基于ARMA和GM(1,1)模型预测四川省新发现棘球蚴病患者检出率变化趋势

doi:10.12140/j.issn.1000-7423.2021.02.010

摘要/Abstract

摘要：

目的探索适用于预测四川省新发现棘球蚴病患者检出率的模型,为制定“十四五”棘球蚴病防治规划和策略提供科学依据。方法收集四川省2007—2020年每年新发现棘球蚴病患者检出率数据,分别建立ARMA时间序列模型和灰色系统GM(1,1)模型,对2021—2023年新发现棘球蚴病患者的检出情况进行预测,同时采用判定系数、平均绝对误差和均方误差等指标比较2种模型的拟合和预测效果。结果 ARMA模型分析结果显示,2017—2020年检出率拟合值和实际值的误差分别为12.44、26.04和33.30,预测2021、2022和2023年四川省新发现棘球蚴病患者检出率分别为50.14/10万、50.04/10万和49.99/10万;GM(1,1)模型分析结果显示,2017—2020年检出率拟合值和实际值的误差分别为6.51、2.94和-1.20,预测2021、2022和2023年四川省新发现棘球蚴病患者检出率分别为 20.55/10万、17.65/10万和15.77/10万。对两种模型进行拟合效果评价结果显示,GM(1,1)模型的预测效果优于ARMA模型。结论可采用GM(1,1)模型预测四川省未来新发现棘球蚴病患者检出率变化趋势,预测的检出率呈现出下降趋势,但仍有新病例检出,需继续加强棘球蚴病的综合防治,巩固防治成果。

关键词: 四川省, 棘球蚴病, ARMA模型, GM(1,1)模型, 预测

Abstract:

Objective To explore a model suitable for predicting the detection rate of newly discovered echinococcosis patients in Sichuan Province, and to provide scientific basis for formulating prevention and control strategies for echinococcosis. Methods The detection rate data of newly discovered echinococcosis patients in Sichuan Province from 2007 to 2020 were collected, and ARMA and GM (1,1) models were established respectively to predict the detection rate from 2021 to 2023. Meanwhile, the fitting and prediction effects of the two models were compared using the coefficient of determination, mean absolute error and mean-square error. Results The ARMA model was established, and the errors between fitting and actual values of detection rate in 2017—2020 were 12.44, 26.04 and 33.30, respectively. The predicted detection rates in 2021, 2022 and 2023 using this model were 50.14/100 000, 50.04/100 000 and 49.99/100 000, respectively. Uing the GM(1,1) model, the errors between fitting and actual values of detection rate in 2017—2020 were 6.51, 2.94 and -1.20, respectively, and the predicted detection rates in 2021, 2022 and 2023 were 20.55/100 000, 17.65/100 000 and 15.77/100 000, respectively. Evaluation of fitting effects showed that the GM(1,1) had better prediction performance than the ARMA model. Conclusion The GM (1,1) model can predict the detection rate of newly discovered echinococcosis patients in Sichuan Province. Although the predicted detection rate show a trend of decrease, new cases are continuously being detected. Therefore, measures should be taken to strength prevention and control of echinococcosis and consolidate the achievements of disease control.

Key words: Sichuan Province, Echinococcosis, ARMA model, GM (1,1) model, Prediction

中图分类号:

R532.32

何伟, 王奇, 喻文杰, 黄燕, 张光葭, 廖沙, 杨柳, 姚人新, 李汭芮, 刘阳, 钟波, 王谦. 基于ARMA和GM(1,1)模型预测四川省新发现棘球蚴病患者检出率变化趋势[J]. 中国寄生虫学与寄生虫病杂志, 2021, 39(2): 185-190.

HE Wei, WANG Qi, YU Wen-jie, HUANG Yan, ZHANG Guang-jia, LIAO Sha, YANG Liu, YAO Ren-xin, LI Rui-rui, LIU Yang, ZHONG Bo, WANG Qian. Trend prediction on the detection rate of newly discovered echinococcosis patients in Sichuan Province based on ARMA and GM (1,1) models[J]. Chinese Journal of Parasitology and Parasitic Diseases, 2021, 39(2): 185-190.

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参考文献 21

[1]	Jenkins DJ. WHO/OIE manual on echinococcosis in humans and animals: a public health problem of global concern[J]. Int J Parasitol, 2001,31(14):1717-1718. doi: 10.1016/S0020-7519(01)00318-6
[2]	Lei ZL, Wang LY. Control situation and primary task of key parasitic diseases in China[J]. Chin J Parasitol Parasit Dis, 2012,30(1):1-5. (in Chinese)
	( 雷正龙, 王立英. 全国重点寄生虫病防治形势与主要任务[J]. 中国寄生虫学与寄生虫病杂志, 2012,30(1):1-5.)
[3]	Budke CM, Deplazes P, Torgerson PR, et al. Global socioeconomic impact of cystic echinococcosis[J]. Emerg Infect Dis, 2006,12(2):296-303. doi: 10.3201/eid1202.050499
[4]	Torgerson PR, MacPherson CN. The socioeconomic burden of parasitic zoonoses: global trends[J]. Vet Parasitol, 2011,182(1):79-95. doi: 10.1016/j.vetpar.2011.07.017
[5]	Brunetti E, Kern P, Vuitton DA, et al. Expert consensus for the diagnosis and treatment of cystic and alveolar echinococcosis in humans[J]. Acta Trop, 2010,114(1):1-16. doi: 10.1016/j.actatropica.2009.11.001
[6]	Xiao ZH, Guo MY. Time series analysis and SAS application[M]. 2nd ed. Wuhan: Wuhan University Press, 2012. (in Chinese)
	( 肖枝洪, 郭明月. 时间序列分析与SAS应用 [M]. 2版. 武汉: 武汉大学出版社, 2012.)
[7]	Jiang QW, Chen QM. Epidemiological methods and model[M]. Shanghai: Fudan University Press, 2007. (in Chinese)
	( 姜庆五, 陈启明. 流行病学方法与模型[M]. 上海: 复旦大学出版社, 2007.)
[8]	Zhao JH, Chen JQ, Guo LZ. Application of Excel in prediction and model checking of dynamic GM(1,1)[J]. J Qingdao Technol Univ, 2007,28(4):69-73. (in Chinese)
	( 赵金环, 陈建强, 郭立智. Excel在动态GM(1,1)模型预测及检验中的应用[J]. 青岛理工大学学报, 2007,28(4):69-73.)
[9]	Liu SF, Deng JL. The range suitable for GM(1,1)[J]. Syst Eng-Theory Pract, 2000,20(5):121-124. (in Chinese)
	( 刘思峰, 邓聚龙. GM(1,1)模型的适用范围[J]. 系统工程理论与实践, 2000,20(5):121-124.)
[10]	Bao YD, Wu YP, He Y. A new forecasting model based on the combination of GM(1,1) model and linear regression[J]. Syst Eng-Theory Pract, 2004,24(3):95-98. (in Chinese)
	( 鲍一丹, 吴燕萍, 何勇. 基于GM(1,1)模型和线性回归的组合预测新方法[J]. 系统工程理论与实践, 2004,24(3):95-98.)
[11]	Yin SJ, Yan XY, Su HX, et al. Forecast the change trend of newly discovered cases of sexually transmitted HIV/AIDS based on ARIMA model[J]. Chin J AIDS & STD, 2020,26(7):709-713. (in Chinese)
	( 尹诗琪, 闫翔宇, 苏鹤轩, 等. 基于ARIMA模型预测性传播HIV/AIDS新发现病例数变化趋势[J]. 中国艾滋病性病, 2020,26(7):709-713.)
[12]	Guo ZQ. Study on methods for infectious diseases prediction[J]. Occup Health, 2012,28(5):610-612. (in Chinese)
	( 郭泽强. 传染病预测方法的研究[J]. 职业与健康, 2012,28(5):610-612.)
[13]	Tang LH, Xu LQ, Chen YD, et al. China’s prevention and control of parasitic diseases and research[M]. Beijing: Beijing Science and Technology Press, 2012: 483-484. (in Chinese)
	( 汤林华, 许隆琪, 陈颖丹, 等. 中国寄生虫病防治与研究[M]. 北京: 北京科学技术出版社, 2012: 483-484.)
[14]	Yang YR, Clements AC, Gray DJ, et al. Impact of anthropogenic and natural environmental changes on Echinococcus transmission in Ningxia Hui Autonomous Region, the People’s Republic of China[J]. Parasit Vectors, 2012,5:146. doi: 10.1186/1756-3305-5-146
[15]	Wu JB, Ye LX, You EK. Prediction of incidence of notifiable contagious diseases by appalication of time series model[J]. J Math Med, 2007,20(1):90-92. (in Chinese)
	( 吴家兵, 叶临湘, 尤尔科. ARIMA模型在传染病发病率预测中的应用[J]. 数理医药学杂志, 2007,20(1):90-92.)
[16]	Zhang LP. Infectious disease prediction and control models study based on grey system theory[D]. Urumqi: Xinjiang Med University, 2015. (in Chinese)
	( 张利萍. 基于灰色系统理论的传染病预测及控制模型研究[D]. 乌鲁木齐: 新疆医科大学, 2015.)
[17]	Wu HC, Xu XQ, Wang Z, et al. Application of ARMA model for estimating the incidence of bacillary dysentery[J]. Zhejiang J Prev Med, 2012,24(1):14-16. (in Chinese)
	( 吴昊澄, 徐旭卿, 王臻, 等. 浙江省细菌性痢疾月发病率ARMA模型建立及预测分析[J]. 浙江预防医学, 2012,24(1):14-16.)
[18]	Zheng YL, Zhang LP, Zhang XL, et al. Research on the incidence of echinococcosis forecasting in Xinjiang based on combined model[J]. Math Pract Theory, 2014,44(6):156-162. (in Chinese)
	( 郑彦玲, 张利萍, 张学良, 等. 基于组合模型的新疆包虫病发病数预测研究[J]. 数学的实践与认识, 2014,44(6):156-162.)
[19]	Wu W, Guan P, Guo JQ, et al. Comparison of GM(1,1) gray model and ARMA model in forecasting the incidence of hemorrhagic fever with renal syndrome[J]. J Chin Med Univ, 2008,37(1):52-55. (in Chinese)
	( 吴伟, 关鹏, 郭军巧, 等. GM(1,1)灰色模型和ARMA模型在HFRS发病率预测中的比较研究[J]. 中国医科大学学报, 2008,37(1):52-55.)
[20]	Cheng Y, Liu RC, Xie HW. Effect comparison of ARMA model and GM(1,1) model in forecasting the incidence rate of AIDS in Changsha[J]. Occup Heal, 2017,33(22):3091-3094. (in Chinese)
	( 程燕, 刘如春, 谢红卫. ARMA模型与灰色系统GM(1,1)模型在长沙市艾滋病发病率预测中的效果比较[J]. 职业与健康, 2017,33(22):3091-3094.)
[21]	Cui C. Application of ARMA and GM(1,1)in prediction of morbidity of dysentery[J]. Occup Heal, 2017,33(8):1078-1081. (in Chinese)
	( 崔策. ARMA模型与GM(1,1)模型在痢疾发病率预测中的应用[J]. 职业与健康, 2017,33(8):1078-1081.)

滞后阶数 Lag order	自相关系数ACF	偏自相关系数 PACF	Q统计量 Q-statistic	相伴概率Associated probability
1	0.546	0.546	5.134	0.023
2	0.221	-0.109	6.049	0.049
3	0.028	-0.067	6.065	0.108
4	-0.022	0.019	6.076	0.194
5	-0.036	-0.021	6.109	0.296
6	-0.099	-0.105	6.385	0.381
7	-0.112	-0.014	6.784	0.452
8	-0.149	-0.093	7.609	0.473
9	-0.158	-0.060	8.732	0.462
10	-0.196	-0.114	10.875	0.367
11	-0.208	-0.082	14.110	0.227
12	-0.190	-0.069	18.156	0.111

变量 Variable	参数估计值 Coefficient	标准误 Std. error	t值 t value	P值 P value
C	49.95 308	22.49 594	2.220 537	0.050 6
AR(1)	0.498 450	0.037 509	13.28 876	0.000 0
MA(1)	-0.997 435	0.202 845	-4.917 227	0.000 6

滞后阶数Lag order	自相关系数ACF	偏自相关系数PACF	Q统计量 Q-statistic	相伴概率Associated probability
1	0.216	0.216	0.758	-
2	-0.037	-0.088	0.782	-
3	-0.048	-0.022	0.828	0.363
4	-0.154	-0.149	1.342	0.511
5	-0.215	-0.164	2.467	0.481
6	-0.266	-0.227	4.432	0.351
7	-0.068	-0.012	4.581	0.469
8	-0.040	-0.109	4.642	0.590
9	0.072	0.032	4.897	0.673
10	0.060	-0.081	5.133	0.743
11	-0.016	-0.118	5.158	0.820
12	-0.005	-0.092	5.163	0.880

年份 Year	实际值/（10万）^-1 Actual value/ 100 000^-1	拟合值/（10万）^-1 Fitted value/ 100 000^-1	误差 Error	相对误差/% Relative error /%
ARMA(1,1)模型 ARMA(1,1) model
2007	2 679.18	-	-	-
2008	1 645.43	1 615.82	-29.61	-1.80
2009	874.01	830.46	-43.55	-4.98
2010	302.02	439.00	136.98	45.35
2011	175.16	243.87	68.71	39.23
2012	262.74	146.61	-116.13	-44.20
2013	98.81	98.13	-0.68	-0.69
2014	141.15	73.97	-67.18	-47.59
2015	70.59	61.92	-8.67	-12.28
2016	113.30	55.92	-57.38	-50.64
2017	41.86	52.93	11.07	26.45
2018	39.00	51.44	12.44	31.90
2019	24.65	50.69	26.04	105.64
2020	17.02	50.32	33.30	195.65
2021	-	50.14	-	-
2022	-	50.04	-	-
2023	-	49.99	-	-
GM(1,1)模型 GM(1,1) model
2007	2 679.18	-	-	-
2008	1 645.43	1 504.12	21.31	1.30
2009	874.01	888.32	-14.31	-1.64
2010	302.02	524.63	-22.61	-7.49
2011	175.16	309.84	-34.68	-19.80
2012	262.74	222.07	40.67	15.48
2013	98.81	126.10	-27.29	-27.62
2014	141.15	150.96	-9.81	-6.95
2015	70.59	101.58	-30.99	-43.90
2016	113.30	99.16	14.14	12.48
2017	41.86	36.57	5.29	12.64
2018	39.00	32.49	6.51	16.69
2019	24.65	21.71	2.94	11.93
2020	17.02	18.22	-1.20	-7.05
2021	-	20.55	-	-
2022	-	17.65	-	-
2023	-	15.77	-	-

模型 Model	拟合效果评价Evaluation of fitting effect
模型 Model	判定系数R² coefficient of determination R²	平均绝对误差MAE	均方误差 MSE
ARMA(1,1)模型 ARMA (1,1) model	0.97	47.06	3 822.28
GM(1,1)模型 GM(1,1) model	0.98	17.83	469.89