应用时间序列分析研究秋冬型恙虫病时间分布特征及趋势

Study on the characteristics of temporal distribution and the epidemic trend of autumn-winter type scrub typhus under time series analysis

目的应用时间序列分析探讨秋冬型恙虫病的时间分布特征及趋势。方法基于山东省疾病报告信息系统2006--2011年恙虫病监测数据，对以年为单位的监测数据采用频谱分析、移动平均分析，预测2012--2014年该病发病数；以月为单位的数据进行乘法季节效应分析，进行差分自回归移动平均模型（ARIMA）建模拟合，预测2011年11、12月秋冬型恙虫病发病情况，并与实际发病数进行比较。结果频谱分析结果显示秋冬型恙虫病流行周期为3年；移动平均分析表明其流行强度将持续增强，2012--2014年各年预测发病数分别为310、337、366例，年增长率约9％。乘法季节效应分析显示该病符合秋冬型流行特点，10、11月季节效应指数分别为8．454、2．230，其他月份指数均〈1．000；ARIMA（0，1，1）（0，1，0）12模型为（1-B）（1--B12）X4=（1—0．81IB）u，残差序列为白噪声，Box-Ljung统计量为3．116，P=0．999，模型拟合效果良好。应用该模型预测2011年11、12月发病数，预测值与实际发病数相符，实际观测值均在预测值的95％CI内。结论秋冬型恙虫病流行可能具有周期性，总体流行强度将持续增强，2012--2014年该病年增长率约为9％；每年以10月流行最严重，应用ARIMA（0，1，I）（0，1，0）12模型可较好地预测发病情况。

Objective to explore the characteristics of temporal distribution and epidemic trend of autumn-winter type scrub typhus using the time series analysis. Methods Based on the data of scrub typhus collected from Shandong Diseases Reporting Information System from 2006 to 2011, both spectral analysis and moving average analysis were used to analyze the annual data of scrub typhus while scrub typhus incidence in 2012-2014 was forecasted. Seasonal decomposition analysis was applied to analyze the monthly data from January of 2006 to October of 2011, followed by Autoregressive Integrated Moving Average Model （ARIMA） which was constructed to forecast case number in November and December of 2011 and compared to the actual incidence. Results The results of spectral analysis showed that the prevalence of autumn-winter type scrub typhus had a feature of ＇ 3-year-periodicity＇. A long-term up-trend was confirmed by method of moving average analysis, with annually case numbers of 310,337 and another number of 366 forecasted for 2012 to 2014, respectively, with the annual increase rate as 9% per-year. Data from analysis of monthly data of scrub typhus showed that through multiple seasonal decomposition analysis, the results indicated that the prevalence of this disease possessed a typical autumn-winter type. The seasonality indexes for scrub typhus in October and November were 8.454 and 2.230, respectively, while others were less than 1.000. The ARIMA （0, 1,1 ） （0, 1,0） 12 model of （ 1 - B） （ 1 - B12） X1 = （ 1 - 0.811 B） u, that was used to forecast the prevalence of autumn-winter type scrub typhus and was constructed with the residual error of 16 lags as white noise. The Box-Ljung test statistic for the model was 3.116, giving a P value of 0.999. The model fitted the data well. Good accordance was achieved between the observed values and the forecasted values of scrub typhus in November and December of 2011 which was produced by the ARIMA model, and all observed values were within the forecasted 95% CI. Conclusion The prevalence of autumn-winter type scrub typhus showed a 3-year-periodicity, with a long-term up-trend, and the case numbers of 2012 to 2014 were forecasted, rising on the end with an increasing rate of 9% per year, which occurred seasonally with October as the peak time in every year. The ARIMA （0, 1, 1 ） （0, 1, 0） 12 model seemed to be quite appropriate in predicting the autumn-winter type scrub typhus.