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Article(id=1241676523686646588, tenantId=1146029695717560320, journalId=1227665162245664772, issueId=1241676522256388920, articleNumber=null, orderNo=null, doi=10.20043/j.cnki.MPM.202406461, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1719158400000, receivedDateStr=2024-06-24, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773968352480, onlineDateStr=2026-03-20, pubDate=1731168000000, pubDateStr=2024-11-10, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773968352480, onlineIssueDateStr=2026-03-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773968352480, creator=13701087609, updateTime=1773968352480, updator=13701087609, issue=Issue{id=1241676522256388920, tenantId=1146029695717560320, journalId=1227665162245664772, year='2024', volume='51', issue='21', pageStart='3841', pageEnd='4032', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773968352140, creator=13701087609, updateTime=1773968629818, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241677686985249701, tenantId=1146029695717560320, journalId=1227665162245664772, issueId=1241676522256388920, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241677686985249702, tenantId=1146029695717560320, journalId=1227665162245664772, issueId=1241676522256388920, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=3877, endPage=3883, ext={EN=ArticleExt(id=1241676524017996606, articleId=1241676523686646588, tenantId=1146029695717560320, journalId=1227665162245664772, language=EN, title=Research on pertussis incidence prediction in Urumqi based on ARIMA and LSTM models, columnId=1240413921954295836, journalTitle=Modern Preventive Medicine, columnName=Epidemiology and Statistical Methods, runingTitle=null, highlight=null, articleAbstract=
Objective

To analyze the application of the ARIMA and LSTM models in predicting pertussis incidence in Urumqi, providing a basis for assessing the epidemic trend of pertussis.

Methods

Monthly reported incidence data of pertussis in Urumqi from 2011 to 2021 were used to establish ARIMA and LSTM models. The incidence data from 2022 to 2023 were utilized to validate the predictive performance of the two models. The models’ performance was evaluated using Root Mean Square Error (RMSE) and Mean Absolute Error (MAE), and the incidence of pertussis in 2024 was predicted.

Results

The incidence of pertussis in Urumqi from 2011 to 2023 showed an upward trend with seasonal variations. Additionally, a high incidence state of pertussis began in August 2023. Both the ARIMA and LSTM models demonstrated good fitting, although there were discrepancies in their predictions for July to December 2023. The overall predictive performance of the LSTM model (RMSE=32.34, MAE=11.41) was superior to that of the ARIMA model (RMSE=42.81, MAE=14.34). The LSTM model, which showed better validation results, predicted a continued increase in pertussis incidence for 2024.

Conclusion

The LSTM model provides a more accurate prediction of the pertussis incidence trend in Urumqi, offering valuable insights for monitoring and controlling the epidemic of pertussis.

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目的

分析ARIMA模型和LSTM模型在乌鲁木齐市百日咳发病预测中的应用，为百日咳的流行趋势研判提供依据。

方法

采用乌鲁木齐市2011—2021年百日咳月报告发病数据建立ARIMA模型和LSTM模型，以2022—2023年的发病数据验证两种模型的预测表现，使用均方根误差（RMSE）和平均绝对误差（MAE）进行模型的预测性能评估，并预测2024年百日咳发病情况。

结果

乌鲁木齐市2011—2023年百日咳发病呈上升趋势，存在季节性变化。同时自2023年8月开始百日咳进入高发状态。ARIMA模型和LSTM模型的拟合效果良好，但均对2023年7—12月的预测存在一定差异。LSTM模型（RMSE=32.34，MAE=11.41）的总体预测效果优于ARIMA模型（RMSE=42.81，MAE=14.34）。应用验证效果更好的LSTM模型预测2024年百日咳发病趋势，提示百日咳发病将持续上升。

结论

LSTM模型对乌鲁木齐市百日咳发病趋势的预测效果更佳，可为百日咳的监测及疫情防控工作提供借鉴与参考。

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王培生，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=22eMIY36r3Ho1z9wmtzEvA==, magXml=gTN16YuKE+P/jldiVZPrrQ==, pdfUrl=null, pdf=HddiRQBhM4sO6xyITaPqHg==, pdfFileSize=991686, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=XzvDH2nG6UQ1kR/Jcg2adg==, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=XNUXJO0ntWE9yP9GRMJRoQ==, mapNumber=null, authorCompany=null, fund=null, authors=

萧楚瑶（2000—），女，硕士在读，研究方向: 疾病预防与控制

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萧楚瑶（2000—），女，硕士在读，研究方向: 疾病预防与控制

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萧楚瑶（2000—），女，硕士在读，研究方向: 疾病预防与控制

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National Medical Journal of China, 2024, 104(15):1258-1279.(In Chinese), articleTitle=Guidelines for diagnosis and management and prevention of pertussis of China (2024 edition), refAbstract=null)], funds=[Fund(id=1241821870769636234, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1241676523686646588, awardId=202346, language=CN, fundingSource=乌鲁木齐市卫生健康委员会科技计划项目(202346), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1241821858115420630, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1241676523686646588, xref=1., ext=[AuthorCompanyExt(id=1241821858123809239, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1241676523686646588, companyId=1241821858115420630, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=School of Public Health, Xinjiang Medical University, Urumqi, Xinjiang 830011, China), AuthorCompanyExt(id=1241821858136392152, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1241676523686646588, companyId=1241821858115420630, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.新疆医科大学公共卫生学院，新疆 乌鲁木齐 830011)]), AuthorCompany(id=1241821858245444068, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1241676523686646588, xref=2., ext=[AuthorCompanyExt(id=1241821858253832678, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1241676523686646588, companyId=1241821858245444068, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2.乌鲁木齐市疾病预防控制中心，新疆 乌鲁木齐 830026)])], figs=[ArticleFig(id=1241821867460330272, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1241676523686646588, language=EN, label=Figure 1, caption=Monthly observed cases of pertussis in Urumqi from 2011 to 2023, figureFileSmall=CDh98O4ry4v7pJBELZUknQ==, figureFileBig=4AanwcYPysuEPNrXKRYC8g==, tableContent=null), ArticleFig(id=1241821867590353705, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1241676523686646588, language=CN, label=图1, caption=2011—2023年乌鲁木齐市百日咳发病数时序图, figureFileSmall=CDh98O4ry4v7pJBELZUknQ==, figureFileBig=4AanwcYPysuEPNrXKRYC8g==, tableContent=null), ArticleFig(id=1241821867753931571, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1241676523686646588, language=EN, label=Figure 2, caption=Seasonal decomposition map of pertussis in Urumqi from 2011 to 2022, figureFileSmall=gOrJ3+S5/1QfWbnGlYGSuw==, figureFileBig=RZy88AKQBG+SFVh5OODhWQ==, tableContent=null), ArticleFig(id=1241821867896537918, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1241676523686646588, language=CN, label=图2, caption=2011—2022年乌鲁木齐市百日咳月发病数时间序列季节性分解图, figureFileSmall=gOrJ3+S5/1QfWbnGlYGSuw==, figureFileBig=RZy88AKQBG+SFVh5OODhWQ==, tableContent=null), ArticleFig(id=1241821868034949959, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1241676523686646588, language=EN, label=Figure 3, caption=ACF and PACF figure after first-order difference, figureFileSmall=og6vVm2ESJu3bBZwMhr6FQ==, figureFileBig=DCuzhzt0VE8doQYEa0Ou0g==, tableContent=null), ArticleFig(id=1241821868185944907, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1241676523686646588, language=CN, label=图3, caption=一阶差分后的ACF和PACF图, figureFileSmall=og6vVm2ESJu3bBZwMhr6FQ==, figureFileBig=DCuzhzt0VE8doQYEa0Ou0g==, tableContent=null), ArticleFig(id=1241821868320162640, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1241676523686646588, language=EN, label=Figure 4, caption=Comparison of fitting results between ARIMA and LSTM model, figureFileSmall=ewh3S+gRnz1qxGTLaWYORQ==, figureFileBig=Yl86XXOe+QgPQcrC3OaIhg==, tableContent=null), ArticleFig(id=1241821868466963288, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1241676523686646588, language=CN, label=图4, caption=ARIMA模型和LSTM模型拟合预测比较

注：a)ARIMA和LSTM模型对2022年1月-2021年12月乌鲁木齐市百日咳发病数的拟合结果；b)两个模型在2022年1月-2023年12月发病数的验证结果；c)LSTM模型对2024年乌鲁木齐市百日咳发病数的预测结果。

, figureFileSmall=ewh3S+gRnz1qxGTLaWYORQ==, figureFileBig=Yl86XXOe+QgPQcrC3OaIhg==, tableContent=null), ArticleFig(id=1241821868605375329, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1241676523686646588, language=EN, label=Table 1, caption=

Parameter estimation of candidate ARIMA models

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模型AICBIC模型残差Ljung-Box检验
χ2值P值
ARIMA（0，1，1）（0，1，1）12577.21585.5532.440.07
ARIMA（0，1，1）（1，1，1）12578.52589.6433.360.04
ARIMA（0，1，2）（0，1，1）12576.78587.9025.460.23
ARIMA（0，1，2）（1，1，1）12578.30592.1925.400.19
ARIMA（1，1，1）（0，1，1）12576.74587.8525.690.22
ARIMA（1，1，1）（1，1，1）12578.16592.0525.120.20
ARIMA（1，1，2）（0，1，1）12577.73591.6325.930.17
ARIMA（1，1，2）（1，1，1）12577.46594.1420.790.35
), ArticleFig(id=1241821868752175981, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1241676523686646588, language=CN, label=表1, caption=

ARIMA备选模型的参数估计

, figureFileSmall=null, figureFileBig=null, tableContent=
模型AICBIC模型残差Ljung-Box检验
χ2值P值
ARIMA（0，1，1）（0，1，1）12577.21585.5532.440.07
ARIMA（0，1，1）（1，1，1）12578.52589.6433.360.04
ARIMA（0，1，2）（0，1，1）12576.78587.9025.460.23
ARIMA（0，1，2）（1，1，1）12578.30592.1925.400.19
ARIMA（1，1，1）（0，1，1）12576.74587.8525.690.22
ARIMA（1，1，1）（1，1，1）12578.16592.0525.120.20
ARIMA（1，1，2）（0，1，1）12577.73591.6325.930.17
ARIMA（1，1，2）（1，1，1）12577.46594.1420.790.35
), ArticleFig(id=1241821868907365238, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1241676523686646588, language=EN, label=Table 2, caption=

Evaluation of fitting and prediction effects of two models

, figureFileSmall=null, figureFileBig=null, tableContent=
精确度评价时间ARIMA模型LSTM模型
RMSEMAERMSEMAE
拟合2.441.121.881.17
拟合2022年1—6月0.560.500.690.55
2022年7—12月3.292.083.803.33
2023年1—6月0.550.490.660.63
2023年7—12月85.5654.2964.5741.14
), ArticleFig(id=1241821870450869116, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1241676523686646588, language=CN, label=表2, caption=

两种模型的拟合及验证效果评价

, figureFileSmall=null, figureFileBig=null, tableContent=
精确度评价时间ARIMA模型LSTM模型
RMSEMAERMSEMAE
拟合2.441.121.881.17
拟合2022年1—6月0.560.500.690.55
2022年7—12月3.292.083.803.33
2023年1—6月0.550.490.660.63
2023年7—12月85.5654.2964.5741.14
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基于ARIMA与LSTM模型的乌鲁木齐市百日咳发病预测研究
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萧楚瑶 1 , 黎婷婷 1 , 付若楠 1 , 尹钰 2 , 邹莹 2 , 王培生 2
现代预防医学 | 流行病与统计方法 2024,51(21): 3877-3883
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现代预防医学 | 流行病与统计方法 2024, 51(21): 3877-3883
基于ARIMA与LSTM模型的乌鲁木齐市百日咳发病预测研究
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萧楚瑶1, 黎婷婷1, 付若楠1, 尹钰2, 邹莹2, 王培生2
作者信息
  • 1.新疆医科大学公共卫生学院，新疆 乌鲁木齐 830011
  • 2.乌鲁木齐市疾病预防控制中心，新疆 乌鲁木齐 830026

    • 萧楚瑶（2000—），女，硕士在读，研究方向: 疾病预防与控制

通讯作者:

王培生，E-mail:
Research on pertussis incidence prediction in Urumqi based on ARIMA and LSTM models
Chu-yao XIAO1, Ting-ting LI1, Ruo-nan FU1, Yu YIN2, Ying ZOU2, Pei-sheng WANG2
Affiliations
  • School of Public Health, Xinjiang Medical University, Urumqi, Xinjiang 830011, China
出版时间: 2024-11-10 doi: 10.20043/j.cnki.MPM.202406461
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摘要
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目的

分析ARIMA模型和LSTM模型在乌鲁木齐市百日咳发病预测中的应用，为百日咳的流行趋势研判提供依据。

方法

采用乌鲁木齐市2011—2021年百日咳月报告发病数据建立ARIMA模型和LSTM模型，以2022—2023年的发病数据验证两种模型的预测表现，使用均方根误差（RMSE）和平均绝对误差（MAE）进行模型的预测性能评估，并预测2024年百日咳发病情况。

结果

乌鲁木齐市2011—2023年百日咳发病呈上升趋势，存在季节性变化。同时自2023年8月开始百日咳进入高发状态。ARIMA模型和LSTM模型的拟合效果良好，但均对2023年7—12月的预测存在一定差异。LSTM模型（RMSE=32.34，MAE=11.41）的总体预测效果优于ARIMA模型（RMSE=42.81，MAE=14.34）。应用验证效果更好的LSTM模型预测2024年百日咳发病趋势，提示百日咳发病将持续上升。

结论

LSTM模型对乌鲁木齐市百日咳发病趋势的预测效果更佳，可为百日咳的监测及疫情防控工作提供借鉴与参考。

百日咳  /  ARIMA模型  /  LSTM神经网络模型  /  预测
Objective

To analyze the application of the ARIMA and LSTM models in predicting pertussis incidence in Urumqi, providing a basis for assessing the epidemic trend of pertussis.

Methods

Monthly reported incidence data of pertussis in Urumqi from 2011 to 2021 were used to establish ARIMA and LSTM models. The incidence data from 2022 to 2023 were utilized to validate the predictive performance of the two models. The models’ performance was evaluated using Root Mean Square Error (RMSE) and Mean Absolute Error (MAE), and the incidence of pertussis in 2024 was predicted.

Results

The incidence of pertussis in Urumqi from 2011 to 2023 showed an upward trend with seasonal variations. Additionally, a high incidence state of pertussis began in August 2023. Both the ARIMA and LSTM models demonstrated good fitting, although there were discrepancies in their predictions for July to December 2023. The overall predictive performance of the LSTM model (RMSE=32.34, MAE=11.41) was superior to that of the ARIMA model (RMSE=42.81, MAE=14.34). The LSTM model, which showed better validation results, predicted a continued increase in pertussis incidence for 2024.

Conclusion

The LSTM model provides a more accurate prediction of the pertussis incidence trend in Urumqi, offering valuable insights for monitoring and controlling the epidemic of pertussis.

Pertussis  /  ARIMA model  /  LSTM neural network model  /  Prediction
萧楚瑶, 黎婷婷, 付若楠, 尹钰, 邹莹, 王培生. 基于ARIMA与LSTM模型的乌鲁木齐市百日咳发病预测研究. 现代预防医学, 2024 , 51 (21) : 3877 -3883 . DOI: 10.20043/j.cnki.MPM.202406461
Chu-yao XIAO, Ting-ting LI, Ruo-nan FU, Yu YIN, Ying ZOU, Pei-sheng WANG. Research on pertussis incidence prediction in Urumqi based on ARIMA and LSTM models[J]. Modern Preventive Medicine, 2024 , 51 (21) : 3877 -3883 . DOI: 10.20043/j.cnki.MPM.202406461
正文
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百日咳是一种通过飞沫传播且具有高度传染性的急性呼吸系统疾病，由百日咳鲍特菌（Bordetella pertussis，BP）感染引起，以反复、剧烈地咳嗽为常见症状[1]。自百日咳疫苗问世并在全球大规模使用后，百日咳发病率一度得到显著下降[2]。中国百日咳在保持多年低水平流行状态后，发病率在2013—2019年间从0.13/10万上升至2.15/10万[3-4]。我国2022年报告病例数较2009年更是增长约20倍，达38 295例[5]。准确预测百日咳流行趋势已成为当前亟待解决的公共卫生问题。
时间序列预测是通过时间序列来反映事物发展趋势的一种外推和预测方法[6]。差分自回归移动平均模型（autoregressive integrated moving average,ARIMA）作为时序预测分析的经典模型之一，已在传染病领域得到了广泛应用[7-9]。随着神经网络的快速发展，许多算法被用于预测分析[10]。其中，循环神经网络（recurrent neural network, RNN）因其结构中的神经元相互连接，使得信息能在神经元之间传递从而实现了对序列数据的短期精准预测[11]。长短期记忆神经网络（long short-term memory, LSTM）模型作为RNN的特殊变体，进一步有效地解决了RNN的长期记忆能力不足的问题，并在处理时间序列中的非线性部分展现出独特优势[12]。目前基于LSTM神经网络模型开展传染病预测研究较少，且缺乏与传统模型的比较验证。本文采用ARIMA模型和LSTM模型拟合乌鲁木齐市2011—2023年百日咳的逐月发病数，验证模型有效性并比较其预测精准性，为百日咳的监测和合理防治提供科学依据。
1　资料与方法
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1.1　资料来源
数据资料来源于中国疾病预防控制系统的传染病监测系统，截取2011年1月—2023年12月的乌鲁木齐市百日咳月发病数进行分析。人口信息数据来源于《乌鲁木齐统计年鉴》。
1.2　研究方法
1.2.1　ARIMA模型
ARIMA模型又称Box-Jenkins模型，是流行病学监测中常用的预测技术[13-14]。在本研究中，由于研究数据显示出周期性和季节性趋势，因此将季节性差分自回归滑动平均模型（SARIMA）应用于百日咳的发病预测[15]。表达式为：（p，d，q）（P，D，Q）s，其中p为自回归阶数、d为差分阶数、q为移动平均阶数、P为季节自回归阶数、D为季节差分阶数、Q为季节移动平均阶数、s为季节周期[16]。
以2011年1月—2021年12月的乌鲁木齐市百日咳发病数据建立时间序列，利用单位根检验（augmented dickey fuller，ADF）判断序列是否平稳，若非平稳，使用差分处理实现序列平稳化。通过自相关函数（autocorrelation function, ACF）图、偏自相关函数（partial autocorrelation function, PACF）图估计参数搜索区间。根据赤池信息准则（Akaike information criterion, AIC）和贝叶斯信息准则（Bayesian information criterion, BIC）最小原则确定最优模型参数。使用Ljung-Box检验验证模型的残差序列是否为白噪声。运用通过模型有效性检验的最优ARIMA模型预测2022—2023年百日咳病发病数。
1.2.2　LSTM模型
LSTM是一种基于RNN结构的深度学习算法，通过引入门控装置和记忆单元来处理长序列数据，有效避免了梯度随时间增加而爆炸和消失的问题。LSTM模型通过在神经元中增加输入门、遗忘门和输出门，以此实现对历史信息的选择性过滤[9]。它们由Sigmoid函数控制，并与tanh函数相结合[17]。LSTM模型的数学公式如下：
以上公式中，ft、it和ot分别表示t时刻的遗忘门、输入门和输出门；σ表示sigmoid函数表示t时刻的神经元单元状态的候选；Ct表示在t时刻神经元单元状态；xt与ht分别表示t时刻神经元的输入和输出。
模型构建主要步骤为：首先，对2011—2021年乌鲁木齐市逐月百日咳发病数进行数据清洗和归一化，之后转换数据格式。其次，确定模型的网络结构：选择网络层数和神经元数量；设置损失函数、随机舍弃率、模型迭代的批量大小和周期数。使用2022—2023年发病数据评估模型的泛化能力，并根据需要调整超参数。最后，将拟合和预测数据反归一化。
1.2.3　模型评价指标
本研究以2011—2021年乌鲁木齐市逐月百日咳发病数为训练集，2022—2023年发病数据为验证集，采用平均绝对误差（mean absolute error, MAE）和均方根误差（root mean squared error, RMSE）评估两种模型的拟合和预测精度。两个指标的误差越小，表明模型预测性能越好。MAE和RMSE和的计算公式如下：
公式中，yi为第i个实际值为第i个预测值，n是样本数。
1.3　统计学方法
使用SPSS 26.0软件建立数据库并完成描述性统计，采用R 4.2.3进行ARIMA模型构建与预测，采用Python 3.9进行LSTM模型的拟合与预测，检验水准α=0.05。
2　结果
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2.1　乌鲁木齐市2011—2023年百日咳发病趋势分析
2011年1月—2023年12月，乌鲁木齐市累积上报百日咳病例共计543例，年均报告发病率为1.23/10万，无死亡病例。乌鲁木齐市百日咳报告病例数总体呈上升趋势，每2～3年出现1个发病高峰，见图1。2011—2022年，乌鲁木齐市百日咳发病趋势平稳，以散发为主，季节发病高峰为7—8月，见图2。2023年乌鲁木齐市百日咳报告发病例数大幅增长，较2022年增加了19倍，发病高峰由以往的7—8月改变为11—12月，见图1。
2.2　ARIMA模型的构建
如图1、2所示，原始时间序列显示出上升趋势并伴有季节性波动。ADF检验显示序列不平稳（P=0.43>0.05），因此对原始序列进行一阶差分及一阶季节性差分。差分后序列平稳（P=0.01），由此参数d=D=1。对平稳化序列进行Ljung-Box检验，提示序列为非白噪声（P<0.001），可以构建ARIMA模型提取其中线性关系。
接下来根据差分后序列的ACF和PACF图选取合适的参数，见图3。观察PACF图，可取p=0或1、P=0或1；观察ACF图，可取q=1或2、Q=1。通过组合每个参数的所有可能值，得出8个备选模型，见表1。采用AIC和BIC最小原则，得到最优模型ARIMA（1，1，1）（0，1，1）12。对该模型残差进行Ljung-Box检验，提示残差为白噪声序列（χ2=25.69，P=0.22> 0.05）。模型通过有效性检验，拟合与预测结果见图4、表2。
2.3　LSTM神经网络的构建
对百日咳月发病数据进行预处理与格式转换后，构建模型网络结构。LSTM网络结构由1个输入层，1个隐含层和1个输出层组成。经过多次尝试，各层神经元数分别为32、4和1时预测效果更准确。设置时间步长为12。选择激活函数为RELU函数，迭代次数为100次，优化器为adam，损失函数为均方误差进行训练。此外，为控制过拟合现象，将Dropout函数设置为0.20。见图4、表2。
2.4　模型效果比较
从图4、表2可以看出，两种模型的拟合精度良好。在对2022年1月-2023年12月的验证效果上，ARIMA模型和LSTM模型的RMSE分别为42.81、32.34，MAE分别为14.34、11.41。以半年为期比较模型验证效果发现，2022年1月-2023年6月两种模型预测准确度近似，其中ARIMA模型预测效果稍优于LSTM模型。而2023年7-12月两种模型预测效果均显示较差，但LSTM模型的预测更符合实际发病的变化趋势。
2.5　模型预测
应用LSTM模型外推预测2024年乌鲁木齐市的百日咳发病情况。结果显示，2024年百日咳发病数将持续走高，其中1-5月百日咳发病数将呈小幅下降，6-12月将保持上升趋势，见图4。
3　讨论
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近年来，我国儿童3剂次百白破疫苗的报告接种率维持在99%以上，但百日咳发病率始终保持相对增长的趋势[1,18]。此外，我国百日咳报告病例数于2018、2019、2021和2022年均居全球首位[4,19]。百日咳再现已成为构成我国人群健康的公共卫生问题。因此，构建准确的预测模型对百日咳的防控具有重要的现实意义。
本研究以2011—2023年乌鲁木齐市百日咳月发病数建立时间序列并构建ARIMA模型和LSTM模型，模型效果显示：LSTM模型预测效果总体上优于ARIMA（1，1，1）（0，1，1）12模型，这与王田田等[20]的研究结果一致。通过拟合预测结果显示，2种模型在预测2023年7—12月发病数时的效果均较差，实际发病数明显高于预测值。尽管预测存在差距，但LSTM模型的预测值在后期逐渐接近实际值，流行曲线趋势基本一致。而ARIMA模型在该时期的预测值与实际值并不吻合。出现这种情况的原因可能是发病序列的非线性部分可能不是白噪声，这意味着对于可能受到多种因素影响而发生的高发变化可能无法被ARIMA模型捕获[10]，导致该部分预测准确性下降。
对于2023年乌鲁木齐市百日咳出现的高发状态，该情况与全国百日咳发病的变化趋势一致[21]。这可能与乌鲁木齐市对百日咳监测的加强、医务人员对百日咳警惕性的提高和实验室检测技术的推广有关[22]；另一方面可能与自然感染和疫苗接种均不能产生终生免疫力以及百日咳鲍特菌耐药率提高有关[23]。这提示应加强对百日咳的监测，并改进对易感人群的防控措施以减少疾病的传播风险。
进一步应用验证效果更好的LSTM模型对2024年乌鲁木齐市百日咳发病情况进行预测。预测结果显示，2024年乌鲁木齐市百日咳的发病数将持续走高，与往年发病趋势基本一致，其中1-5月发病数将呈季节性小幅下降，自6月开始将保持上升趋势，与我国以往百日咳报告病例的季节发病特征相似[4]。此外LSTM模型已在多种传染病的流行状态预测研究中取得良好的效果，如肝炎[9,20]、出血热[10]、HIV[12]、手足口病[17]等。上述研究表明，LSTM模型对传染病的预测具备较高的准确性和较强的适用性。
本研究存在一定局限性：一方面，百日咳发病受复杂因素影响，由于数据可得性，本研究未将其他因素考虑在内；另一方面，发病数据为被动监测报告所得，漏诊会导致实际发病情况被低估。因此，未来应纳入更多百日咳发病相关影响因素并加强病例报告质量，从而提升模型的预测效果。
综上，本研究显示LSTM模型预测精度优于ARIMA模型，更适合用于乌鲁木齐市百日咳的发病趋势预测，可百日咳防控策略提供一定的参考依据。同时，在当前百日咳再现的背景下，应积极开展百日咳的健康教育及主动监测工作，加强百日咳病例诊断并完善百日咳疫苗的免疫策略。
基金
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  • 乌鲁木齐市卫生健康委员会科技计划项目(202346)
文献
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2024年第51卷第21期
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doi: 10.20043/j.cnki.MPM.202406461
  • 接收时间：2024-06-24
  • 首发时间：2026-03-20
  • 出版时间：2024-11-10
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  • 收稿日期：2024-06-24
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乌鲁木齐市卫生健康委员会科技计划项目(202346)
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    1.新疆医科大学公共卫生学院，新疆 乌鲁木齐 830011
    2.乌鲁木齐市疾病预防控制中心，新疆 乌鲁木齐 830026

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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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