三种预测模型对中国流行性腮腺炎月度发病率预测的应用与比较

Application and comparison of three models for predicting the monthly incidence rates of mumps in China

目的建立三种预测模型分析流行性腮腺炎的季节发病情况,为流行性腮腺炎的预测方法提供理论依据。方法收集2004年1月—2018年12月全国流行性腮腺炎月度发病率数据,训练集数据为2004年1月—2017年12月流行性腮腺炎月度发病率,分别建立季节性差分自回归移动平均(seasonal autoregressive integrated moving average,SARIMA)模型、温特线性与季节指数平滑(Winter linear and seasonal exponential smoothing,Holt-Winters)模型和神经网络自回归(neural network autoregressive,NNAR)模型,以2018年1—12月中国流行性腮腺炎月度发病率数据作为测试集,评估三种模型的预测效果。结果2004年1月—2018年12月全国流行性腮腺炎月度发病率最高月份是2012年6月,发病率最低月份是2016年2月,每年有两个发病高峰,大高峰发生在每年的4—7月,小高峰发生在每年的11月至次年1月;SARIMA模型、Holt-Winters模型和NNAR模型预测的平均相对误差的绝对值(mean absolute percentage error,MAPE)分别是18.63%、18.65%和16.31%,均方根误差(root mean square error,RMSE)分别为0.29、0.36和0.39,平均绝对误差(mean absoluteerror,MAE)0.26、0.30和0.30,R^(2)分别为93.43%、83.79%和78.24%。预测效果最好的为SARIMA模型,其次为Holt-Winters模型,NNAR模型的预测效果最差。结论SARIMA模型能很好地预测全国流行性腮腺炎的发病情况,可为今后流行性腮腺炎的预防控制工作提供借鉴方法。

Objective To establish three forecast models for analyzing the seasonal incidence of mumps so as to provide a theoretical basis for the prediction method for mumps.Methods We collected the data about the monthly incidence rates of mumps in China from January 2004 to December 2018,and the monthly incidence rates of mumps from January 2004 to December 2017 served as the training data.We established the seasonal autoregressive integrated moving average(SARIMA)model,Winter linear and seasonal exponential smoothing(Holt-Winters)model and neural network autoregressive(NNAR)model respectively.The data concerning the monthly incidence rates of mumps from January to December 2018 were used as the test set.The prediction effects of the three models were evaluated.Results From January 2004 to December 2018,the monthly incidence rate of mumps in China was found to be the highest in June 2012 and the lowest in February 2016.There were two annual peaks of incidence,with the annual maximum peak occurring in April-July and the annual minor peak in November-January.The mean absolute percentage errors(MAPEs)of SARIMA model,Holt-Winters model and NNAR model prediction were 18.63%,18.65%and 16.31%respectively,the root mean square errors(RMSEs)were 0.29,0.36 and 0.39 respectively,the mean absolute errors(MAEs)were 0.26,0.30 and 0.30 respectively,and R^(2)were 93.43%,83.79%and 78.24%respectively.The time series forecasting model with the best forecast effect was SARIMA model,followed by Holt-Winters model,and the forecasting effect of NNAR model was the worst.Conclusion SARIMA model can well predict the incidence of mumps in China,and provide references for mumps prevention and control in future.