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Article(id=1240730056188809637, tenantId=1146029695717560320, journalId=1227665162245664772, issueId=1240730050669113883, articleNumber=null, orderNo=null, doi=10.20043/j.cnki.MPM.202411104, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1730736000000, receivedDateStr=2024-11-05, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773742697044, onlineDateStr=2026-03-17, pubDate=1745510400000, pubDateStr=2025-04-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773742697044, onlineIssueDateStr=2026-03-17, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773742697044, creator=13701087609, updateTime=1773742697044, updator=13701087609, issue=Issue{id=1240730050669113883, tenantId=1146029695717560320, journalId=1227665162245664772, year='2025', volume='52', issue='8', pageStart='1345', pageEnd='1536', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773742695728, creator=13701087609, updateTime=1773742807836, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1240730520988995837, tenantId=1146029695717560320, journalId=1227665162245664772, issueId=1240730050669113883, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1240730520988995838, tenantId=1146029695717560320, journalId=1227665162245664772, issueId=1240730050669113883, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1490, endPage=1496, ext={EN=ArticleExt(id=1240730056574685626, articleId=1240730056188809637, tenantId=1146029695717560320, journalId=1227665162245664772, language=EN, title=Comparison of SARIMA and its combined models in predicting the incidence of hand foot and mouth disease, columnId=1228016573156360233, journalTitle=Modern Preventive Medicine, columnName=Disease Control and Prevention, runingTitle=null, highlight=null, articleAbstract=
Objective

To compare the prediction effect of SARIMA and its combined models on the incidence of hand foot and mouth disease (HFMD), and to explore the influence of COVID-19 on the SARIMA model.

Methods

The incidence trend of HFMD in Shenzhen was analyzed through the time series decomposition method. A SARIMA model was established based on the monthly incidence of HFMD from 2011 to 2023. The optimal model was selected by comparing the performance of MAE, MSE, RMSE, and MAPE, and was used to construct a combined model with the SVR model and the XGBoost model. The incidence from January to July 2024 was predicted using the optimal model.

Results

The incidence trend of HFMD in Shenzhen from 2011 to 2023 was seasonal, and the peak was from May to June and September to October each year. The SARIMA model that did not include incidence data during the COVID-19 pandemic outperformed the included model. Based on MAE, MSE and RMSE indicators, the combined model performed better than the single SARIMA model when the prediction time exceeded 4 months. The SARMI-SVR model wassuperior to the SARMI-XGBoost model in overall performance, especially in the performance of MAPE.

Conclusion

Including the incidence data during the COVID-19 epidemic will degrade the performance of the SARIMA model. The prediction effect of SARMI-SVR model is better than SARIMA model and SARMI-XGboost model, which can be used to predict the incidence of HFMD and provide a reference for disease surveillance and early warning.

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目的

比较SARIMA及其组合模型对手足口病发病率的预测效果,并探讨新冠疫情对手足口病SARIMA模型的影响。

方法

通过时间序列分解法分析深圳市手足口病发病趋势，以2011—2023年的手足口病月发病率建立SARIMA模型,利用最优模型分别与SVR、XGBoost构建组合模型，并预测2024年1—7月发病率，通过比较MAE、MSE、RMSE、MAPE性能得出最优模型。

结果

深圳市2011—2023年手足口病发病趋势具有明显季节性,发病高峰为每年5—6月及9—10月；未纳入新冠疫情期间的发病数据构建的SARIMA模型优于纳入的模型。基于MAE、MSE、RMSE指标，组合模型在预测时间超过4个月时比单个SARIMA模型表现更佳；在综合性能上SARIMA-SVR模型优于SARIMA-XGBoost模型，尤其在MAPE性能上。

结论

纳入新冠疫情期间的发病数据会降低SARIMA模型的性能；SARIMA-SVR组合模型预测效果优于单个SARIMA模型及SARIMA-XGBoost组合模型，可用于手足口病发病率预测，为疾病监测预警提供参考依据。

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陈志高，E-mail:
, copyrightStatement=本刊刊出的所有文章不代表中华预防医学会和本刊编委会的观点，除非特别声明。, copyrightOwner=中华预防医学会和四川大学华西公共卫生学院, extLink=null, articleAbsUrl=null, sourceXml=ORyOafxPdNVTHMcooh4npA==, magXml=XaiLgRS5ke0sELY4MDFpCg==, pdfUrl=null, pdf=ekHdm1EhrgQHVD9dWuXSVA==, pdfFileSize=1336363, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=VEsEpaMEFn+ZUBFdXkqeAg==, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=BIQWKFUjIkLivXbNIgPS3w==, mapNumber=null, authorCompany=null, fund=null, authors=

宋丽霞(1993—)，女，本科，主管医师，研究方向：传染病流行病学

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宋丽霞(1993—)，女，本科，主管医师，研究方向：传染病流行病学

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(In Chinese), articleTitle=Establishment of early warning threshold of hand, foot and mouth disease based on moving epidemic method and synthetic index method in Guangzhou, refAbstract=null), Reference(id=1241070744659095604, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, doi=null, pmid=null, pmcid=null, year=2019, volume=35, issue=5, pageStart=643, pageEnd=645, url=null, language=null, rfNumber=[23], rfOrder=31, authorNames=张泽娜, 逯建华, 许舒乐, journalName=中国公共卫生管理, refType=null, unstructuredReference=张泽娜，逯建华，许舒乐，等.深圳市手足口病风险指数运行结果分析[J].中国公共卫生管理，2019, 35(5): 643-645., articleTitle=深圳市手足口病风险指数运行结果分析, refAbstract=null), Reference(id=1241070744759758904, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, doi=null, pmid=null, pmcid=null, year=2019, volume=35, issue=5, pageStart=643, pageEnd=645, url=null, language=null, rfNumber=[23], rfOrder=32, authorNames=Zhang ZN, Lu JH, Xu SL, journalName=Chinese Journal of Public Health Management, refType=null, unstructuredReference=Zhang ZN, Lu JH, Xu SL, et al. Analysis on the results of hand-foot-mouth disease index releasing in Shenzhen[J]. Chinese Journal of Public Health Management, 2019, 35(5): 643-645. (In Chinese), articleTitle=Analysis on the results of hand-foot-mouth disease index releasing in Shenzhen, refAbstract=null)], funds=[Fund(id=1241070741622420384, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, awardId=JCYJ20240813160803005, language=CN, fundingSource=深圳市科技计划项目(JCYJ20240813160803005), fundOrder=null, country=null), Fund(id=1241070741706306468, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, awardId=SZSM202011008, language=CN, fundingSource=深圳市医疗卫生三名工程项目(SZSM202011008), fundOrder=null, country=null), Fund(id=1241070741815358378, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, awardId=RKX20200327095612234, language=CN, fundingSource=深圳市科技计划项目(RKX20200327095612234), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1241070734722789904, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, xref=1., ext=[AuthorCompanyExt(id=1241070734731178512, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, companyId=1241070734722789904, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=Department of Infectious Disease Control, Shenzhen Center for Disease Control and Prevention, Shenzhen,Guangdong 518055, China), AuthorCompanyExt(id=1241070734739567122, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, companyId=1241070734722789904, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.深圳市疾病预防控制中心传染病防制所，广东　深圳　518055)]), AuthorCompany(id=1241070734836036125, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, xref=2., ext=[AuthorCompanyExt(id=1241070734844424735, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, companyId=1241070734836036125, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2.深圳市龙岗区坪地公共卫生服务中心)]), AuthorCompany(id=1241070734974448168, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, xref=3., ext=[AuthorCompanyExt(id=1241070734995419692, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, companyId=1241070734974448168, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=3.加州大学洛杉矶分校公共卫生学院流行病学系)])], figs=[ArticleFig(id=1241070740045362000, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, language=EN, label=Fig.1, caption=Monthly incidence trend of HFMD in Shenzhen, 2011-2024, figureFileSmall=/Z711cRM5VOTTkro38318Q==, figureFileBig=xstlni2AuLO6rewYK8l+0g==, tableContent=null), ArticleFig(id=1241070740158608212, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, language=CN, label=图1, caption=深圳市2011—2024年手足口病月发病趋势图, figureFileSmall=/Z711cRM5VOTTkro38318Q==, figureFileBig=xstlni2AuLO6rewYK8l+0g==, tableContent=null), ArticleFig(id=1241070740271854428, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, language=EN, label=Fig.2, caption=STL analysis of incidence of HFMD in Shenzhen, 2011-2023, figureFileSmall=iKSQpl6z5sDtQooNyhrHyQ==, figureFileBig=UyXgCK+/ZYkgZF8UeQw9sg==, tableContent=null), ArticleFig(id=1241070740397683558, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, language=CN, label=图2, caption=深圳市2011—2023年手足口病发病率STL分解图, figureFileSmall=iKSQpl6z5sDtQooNyhrHyQ==, figureFileBig=UyXgCK+/ZYkgZF8UeQw9sg==, tableContent=null), ArticleFig(id=1241070740510929772, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, language=EN, label=Fig.3, caption=Time series of ACF and PACF, figureFileSmall=LCOEZxENQVP0RSMHn3f6FA==, figureFileBig=a3geOoukSPvQcb/iwGGrzw==, tableContent=null), ArticleFig(id=1241070740649341809, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, language=CN, label=图3, caption=时间序列的ACF和PACF图

注：图A和图B包含2020—2022年数据；图C和图D未包含2020—2022年数据。

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注：Model1为SARIMA（0，0，2）（0，1，1）12；Model2为SARIMA（2，0，0）（0，1，1）12。

, figureFileSmall=QLCNzTqMD7+oKHYlv4W+Xw==, figureFileBig=tiyglQGi6wf5UPqFxW9jEw==, tableContent=null), ArticleFig(id=1241070740938748800, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, language=EN, label=Fig.5, caption=Results of fitting and predicting incidence of HFMD in Shenzhen, figureFileSmall=Y02TFwxcgxJKp2q+kgP0Zw==, figureFileBig=6wzBCg5E8CXdcVztysfhTQ==, tableContent=null), ArticleFig(id=1241070741072966534, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, language=CN, label=图5, caption=模型拟合、预测深圳市HFMD发病率情况, figureFileSmall=Y02TFwxcgxJKp2q+kgP0Zw==, figureFileBig=6wzBCg5E8CXdcVztysfhTQ==, tableContent=null), ArticleFig(id=1241070741173629835, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, language=EN, label=Fig.6, caption=Comparison of predictive performance of various models, figureFileSmall=MLsMMlAne64a7QVk0U3PFg==, figureFileBig=CgJg3ZM6v2K/pA17nGL+lA==, tableContent=null), ArticleFig(id=1241070741270098833, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, language=CN, label=图6, caption=各模型预测性能比较, figureFileSmall=MLsMMlAne64a7QVk0U3PFg==, figureFileBig=CgJg3ZM6v2K/pA17nGL+lA==, tableContent=null), ArticleFig(id=1241070741366567831, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, language=EN, label=Table 1, caption=

Parameter estimation and testing of Model 1 and Model 2

, figureFileSmall=null, figureFileBig=null, tableContent=
模型参数估计标准差tP
Model1
MA11.0950.08013.737<0.001
MA2-0.2890.081-3.589<0.001
SMA1-0.8150.108-7.555<0.001
Model2
AR10.9260.09110.12<0.001
AR2-0.3160.092-3.44<0.001
SMA1-0.8780.206-4.27<0.001
), ArticleFig(id=1241070741437871001, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240730056188809637, language=CN, label=表1, caption=

Model 1和Model 2模型参数估计与检验

, figureFileSmall=null, figureFileBig=null, tableContent=
模型参数估计标准差tP
Model1
MA11.0950.08013.737<0.001
MA2-0.2890.081-3.589<0.001
SMA1-0.8150.108-7.555<0.001
Model2
AR10.9260.09110.12<0.001
AR2-0.3160.092-3.44<0.001
SMA1-0.8780.206-4.27<0.001
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SARIMA及其组合模型对手足口病发病率预测效果比较
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宋丽霞 1 , 卢文海 2 , 张振 1 , 路滟 1 , 吕秋莹 1 , 程雁鹏 1, 3 , 陈志高 1
现代预防医学 | 疾病预防控制 2025,52(8): 1490-1496
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现代预防医学 | 疾病预防控制 2025, 52(8): 1490-1496
SARIMA及其组合模型对手足口病发病率预测效果比较
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宋丽霞1, 卢文海2, 张振1, 路滟1, 吕秋莹1, 程雁鹏1, 3, 陈志高1
作者信息
  • 1.深圳市疾病预防控制中心传染病防制所，广东　深圳　518055
  • 2.深圳市龙岗区坪地公共卫生服务中心
  • 3.加州大学洛杉矶分校公共卫生学院流行病学系

    • 宋丽霞(1993—)，女，本科，主管医师，研究方向：传染病流行病学

通讯作者:

陈志高，E-mail:
Comparison of SARIMA and its combined models in predicting the incidence of hand foot and mouth disease
Li-xia SONG1, Wen-hai LU2, Zhen ZHANG1, Yan LU1, Qiu-ying LV1, Yan-peng CHENG1, 3, Zhi-gao CHEN1
Affiliations
  • Department of Infectious Disease Control, Shenzhen Center for Disease Control and Prevention, Shenzhen,Guangdong 518055, China
出版时间: 2025-04-25 doi: 10.20043/j.cnki.MPM.202411104
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摘要
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目的

比较SARIMA及其组合模型对手足口病发病率的预测效果,并探讨新冠疫情对手足口病SARIMA模型的影响。

方法

通过时间序列分解法分析深圳市手足口病发病趋势，以2011—2023年的手足口病月发病率建立SARIMA模型,利用最优模型分别与SVR、XGBoost构建组合模型，并预测2024年1—7月发病率，通过比较MAE、MSE、RMSE、MAPE性能得出最优模型。

结果

深圳市2011—2023年手足口病发病趋势具有明显季节性,发病高峰为每年5—6月及9—10月；未纳入新冠疫情期间的发病数据构建的SARIMA模型优于纳入的模型。基于MAE、MSE、RMSE指标，组合模型在预测时间超过4个月时比单个SARIMA模型表现更佳；在综合性能上SARIMA-SVR模型优于SARIMA-XGBoost模型，尤其在MAPE性能上。

结论

纳入新冠疫情期间的发病数据会降低SARIMA模型的性能；SARIMA-SVR组合模型预测效果优于单个SARIMA模型及SARIMA-XGBoost组合模型，可用于手足口病发病率预测，为疾病监测预警提供参考依据。

手足口病  /  SARIMA模型  /  SVR模型  /  XGBoost模型  /  预测
Objective

To compare the prediction effect of SARIMA and its combined models on the incidence of hand foot and mouth disease (HFMD), and to explore the influence of COVID-19 on the SARIMA model.

Methods

The incidence trend of HFMD in Shenzhen was analyzed through the time series decomposition method. A SARIMA model was established based on the monthly incidence of HFMD from 2011 to 2023. The optimal model was selected by comparing the performance of MAE, MSE, RMSE, and MAPE, and was used to construct a combined model with the SVR model and the XGBoost model. The incidence from January to July 2024 was predicted using the optimal model.

Results

The incidence trend of HFMD in Shenzhen from 2011 to 2023 was seasonal, and the peak was from May to June and September to October each year. The SARIMA model that did not include incidence data during the COVID-19 pandemic outperformed the included model. Based on MAE, MSE and RMSE indicators, the combined model performed better than the single SARIMA model when the prediction time exceeded 4 months. The SARMI-SVR model wassuperior to the SARMI-XGBoost model in overall performance, especially in the performance of MAPE.

Conclusion

Including the incidence data during the COVID-19 epidemic will degrade the performance of the SARIMA model. The prediction effect of SARMI-SVR model is better than SARIMA model and SARMI-XGboost model, which can be used to predict the incidence of HFMD and provide a reference for disease surveillance and early warning.

Hand foot and mouth disease  /  SARIMA model  /  SVR model  /  XGBoost model  /  Prediction
宋丽霞, 卢文海, 张振, 路滟, 吕秋莹, 程雁鹏, 陈志高. SARIMA及其组合模型对手足口病发病率预测效果比较. 现代预防医学, 2025 , 52 (8) : 1490 -1496 . DOI: 10.20043/j.cnki.MPM.202411104
Li-xia SONG, Wen-hai LU, Zhen ZHANG, Yan LU, Qiu-ying LV, Yan-peng CHENG, Zhi-gao CHEN. Comparison of SARIMA and its combined models in predicting the incidence of hand foot and mouth disease[J]. Modern Preventive Medicine, 2025 , 52 (8) : 1490 -1496 . DOI: 10.20043/j.cnki.MPM.202411104
正文
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手足口病（hand foot and mouth disease，HFMD）是由多组肠道病毒感染引起的一种儿童传染病，常在托幼机构、中小学等引起暴发流行[1]，严重影响学校教学秩序。2008年至2017年仅由EV71导致的儿童HFMD死亡数超3 000人[2]，给我国造成了严重的经济和社会负担，已成为不容忽视的重要公共卫生问题。目前有各种时间序列预测模型可对HFMD发病趋势进行预测[3-4],其中季节性差分自回归滑动平均(seasonal auto regressive integrated moving average model，SARIMA)模型被广泛应用于有周期性或季节性趋势的传染病预测[5-6]。实践证明HFMD的时间序列通常包含线性和非线性模式，但SARIMA模型只能分析线性趋势，而支持向量机回归（Support vector regression machine，SVR）可捕捉非线性信息[7]。除SVR模型外，极端梯度提升（xtreme gradient boosting，XGBoost）模型[8]在处理时间序列数据时，其决策树算法能更好地捕捉预测变量和结果之间的非线性联系，该算法已在医学领域中广泛运用[9-10]。本研究拟比较SARIMA、SARIMA-SVR、SARIMA-XGBoost等不同模型对HFMD发病率的预测效果,并探讨新冠疫情对SARIMA模型的影响，为深圳市HFMD监测预警提供参考依据。
1　资料与方法
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1.1　资料来源
2011年1月至2024年7月深圳市人口资料来源于深圳市统计局，以年中数据为该年的人口数。2011年1月至2024年7月深圳市HFMD发病数据来源于“中国疾病预防控制信息系统”。
1.2　SARIMA模型构建
SARIMA模型的一般形式为（p，d，q）（P，D，Q）S，其中p、d、q分别是非季节性自回归阶数、差分阶数、移动平均阶数；P、D、Q 分别为季节性自回归阶数、差分阶数、移动平均阶数；s为季节性周期[6]。具体建模过程：①平稳性及白噪声检验：通过单位根检验判断时间序列平稳性，若为非平稳序列，则通过差分运算转为平稳序列，并判断是否为平稳非白噪声序列。②模型识别及定阶：根据自相关函数(auto-correlation function, ACF)和偏自相关函数(partial auto-correlation function, PACF)初步定阶。③模型参数估计与检验：根据赤池信息准则 （akaike information criterion AIC）、贝叶斯信息准则(bayesian information criterion，BIC)选择最优模型，AIC、BIC值越小，模型拟合优度越好。使用Ljung-Box检验对拟合模型的残差进行白噪声检验，用t检验对各参数进行检验。④模型预测、验证：利用最优模型对2024年HFMD月发病率进行预测，并与实际值比较，评价模型的拟合和预测效果。
1.3　SARIMA-SVR组合模型
SVR模型利用核函数将样本数据从原始低维特征空间隐式地映射至高维特征空间，在更高维度上实现样本分离，使原空间中线性不可分的样本转化为可分状态，从而实现线性回归[11]。在求解非线性可分问题时，核函数的类型及参数的选择直接影响SVR模型的性能。本研究选择支持向量机中最常用的高斯径向基核函数，核参数g和相应的惩罚因子C通过R语言中的tune.svm函数通过网格搜索方式确定。SARIMA-SVR组合模型构建，首先用SARIMA最优模型分析HFMD时间序列的线性部分得到预测值，然后将SARIMA模型的残差et作为SVR模型的目标变量，预测值作为SVR模型的自变量进行分析，最终预测结果L为SVR模型预测值es与SARIMA模型预测值之和。表达式如下：
式中L为SARIMA-SVR组合模型最终预测值，为SARIMA模型预测值，es为SVR模型预测值。
1.4　SARIMA-XGBoost组合模型
XGBoost算法是以梯度提升决策树为理论基础的高效集成学习算法[12]，通过残差拟合建立多个弱评估器最终累加得到强评估器，每增加一个弱评估器周期，模型的效果能够得到提升[13]，同时又引入正则化项来控制模型复杂性并避免过拟合。XGBoost表达式如下：
式中为预测值，K为决策树的数量；fk为第k个子模型，xk为第i个输入样本，F为所有的决策树合集。由于XGBoost模型优化超参数众多，过多的参数调整会增加模型计算复杂性，影响整体性能。本研究选取最能够显著影响模型性能的3个超参数（eta、max_depth 、nrounds）使用网格搜索的方式进行优化，其他超参数使用默认值。采用移动窗口技术对模型进行训练，初始窗口长度设定为六年，随后每次以1年为步长进行窗口的平移。SARIMA-XGBoost组合模型构建的思想同上。
1.5　效果评估指标
本文使用均方根误差（root mean squared error，RMSE)、平均绝对百分比误差（mean absolute percent error，MAPE）和绝对误差（mean absolute error，MAE）对模型预测精度进行评价。评价指标公式如下：；；；其中n为样本量，yi为实际值，为预测值。
1.6　统计分析
使用局部加权回归的季节-趋势分解（seasonal and trend decomposition using loess，STL）探究数据的趋势及季节性。所有数据的处理及统计分析均采用R 4.2.3软件完成，检验水准α=0.05。
2　结果
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2.1　疾病流行情况
2011年1月至2024年7月深圳市共报告HFMD 660 154例，发病率从0.13/10万到217.21/10万不等，见图1。对2011—2023年深圳市HFMD时间序列进行STL分解后，发病率趋势性和季节性更加明显，发病率呈现波动上升趋势，并在2015年达到高峰；每年5—6月出现主高峰、9—10月出现次高峰，见图2。
2.2　SARIMA模型建立
为探究新冠疫情期间HFMD发病率对SARIMA模型的影响，根据是否纳入2020—2022年数据构建了不同的SARIMA模型。首先对2011—2024年数据进行对数转换，迪基福勒检验(augmented dickey-fuller test, ADF)显示转换后的数据是平稳的时间序列(P=0.01)，Ljung-Box检验显示数据为非白噪声时间序列（P<0.001），数据具有分析的意义。图3结果显示，在含2020—2022年数据的季节性差分中，自相关（图A）非季节性部分在5阶处截尾，提示q≤5，季节性部分在24阶处截尾，提示Q≤2；偏自相关（图B）非季节性部分在2阶处截尾，提示p≤2，季节性部分在12阶处截尾，提示P≤1。由于q值极少超过3，因此选择q≤3，对以上所有的参数进行组合，根据AIC、BIC值最小原则，筛选出最优模型为SARIMA（0，0，2）（0，1，1）12，其AIC值为274.79，BIC值为286.67。对该模型残差序列做Ljung-box检验，检验结果显示差异无统计学意义(P=0.883)，可知残差序列为白噪声序列，表明所建立的模型很好的提取了数据中的信息。模型SARIMA（0，0，2）（0，1，1）12参数估计和检验结果见表1，参数均具有统计学意义。
在去除2020—2022年数据后的季节性差分中，同理根据自相关（图C）可判断q≤2、Q≤2；偏自相关（图D）可判断p≤2、P≤1。对以上所有的参数进行组合，筛选出最优模型为SARIMA（2，0，0）（0，1，1）12，其AIC值为185.11，BIC值为195.84。对该模型残差序列做Ljung-box检验，结果显示残差序列为白噪声序列(P=0.879)，模型很好的提取了数据中的信息。模型SARIMA（2，0，0）（0，1，1）12参数估计和检验结果见表1，参数均具有统计学意义。
2.3　SARIMA模型预测性能比较
用Model 1和Model 2分别对深圳市2024年1—7月HFMD发病率进行预测，并比较二者的预测性能。图4结果显示Model 2在预测时间跨度超过3个月时，MSE、RMSE、MAE均优于Mode 1，而Model 2的MAPE性能均一直优于Model 1。表明新冠疫情期间HFMD发病率对SARIMA模型建立存在显著影响,去除后模型性能更佳。
2.4　组合模型构建
2.4.1　SARIMA-SVR模型
用Model 2预测的残差构建SVR模型，通过tune.svm函数用网格搜索法得到SVR模型的最优参数为cos=10 000，gamma=0.001。利用最优参数构建SVR模型，预测HFMD发病率的残差。将SVR模型预测的发病率残差与Model2模型预测的发病率结合，得到SARIMA-SVR模型的最终预测值，模型拟合、预测结果如图5所示。可发现SARIMA模型和SARIMA-SVR组合模型预测的HFMD发病率变化趋势和实际一致,预测的HFMD发病率峰值月份与实际一致，但SARIMA-SVR组合模型拟合值与实际值吻合程度高于SARIMA模型。
2.4.2　SARIMA-XGBoost模型
同理将Model 2预测的HFMD残差作为XGBoost模型的因变量，SARIMA模型预测值作为自变量，构建XGBoost模型。网格搜索法确定树的最大深度为1，学习率为0.05，迭代次数为40。模型、拟合预测结果如图5所示，可看到模型预测的HFMD发病率变化趋势和实际基本一致,但峰值时间出现偏差。
2.5　模型性能评价
图6显示了SARIMA、SARIMA-SVR、SARIMA-XGBoost等模型预测2024年1—7月HFMD发病率的MAE、MAPE、MSE、RMSE值。基于以上指标，SARIMA-SVR模型综合性能优于其他模型。在预测时间跨度在4个月内时，除MAPE指标外，单独模型与组合模型性能相差较小，超过4个月时组合模型的性能均优于单独模型，表明在长期预测时组合模型更适合。在MAE、MSE、RMSE上SARIMA-SVR模型与SARIMA-XGBoost模型表现性能一致，但在MAPE上，除1月份外，SARIMA-SVR模型远优于SARIMA-XGBoost模型。
3　讨论
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自2008年以来HFMD在中国的发病率持续上升[1]，分析、预测HFMD发病趋势和季节性变化对HFMD防控至关重要。深圳的亚热带季风气候特点有利于HFMD在每年的夏秋季传播[14]，而每年7—8月为中国中小学暑假，这种假期效应对HFMD的传播模式具有一定影响[15]。本研究表明2011—2023年深圳市HFMD发病率具有明显的季节性，呈现夏、秋两个流行高峰，季节性分解更加明确了这一特点，与以往的研究结果基本一致[1, 15]。
SARIMA模型在各类传染病预测中取得了良好的效果[5-6]。本研究发现新冠疫情期间HFMD发病率对SARIMA模型的构建存在影响，基于MAE、MSE、RMSE、MAPE评价指标，去除该部分数据，模型性能更佳。SARIMA模型原理是假设当前时刻的观测值与过去时刻的观测值存在相关性，对历史数据进行拟合确定最佳参数，再利用参数构建模型预测未来。该模型要求数据平稳，然而新冠疫情期间受疫情防控政策影响，HFMD发病率显著降低，无法真实反应HFMD流行状况，模型可能无法捕捉到由外部因素引起的突然变化，从而影响模型的预测精度。尽管非平稳的时间序列可以通过差分使其平稳，但其是以牺牲部分原始信息为代价，这也可能导致模型的性能不佳。这种影响在SARIMA模型预测新冠疫情期间流感时也有被观察到[16]，提示在构建HFMD SARIMA模型或其他时间序列预测模型时应当考虑新冠疫情期间的影响。后疫情时代使用SARIMA模型预测HFMD，应当关注数据的季节性是否发生变化，如使用季节指数法、集中度法等[17]对HFMD的季节性进行定量分析；其次保证纳入的数据满足模型要求，如平稳性、数据包含足够的周期等，通常SARIMA模型要求时间序列至少包含7—8个季节周期[18]，以保证充分提取时间序列中的规律。
在预测时间跨度超过4个月时，组合模型的MSE、MAE、RMSE性能均优于单独SARIMA模型，这是由于传染病现实流行中存在很多不确定性因素，其发病时间序列通常包含线性和非线性信息[19]，而SARIMA模型只能有限提取其中的线性信息。为了克服线性模型的局限性，人们通常会将线性模型（如SARIMA模型）与可提取非线性信息的机器学习模型（如SVR模型、XGBoost模型、ANN模型等）[19-21]相结合以提高模型的性能。本研究发现，与SARIMA-XGBoost模型相比，SARIMA-SVR模型总体性能更优。SARIMA-XGBoost模型预测峰值月份出现偏差，基于MAPE指标性能较差，而基于MAE、MSE、RMSE指标在预测时间跨度超过4个月时，其性能略优于SARIMA-SVR模型。这可能和SVR模型适合小样本、非线性、高维数据，而XGBoost模型通常更适合处理大规模的数据集等有关。
在HFMD发病率预测上，各模型预测值与实际值仍存在一定的差距。可能原因有：①本文运用的模型均为单因素模型，而HFMD的流行还受气候、经济、环境等诸多因素的影响[19-20]，这可能会影响模型的精度。②在HFMD高发月份往往还存在聚集性或暴发性疫情，使发病数出现突增，如2023年深圳市HFMD月发病率达2011—2024年最高值，该值对HFMD的时间趋势存在一定的影响。③本研究数据均来自被动监测系统，且数据跨度年限较长，无法保证纳入所有病例，且不同历史阶段有不同的防控策略、疫苗计划、健康教育宣传，这些均可能影响模型的准确性。④本文组合模型的前置模型为SARIMA模型，单独的SARIMA模型预测精度不佳，其预测残差作为后续的输入数据可能会对模型的整体性能产生影响。因此，为获得准确和长期的预测结果，需不断收集和更新数据。在未来研究中，我们将考虑各种协变量构建更合适的组合模型，如构建考虑外生变量的SARIMAX模型[20]与机器学习模型的组合、考虑假期聚集性效应的Prophet模型[14]与机器学习模型的组合等，以进一步提高模型的性能。
尽管存在不足，但SARIMA-SVR模型相对较优的预测值仍可为HFMD实际防控工作提供科学参考。根据预测值，可以观察HFMD的传播规律和流行趋势，在疫情高峰来临前有针对性的开展传染病健康宣传教育和干预措施，为政府部门及医疗机构提前反应和优化资源配置提供参考。同时预测值还可与移动流行区间法[22]结合，根据其阈值判断流行强度，为深圳市HFMD风险指数[23]计算提供科学依据。
基金
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  • 深圳市科技计划项目(JCYJ20240813160803005)
  • 深圳市医疗卫生三名工程项目(SZSM202011008)
  • 深圳市科技计划项目(RKX20200327095612234)
文献
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2025年第52卷第8期
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doi: 10.20043/j.cnki.MPM.202411104
  • 接收时间：2024-11-05
  • 首发时间：2026-03-17
  • 出版时间：2025-04-25
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  • 收稿日期：2024-11-05
基金
深圳市科技计划项目(JCYJ20240813160803005)
深圳市医疗卫生三名工程项目(SZSM202011008)
深圳市科技计划项目(RKX20200327095612234)
作者信息
    1.深圳市疾病预防控制中心传染病防制所，广东　深圳　518055
    2.深圳市龙岗区坪地公共卫生服务中心
    3.加州大学洛杉矶分校公共卫生学院流行病学系

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陈志高，E-mail:
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
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