ARIMA模型和GM(1,1)模型预测全国3种肠道传染病发病率

 【摘要】目的 分别采用求和自回归滑动平均模型（ARIMA模型）和灰色模型GM(1,1)对全国法定报告的3种肠道传染病年发病率进行预测，并比较两者预测的准确性。方法 采用1995年1月至2005年12月的月发病率建立ARIMA模型。采用1995年至2005年的年发病率建立GM(1,1)模型。采用2006年的实际年发病率验证两种模型的预测效果，评价指标为相对误差。选取相对误差最小的模型预测2007年至2008年的年发病率。结果 对于甲型肝炎、痢疾、伤寒副伤寒的年发病率，预测准确率较高的模型分别是GM(1,1)、ARIMA、GM(1,1)模型，相对误差分别为0.05%、5.47%、38.89%。对2007年甲型肝炎、痢疾、伤寒副伤寒预测的年发病率分别为4.59/105、30.84/105、2.53/105；对2008年预测的年发病率分别为4.03/105、29.03/105、2.34/105。结论 对于某种肠道传染病发病率的预测，应同时拟合几种模型，并选择其中拟合效果最好的一种模型。

Forecasting incidence of intestinal infectious diseases in mainland China with ARIMA model and GM(1,1) model

Objective To forecast the incidence of three types of notifiable intestinal infectious diseases in mainland China with integrated autoregressive moving average model(ARIMA model) and grey model GM(1,1) respectively,and to assess the predictability of these models. Methods The ARIMA model was developed based on the monthly incidence of these diseases from January 1995 to December 2005.GM(1,1) model was developed based on the yearly incidence from 1995 to 2005.Both models were tested by the data in 2006.Relative error was used to validate the predictability of these models.The model with the least relative error was adopted to predict the yearly incidence in 2007 and 2008. Results The preferable model to forecast the yearly incidence of hepatitis A,diarrhea and typhoid fever was GM(1,1),ARIMA and GM(1,1) model respectively.Their corresponding relative error was 0.05%,5.47% and 38.89%.The estimated yearly incidence in 2007 for hepatitis A,diarrhea and typhoid fever was 4.59/105,30.84/105 and 2.53/105 respectively.In 2008,it was 4.03/105,29.03/105 and 2.34/105. Conclusions Several models should be estimated to forecast incidence of a certain intestinal infectious disease,and the best fitted model would be chosen for forecasting.