自回归移动平均模型在全国手足口病疫情预测中的应用

目的探讨应用时间序列基于季节性差分的自回归移动平均模型(autoregressive integrated moving average,ARIMA)预测全国手足口病的发病情况。方法利用"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"(又称"传染病疫情信息网络直报系统")的资料,应用SPSS 19.0统计软件、采用ARIMA,对全国2009年1月至2012年12月手足口病逐月发病情况进行建模和拟合,利用所得到的模型对2013年1-6月的发病情况进行预测,并评价其预测效果。结果分析结果显示,手足口病发病以年为周期,1年中5-6月为高发月。非季节移动平均参数滞后两次后为0.532,t检验的P值为0.003,差异有统计学意义。BIC=21.955,Ljung-Box统计量检验残差序列为白噪声序列。最佳ARIMA(0,1,2),(0,1,0)12预测的平均相对误差为0.52,预测效果一般。按照不同发病模式分为两层后分别建立ARIMA,平均相对误差为0.12,预测效果好。结论对监测数据进行时间序列分析是用于传染病预测的一个重要的工具。分析发现中国不能用一个ARIMA拟合手足口病资料,因地区间发病的变异和模式不同;按手足口病的发病模式将各省分为单峰和双峰两层,分别拟合ARIMA,模型拟合效果更好。

Application of multiple seasonal autoregressive integrated moving average model in prediction of incidence of hand foot and mouth disease in China

Objective To predict the incidence of hand foot and mouth disease(HFMD)in China by using multiple seasonal autoregressive integrated moving average(ARIMA)model, and provide scientific evidence for the improvement of HFMD prevention and control. Methods The ARIMA model was established based on the monthly case numbers of HFMD in China from January 2009 to June 2013,which was collected from national disease reporting information system, by using SPSS 19.0 software. The model was used to predict the incidence of HFMD during January-June 2013. Results The annual incidence peak of HFMD occurred during May-June. There were significant difference between the fitted multiple seasonal moving average coefficients and the non-seasonal moving average coefficients(0.532). Through the test of parameters and goodness of fit as well as white-noise residuals, we established the ARIMA(0,1,2)(0,1,0)12, of which Bayesian Information Criterion(BIC)=21.955 and the mean error of the model was 0.52. The model was not fitted well. After the provinces were categorized into two strata by the incidence pattern of HFMD, the ARIMA was employed to fit two models respectively, the prediction was improved and the mean error of the model was 0.12. Conclusion Time series analysis for historical reporting data is an important tool for communicable disease surveillance. ARIMA model is suitable to predict the incidence of HFMD in China, but due to the different incidence patterns of HFMD in different provinces the prediction can be improved by fitting different ARIMA model.