构建预测陕西省咸阳市日本脑炎疫情的季节性时间序列模型

doi:10.24920/J1001-9294.2017.036

Abstract

Objective

To construct a model of Seasonal Autoregressive Integrated Moving Average (SARIMA) for forecasting the epidemic of Japanese encephalitis (JE) in Xianyang, Shaanxi, China, and provide valuable reference information for JE control and prevention.

Methods

Theoretically epidemiologic study was employed in the research process. Monthly incidence data on JE for the period from Jan 2005 to Sep 2014 were obtained from a passive surveillance system at the Center for Diseases Prevention and Control in Xianyang, Shaanxi province. An optimal SARIMA model was developed for JE incidence from 2005 to 2013 with the Box and Jenkins approach. This SARIMA model could predict JE incidence for the year 2014 and 2015.

Results

SARIMA (1, 1, 1) (2, 1, 1)₁₂ was considered to be the best model with the lowest Bayesian information criterion, Akaike information criterion, Mean Absolute Error values, the highest R², and a lower Mean Absolute Percent Error. SARIMA (1, 1, 1) (2, 1, 1)₁₂was stationary and accurate for predicting JE incidence in Xianyang. The predicted incidence, around 0.3/100 000 from June to August in 2014 with low errors, was higher compared with the actual incidence. Therefore, SARIMA (1, 1, 1) (2, 1, 1)₁₂ appeared to be reliable and accurate and could be applied to incidence prediction.

Conclusions

The proposed prediction model could provide clues to early identification of the JE incidence that is increased abnormally (≥0.4/100 000). According to the predicted results in 2014, the JE incidence in Xianyang will decline slightly and reach its peak from June to August.

Key words: Japanese encephalitis, time series models, incidence, prediction

Zhang Rong-qiang, Li Feng-ying, Liu Jun-li, Liu Mei-ning, Luo Wen-rui, Ma Ting, Ma Bo, Zhang Zhi-gang. Time Series Models for Short Term Prediction of the Incidence of Japanese Encephalitis in Xianyang City, P R China^△[J].Chinese Medical Sciences Journal, 2017, 32(3): 152-160.

Figures/Tables 8

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Models	R²	Adjusted R²	BIC	AIC	MAE	MAPE	White noise
SARIMA(1, 1, 1)(0, 1, 0)₁₂	0.3593	0.3523	-1.5550	-1.6091	0.0448	42.4177	No
SARIMA(1, 1, 1)(0, 1, 1)₁₂	0.5253	0.5149	-1.8066	-1.8878	0.0349	20.2465	Yes
SARIMA(1, 1, 1)(0, 1, 2)₁₂	0.7281	0.7281	-2.4714	-2.4983	0.0298	25.5302	No
SARIMA(1, 1, 1)(1, 1, 0)₁₂	0.3921	0.3767	-1.7403	-1.8284	0.0388	48.3811	Yes
SARIMA(1, 1, 1)(1, 1, 1)₁₂	0.5767	0.5604	-2.0486	-2.1660	0.0355	43.4823	Yes
SARIMA(1, 1, 1)(1, 1, 2)₁₂	0.5229	0.5110	-3.1737	-2.0836	0.0336	34.8344	No
SARIMA(1, 1, 1)(2, 1, 0)12	0.6557	0.6507	-3.0530	-3.1167	0.0205	18.4136	Yes
SARIMA(1, 1, 1)(2, 1, 1)12	0.7675	0.7569	-3.3085	-3.4370	0.0181	21.1313	Yes
SARIMA(1, 1, 1)(2, 1, 2)₁₂	0.7142	0.7012	-3.1024	-3.2309	0.0186	17.0829	Yes
SARIMA(2, 1, 1)(0, 1, 0)₁₂	0.2399	0.2315	-1.3727	-1.4271	0.0670	45.8096	No
SARIMA(2, 1, 1)(0, 1, 1)₁₂	0.4602	0.4482	-1.6661	-1.7478	0.0490	31.168	No
SARIMA(2, 1, 1)(0, 1, 2)₁₂	0.8080	0.8038	-2.7001	2.7818	0.0327	24.6900	No
SARIMA(2, 1, 1)(1, 1, 0)₁₂	0.3187	0.3012	-1.6125	-1.7012	0.0543	48.0692	No
SARIMA(2, 1, 1)(1, 1, 1)₁₂	0.5012	0.4817	-1.8700	-1.9982	0.0505	34.5438	No
SARIMA(2, 1, 1)(1, 1, 2)₁₂	0.8623	0.8569	-3.1569	-3.2752	0.0258	22.5722	No
SARIMA(2, 1, 1)(2, 1, 0)₁₂	0.6558	0.6454	-2.9607	-3.0578	0.0211	48.9294	Yes
SARIMA(2, 1, 1)(2, 1, 1)₁₂	0.7342	0.7220	-3.1580	-3.2874	0.0248	21.8292	No
SARIMA(2, 1, 1)(2, 1, 2)₁₂	0.6763	0.6668	-3.3054	-3.1503	0.0278	16.7768	Yes

Variables		Coefficient	Std. error	t-Statistic	P value
Non-Seasonal Lags	AR(1)	0.3323	0.1271	2.6154	0.0110
Non-Seasonal Lags	MA(1)	-0.2217	0.0473	-4.6867	0.0000
Seasonal Lags	SAR(2)	-0.9975	0.0001	-906103.6	0.0000
Seasonal Lags	SMA(1)	-0.9290	0.0418	-22.2026	0.0000

Months	Observed incidence (1/10⁵)	Forecast incidence (1/10⁵)	Upper limit of 95%CI	Low limit of 95%CI
Jan-14	0.0000	-0.0062	0.1413	-0.1538
Feb-14	0.0000	-0.0072	0.1430	-0.1575
Mar-14	0.0000	-0.0073	0.1431	-0.1577
Apr-14	0.0000	-0.0072	0.1432	-0.1576
May-14	0.0000	-0.0071	0.1434	-0.1575
Jun-14	0.0000	-0.0069	0.1435	-0.1574
Jul-14	0.0000	0.0220	0.1725	-0.1284
Aug-14	0.0203	0.1505	0.3010	0.0001
Sep-14	0.0203	0.0451	0.1955	-0.1054
Oct-14	-	-0.0064	0.1440	-0.1568
Nov-14	-	-0.0063	0.1442	-0.1567
Dec-14	-	-0.0061	0.1443	-0.1566
Jan-15	-	-0.0101	0.1705	-0.1907
Feb-15	-	-0.0106	0.1711	-0.1924
Mar-15	-	-0.0106	0.1713	-0.1924
Apr-15	-	-0.0103	0.1715	-0.1922
May-15	-	-0.0101	0.1717	-0.192
Jun-15	-	-0.0099	0.1719	-0.1917
Jul-15	-	0.0010	0.1828	-0.1809
Aug-15	-	0.1358	0.3176	-0.046
Sep-15	-	0.0427	0.2245	-0.1391
Oct-15	-	-0.0090	0.1728	-0.1908
Nov-15	-	-0.0088	0.1731	-0.1906
Dec-15	-	-0.0085	0.1733	-0.1903

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