SARIMA模型在肾综合征出血热发病率预测中的应用  

Prediction of Incidence of Hemorrhagic Fever with Renal Syndrome based on SARIMA Model

作　　者：黄德生[1] 郭海强[2] 沈铁峰[3] 关鹏[4] 吴伟[4] 周宝森[4] 

机构地区：[1]中国医科大学基础医学院数学教研室,辽宁沈阳110001 [2]中国医科大学中国卫生统计编辑部,辽宁沈阳110001 [3]辽宁省葫芦岛市疾病预防控制中心传染病防制科,辽宁葫芦岛125000 [4]中国医科大学公共卫生学院流行病学教研室,辽宁沈阳110001

出　　处：《数学的实践与认识》2009年第23期100-106,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(70503028;30771860);教育部留学回国人员科研启动基金(教外司留[2008]890号)

摘　　要：目的:探讨应用时间序列SAR IM A模型进行肾综合征出血热发病率预测的可行性.方法:首先利用余弦函数模型分析肾综合征出血热季节性发病规律,其次进行扩充迪基富勒的平稳性单位根检验,然后根据自相关函数和偏自相关函数判别月别疫情间的相关性,最后基于1990年-2004年逐月发病率进行SAR IM A模型建模拟合,利用2005年各月发病率进行外推预测,并与实际值进行比较.上述统计分析采用Ev iew s3.1和SPSS12.0软件完成.结果:余弦函数确定的高峰时点为3月中旬,高峰时区为3月1日到4月3日.含第一谐量的余弦方程为:^Y1 i=1.274-0.945cos(ti-76.684),决定系数R2=0.853;在备选模型中,SAR IM A(1,0,0)×(2,0,0)12模型不仅很好地拟合了既往时间段上的发病率序列,而且对2005年各月发病率的预测值符合实际发病率变动趋势.结论:余弦函数对于褐家鼠型肾综合征出血热疫情季节分布拟合较好,SAR IM A模型能很好地模拟传染病发病率在时间序列上的变动趋势,并对未来的发病率进行预测,为传染病防制工作服务.Objective：To explore the feasibility of Seasonal Autoregressive Integrated Moving Average（SARIMA） model to predict the incidence of hemorrhagic fever with renal syndrome（HFRS） in Huludao City.Methods： Firstly,cosine function models were use to analyze the seasonal rule of HFRS.Secondly,Augmented Dickey Fuller（ADF） unit root test was applied for series trend analysis.Thirdly,Autocorrelation function（ACF） and partial autocorrelation function（PACF） were used to detect autocorrelations of the HFRS incidence.Finally,EViews3.1 and SPSS 12.0 software were performed to construct the ARIMA model based on the month incidence of contagious disease in Huludao City from January 1990 to December 2004. Then the constructed model was used to predict the month incidence in 2005 with a comparison to actual value. Results： The cosine function showed that the high incidence rate was in the middle of March （March 1 to April 3）. Single cosine function equation was ^Y1i= 1. 274 - 0. 945cos（ti - 76. 684） with determinant coefficient R^2 equal to 0. 853. SARIMA（1,0, 0） ×（2,0,0）12 exactly fitted the incidence of the previous month. Incidence in 2005 by the model was consistent with the actual incidence. Conclusion： The method of time series analysis included cosine function and SARIMA can be used to fit exactly the changes of the incidence of HFRS and to predict the incidence in future.

关 键 词：季节自回归单整移动平均 预测 肾综合征出血热 发病率 

分 类 号：R512.8[医药卫生—内科学] R181.3[医药卫生—临床医学]