ARIMA模型与GM(1,1)对其他感染性腹泻病流行趋势预测效果比较

Comparison of the effectiveness of ARIMA model and GM(1,1)in predicting the epidemic trend of other infectious diarrheal diseases

目的分析2011—2022年河北省其他感染性腹泻病的流行趋势,建立差分自回归移动平均(autoregressive integrated moving average,ARIMA)模型和灰色预测模型[gray forecast model,GM(1,1)],比较两种模型预测效果,探讨预测模型在传染病预测中的应用价值,为科学防控提供参考。方法收集2011年1月—2022年12月其他感染性腹泻病发病率数据,建立时间序列,对其进行平稳性和白噪声检测,确定最优的ARIMA模型与GM(1,1)拟合方程,对2023年1—6月其他感染性腹泻病发病率的预测值与实际值进行拟合评价,对预测效果进行比较。结果ARIMA(0,1,1)(1,0,0)_(12)为最优模型,Ljung-Box统计量为24.263(P=0.084),平稳的决定系数(coefficient of determination,R^(2))=0.620,贝叶斯信息准则(bayesian information criterion,BIC)=0.625,平均绝对误差(mean absolute error,MAE)=0.977,残差不存在自相关性。在建模的良好范围,预测数据与实际数据相对误差平均值为23.70%,实际值在预测值95%CI内;GM(1,1)的平均相对误差值为27.71%,最小误差值为6.68%,两种模型预测结果在建模的良好范围,均可用于对其他感染性腹泻病的预测。结论在选择最优参数的条件下,ARIMA模型和GM(1,1)对其他感染性腹泻病发病率的预测拟合度较好,能有效预测发病趋势,可外推至其他传染病的预测研究。

Objective To analyze the epidemic trend of other infectious diarrheal diseases in Hebei Province from 2011 to 2022,establish the differential autoregressive integrated moving average(ARIMA)model and the[gray forecast model,GM(1,1)],compare the predictive effects of the two models,explore the application value of predictive models in the prediction of infectious diseases,and provide a reference for scientific prevention and control.Methods The incidence data of other infectious diarrheal diseases from January 2011 to December 2022 were collected,time series were established,and the smoothness and white noise of the data were tested to determine the optimal fitting equations of ARIMA model and GM(1,1).The predicted and actual values of the incidence rate of other infectious diarrheal diseases from January to June 2023 were fitted and evaluated,and the prediction effects were compared.Results ARIMA(0,1,1)(1,0,0)_(12)was the optimal model with the Ljung-Box statistic was 24.263(P=0.084),the stable coefficient of determination(R^(2))=0.620,the Bayesian information criterion(BIC)=0.625,the mean absolute error(MAE)=0.977.No autocorrelation existed in the residual difference.In the good range of the modeling,the mean relative error between predicted and actual data was 23.70%,and the actual value was within the 95%CI of the predicted value.The average relative error value of the GM(1,1)was 27.71%,and the minimum value of error was 6.68%.Both models predicted the results in the good range of modeling and both can be used for the prediction of other infectious diarrheal diseases.Conclusion Under the condition of selecting the optimal parameters,the ARIMA model and the GM(1,1)have a good fit for predicting the incidence rate of other infectious diarrheal diseases,can effectively predict the incidence trend,and can be extrapolated to the prediction study of other infectious diseases.