乘积季节自回归积分滑动平均模型在流行性腮腺炎发病率预测中的应用

Application of multiple seasonal autoregressive integrated moving average model in predicting the mumps incidence

目的建立流行性腮腺炎（腮腺炎）月发病率的乘积季节白回归积分滑动平均模型（ARIMA模型），并对湖南省2015年5月至2016年4月腮腺炎月发病率进行预测。方法数据来源于中国疾病预防控制信息系统中的“疾病监测信息报告管理系统”。按发病日期收集2004年1月至2015年4月湖南省腮腺炎的月发病率资料，包括临床诊断病例和实验室确诊病例。采用SPSS18．0软件中的ARIMA模型作为预测分析方法，利用2004年1月至2014年4月湖南省腮腺炎的月发病率资料进行建模，用2014年5月至2015年4月的月发病率数据作为模型预测效果的检验样本，采用Box-LjungQ检验法对选定模型残差是否为白噪声进行检验。最后采用建立的模型对2015年5月至2016年4月湖南省的腮腺炎月发病率进行预测。结果湖南省2004年1月至2014年4月期间，每年5—7月为腮腺炎的发病高峰期，11月至次年1月为次高峰。通过序列的平稳化，模型的识别、建立、诊断，建立模型ARIMA（2，1，1）x（0，1，1）。对该模型的残差进行Box—LiungQ检验发现，Q=8．40，P=0．868，认为残差序列为白噪声序列，说明所建立的模型对数据信息的提取较为完全，模型建立比较合理。该模型拟合度R2=0．871，BIC值为-1．646，预测值与实际值的平均绝对误差为0．025／10万，平均相对误差为13．004％，说明该模型对湖南省腮腺炎月发病率预测的相对误差较小，预测结果基本可靠。用选定的ARIMA（2，1，1）x（0，1，1）12模型对湖南省2015年5月至2016年4月腮腺炎的月发病率进行预测发现，发病率出现的高峰月份为5—7月，次高峰出现在11月至次年1月，高峰期的发病率与以往同期的发病率水平接近。结论ARIMA（2，1，1）×（0，1，1）12较好地拟合了湖南省腮腺炎的月发病率的变化趋势，对该病的预防控制具有一定的实用价值。

Objective To establish multiple seasonal autoregressive integrated moving average model（ARIMA） according to mumps disease incidence in Hunan province, and to predict the mumps incidence from May 2015 to April 2016 in Hunan province by the model. Methods The data were downloaded from ＂Disease Surveillance Information Reporting Management System＂ in China Information System for Disease Control and Prevention. The monthly incidence of mumps in Hunan province was collected from January 2004 to April 2015 according to the onset date, including clinical diagnosis and laboratory confirmed cases. The predictive analysis method was the ARIMA model in SPSS 18.0 software, the ARIMA model was established on the monthly incidence of mumps from January 2004 to April 2014, and the date from May 2014 to April 2015 was used as the testing sample, Box-Ljung Q test was used to test the residual of the selected model. Finally, the monthly incidence of mumps from May 2015 to April 2016 was predicted by the model. Results The peak months of the mumps incidence were May to July every year, and the secondary peak months were November to January of the following year, during January 2004 to April 2014 in Hunan province. After the data sequence was handled by smooth sequence, model identification, establishment and diagnosis, the ARIMA（2,1,1）x（0,1,1）12 was established, Box-Ljung Q test found, Q=8.40, P=0.868, the residual sequence was white noise, the established model to the data information extraction was complete, the model was reasonable. The R2 value of the model fitting degree was 0.871, and the value of BIC was - 1.646, while the average absolute error of the predicted value and the actual value was 0.025/100 000, the average relative error was 13.004%. The relative error of the model for the prediction of the mumps incidence in Hunan province was small, and the predicting results were reliable. Using the ARIMA（2,1,1）X（0,1,1）12 model to predict the mumps incidence from April 2016 to May 2015 in Hunan province, the peak months of the mumps incidence were May to July, and the secondary peak months were November to January of the following year, the incidence of the peak month was close to the same period. Conclusion The ARIMA（2,1,1）x（0,1,1）12 model is well fitted the trend of the mumps disease incidence in Hunan province, it has some practical value for the prevention and control of the disease.