自回归求和移动平均乘积季节模型在我国布鲁菌病短期月发病人数预测中的应用

摘要

目的：研究我国布鲁菌病（布病）月发病人数的趋势性和季节性，探讨自回归求和移动平均（ARIMA）乘积季节模型预测我国布病短期月发病人数的效果。方法收集2004年1月—2015年5月我国布病月发病人数（共137组），进行时间序列分析。数据来自国家卫生和计划生育委员会公布的疫情监测数据。观察我国布病月发病人数的趋势性和季节性，以我国2004—2013年的布病月发病人数作为训练样本，拟合 ARIMA 乘积季节模型；用2014年1月—2015年5月的发病数据作为校验样本，验证模型；确定最优模型后，预测2015年6—12月我国布病月发病人数。结果2004—2008年我国布病月发病人数相对平稳，从2009年以后有了明显的上升趋势。从季节性来看，每年的6、7、8月属高发病期，每年的1月和12月处于全年的最低发病期。选取的最优模型为 ARIMA（0，1，0）（1，1，0）12，其平均绝对百分误差（MAPE）＝13.60，决定系数（R2）＝0.881；对模型进行参数显著性检验，一阶季节自回归项（SAR）参数估计值＝-0.292，P ＝0.048。运用 ARIMA（0，1，0）（1，1，0）12对2015年6—12月我国布病月发病人数进行预测，其预测值分别为7709、7524、6113、4458、3450、3576、3760例。结论从2009年以后，我国布病月发病人数有明显的上升趋势；季节性表现在6～8月为高发病期，12月至来年1月为低发病期。ARIMA乘积季节模型拟合我国布病月发病人数的时间序列模型精度较高，可以用来预测我国布病短期月发病人数。%Objective To investigate the trend and seasonality of monthly prevalence of brucellosisin China and to explore the effect of multiple seasonal ARIMA model in the prediction of monthly prevalence of brucella in China. Methods Collected the data about the prevalence(137)of brucella in China from January 2004 to May 2015,and time series analysis was made on the data. The data were obtained from epidemic monitoring by National Health and Family Planning Commission. The trend and seasonality of the disease in China were observed. The prevalence of the disease from 2004 to 2013 was taken as the training sample to fit multiple seasonal ARIMA model. The data of prevalence of the disease from January 2014 to May 2015 were taken as check - up sample to verify the model. After the optimal model was determined,the monthly prevalence of brucellosis from June to December in 2015 was predicted. Results From 2004 to 2008,the prevalence of brucellosisin was at a relatively stable stage,while an increasing trend was shown since 2009. From the perspective of seasonality,June,July and August are high prevalence months,while January and December are low prevalence months. The optimal model selected was ARIMA(0, 1,0)(1,1,0)12 ,with a mean absolute percentage of(MAPE) = 13. 60 and a determination coefficient of(R2 ) = 0. 881;the significance test of coefficient showed that SAR parameter estimate value was - 0. 292(P = 0. 048). After the prediction of the monthly prevalence of the disease from June to December in 2015 by using ARIMA(0,1,0)(1,1,0)12 ,we found the predicted prevalence was 7 709,7 524,6 113,4 458,3 450,3 576 and 3 760 respectively. Conclusion Since 2009,the prevalence of brucellosis has been at an increasing trend,with June to August as the high prevalence months and December and January as the low prevalence months. Multiple seasonal ARIMA model has a high precision in fitting the time series model of monthly prevalence of brucellosis in China and can be used to predict monthly prevalence of brucella in China.