基于ARIMA乘积季节模型的新疆喀什百日咳流行趋势分析

Base on the multiple seasonal ARIMA model to analysis the epidemic of pertussis in Xinjiang Kashi

目的采用时间序列分析方法建立ARIMA乘积季节模型,拟合具有趋势性和季节性的2008-2015年新疆喀什地区百日咳的每月新发数量并作短期预测,为百日咳的预防与控制提供决策依据。方法以百日咳的每月新发病数为原始序列,用差分和季节差分方法对序列做平稳化操作,用具有季节性的自回归移动平均(ARIMA(p,d,q)(P,D,Q)s)模型拟合序列,根据ACF和PACF图对模型定阶并估计参数,再对模型及其参数进行显著性检验,应用残差和AIC和SBC进行评价,建立最优ARIMA乘积季节模型。结果用ARIMA(2,1,2)(0,1,1)_(12)模型模拟2008年1月-2015年6月百日咳每月新发数量,模拟的MAPE=52.05,值稍偏大,但在可接受的范围内。再用该模型预测出2015年7-12月的百日咳每月新发数量,MAPE=18.05,模型预测效果较好。最后用该模型预测2016年的百日咳每月新发病数,发现2016年新疆喀什百日咳新发病数仍处于较高水平,最大值出现在8月,新发病数为87(28,146)。结论 ARIMA(2,1,2)(0,1,1)_(12)模型可用于拟合并且短期预测新疆喀什地区百日咳新发数量,为相关政府部门提供可靠信息。

Objective The time series analysis method was used to establish the ARIMA product season model to fit with the trend and seasonality of the new monthly number of pertussis from 2008 to 2015 in Xinjiang Kashi and make short-term prediction to provide decision basis for prevention and control of per- tussis. Methods Monthly new onset of whooping cough was as the original sequence, with the difference and the seasonal difference method to do smooth operation sequence. The seasonal autoregressive moving average （ARIMA （p, d, q） （p, d, q） s） was as model fitting sequence, according to the ACF and PACF figure order and estimate the parameters of the model, then do the significance test of model and its pa- rameters, application of residual and AIC and SBC evaluation, establish the optimal model of ARIMA. Results ARIMA （2, 1, 2）（0, 1, 1）12 model was used to fit out the new monthly incidence of pertussis in xinjiang kashi region from January 2008 to June 2015 and calculated the simulated MAPE was 52.05, which is slightly larger, but within acceptable range. At the same time, using the model to predict the new monthly incidence of pertussis from June 2015 to December 2015, the average absolute percentage error MAPE was 18.05, which indicated that predicting effect of the model is better. Finally, the model was used to predict the number of new cases of pertussis per month in 2016. It was found that the number of new cases of pertussis in Kashi in Xinjiang in 2016 was still at a high level, with the maximum occurring in August and the new incidence was 87 （28,146）. Conclusion ARIMA （2, 1, 2）（0, 1, 1）12 model can be used to simulate and forecast the new monthly number of pertussis in xinjiang kashi. It will provide the reliable information of prevention and control for the relevant government departments.