于全国流腮发病率预测精度高；SARIMA-GRNN组合模型次之；SARIMA模型拟合及预测效果一般；指数平滑模型拟合效果较好，但预测效果较差。

Comparison of Fitting and Predicting Effects of Models on Mumps in China

Background Mumps is a serious public health concern in China.It is necessary to fully understand the regular pattern of mumps,and then model and forecast the disease to provide the scientific theoretical evidences for its prevention and control.Objective To evaluate the effect of seasonal autoregressive integrated moving average( SARIMA) model,exponential smoothing model,SARIMA-Generalized Regression Neural Network( GRNN) combined model and exponential smoothing-GRNN combined model in the fitting and prediction of mumps in China.Methods The monthly incidence from January 2004 to June 2016 in China was used to fit and train the models,and SARIMA,exponential smoothing model,SARIMA-GRNN combined model and exponential smoothing-GRNN combined model were established respectively.The monthly incidence from July to December 2016 was predicted and compared with the actual value.Four evaluation indicators,such as mean absolute percentage error( MAPE),mean error rate( MER),mean square error( MSE),and mean absolute error( MAE),were used to evaluate the fitting and prediction effects of the models.Results The SARIMA(0,0,2)(0,1,1)12 model was the most appropriate SARIMA model.The Holt-Winters multiplication model was the optimal exponential smoothing model.The SPREAD optimal parameters of the SARIMA-GRNN combined model and the exponential smoothing-GRNN combined model were 0.026 and 0.031,respectively.In the fitting phase,the MAPE,MER,MSE and MAE fitted by SARIMA,exponential smoothing model,SARIMA-GRNN combined model and exponential smoothing-GRNN combined model were 15.350%,14.976%,0.336,0.286;14.346%,14.249%,0.326,0.272;7.390%,6.320%,0.034,0.123;6.952%,5.776%,0.028,0.113,respectively.The MAPE,MER,MSE and MAE predicted by SARIMA,exponential smoothing model,SARIMA-GRNN combined model and exponential smoothing-GRNN combined model were 11.998%,12.260%,0.022,0.138;39.582%,38.462%,0.199,0.432;8.892%,9.677%,0.020,0.109;8.872%,9.672%,0.021,0.109,respectively.Conclusion The exponential smoothing-GRNN combined model was the optimal model for predicting the incidence of mumps in China with higher accuracy,followed by SARIMA-GRNN combined model.The SARIMA model has poor fitting and prediction accuracy,and the exponential smoothing model has good fitting accuracy,but its prediction accuracy is poor.