基于ARIMAX模型的乌鲁木齐市流感样病例预测分析

目的 探讨ARIMAX模型（autoregressive integrated moving average model-X，ARIMAX）在流感发病趋势预测方面的效果，为提高此模型在传染病发病预测方面的使用提供依据。方法 收集乌鲁木齐市（乌市）2013年1月~2016年12月的流感样病例（ILI）病例数和大气颗粒物PM_2.5及PM₁₀浓度数据，用R软件建立ARIMA及ARIMAX模型，并对2017年前10周ILI病例数做预测。结果 乌市2013年1月~2016年12月ILI病例总数161 773例，周平均发病数为777例；时序图显示呈冬春季高发的特点。流感周发病数建立ARIMA（1，0，0）模型，赤池信息准则（akaike information criterion，AIC）=2 549.03；以大气颗粒物PM_2.5及PM₁₀为影响变量，带入转换函数建立ARIMAX模型，AIC=2 535.51，且模型各参数有统计学意义。使用迭代法对前10期（10周）数据进行预测，预测结果显示仅预测3期（3周）误差最小；两模型预测误差百分比绝对值均值（mean absolute percentage error，MAPE）分别为12.019 74%，12.014 17%，显示两模型均有较好的预测精度。结论 ARIMA模型和ARIMAX模型均能较好预测短时间内ILI病例数的发病趋势，为流感监测和预防控制提供依据。

Forecasting influenza like illness in Urumqi based on ARIMAX model

Objective To explore the effect of auto-regressive integrated moving average model-X(ARIMAX) model on predicting influenza trend in Urumqi, and to provide basis for further application of modeling in forecasting infectious diseases. Methods Data on the number of influenza-like illness(ILI) cases and atmospheric particulate matter(PM_2.5 and PM₁₀) concentrations were collected from January 2013 to December 2016 in Urumqi. We used R to construct auto-regressive integrated moving average (ARIMA) model and predicted the number of ILI cases in the first 10 weeks in 2017 using ARIMAX model. Results From January 2013 to December 2016, the total number of ILI cases was 161 773 and the number of average weekly ILI cases was 777. The time series of ILI cases indicated that there was a high prevalence during winter and spring. ARIMA (1, 0, 0) model was established based on weekly ILI cases and akaike information criterion (AIC)=2 549.03. PM_2.5 and PM₁₀ were considered as parameters to build ARIMAX model (AIC=2 535.51) and they were shown to be statistically significant. Using iterative method to predict the data of the first ten periods (i.e. 10 weeks), the results indicated only 3 period (i.e. 3 weeks) prediction had the minimal error.The mean absolute percentage error (MAPE) of the two models was 12.019 74% and 12.014 17% respectively, suggesting both of them had a good predictive accuracy. Conclusions ARIMA model and ARIMAX model can predict trend of ILI cases incidence in short time and provide evidence for influenza monitoring and prevention.