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Article(id=1324077480956539006, tenantId=1146029695717560320, journalId=1227665162245664772, issueId=1324077443828560770, articleNumber=null, orderNo=null, doi=10.20043/j.cnki.MPM.202507165, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1752336000000, receivedDateStr=2025-07-13, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793614271630, onlineDateStr=2026-11-02, pubDate=1775750400000, pubDateStr=2026-04-10, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793614271630, onlineIssueDateStr=2026-11-02, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793614271630, creator=13701087609, updateTime=1793614271630, updator=13701087609, issue=Issue{id=1324077443828560770, tenantId=1146029695717560320, journalId=1227665162245664772, year='2026', volume='53', issue='7', pageStart='1153', pageEnd='1344', issueExtLink='null', onlineDate='null', pubDate='1775750400000', pubDateStr='2026-04-10', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=0, createTime=1793614262778, creator='13701087609', updateTime=1793614352085, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1324077818509918661, tenantId=1146029695717560320, journalId=1227665162245664772, issueId=1324077443828560770, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1324077818509918662, tenantId=1146029695717560320, journalId=1227665162245664772, issueId=1324077443828560770, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=1172, endPage=1179, ext={EN=ArticleExt(id=1324077482588123263, articleId=1324077480956539006, tenantId=1146029695717560320, journalId=1227665162245664772, language=EN, title=Comparison of different Python-based time series models in the prediction of other infectious diarrhea diseases in Baoshan District, Shanghai, columnId=1240413921954295836, journalTitle=Modern Preventive Medicine, columnName=Epidemiology and Statistical Methods, runingTitle=null, highlight=null, articleAbstract=
Objective

To compare the predictive performance of seasonal autoregressive integrated moving average (SARIMA) model, Prophet model, random forest (RF) model, extreme gradient boosting (XGBoost) model, and support vector regression (SVR) model on the incidence of other infectious diarrhea diseases in Baoshan District, Shanghai, and to explore the optimal forecasting model.

Methods

Using the monthly incidence rates of other infectious diarrhea diseases in Baoshan District, Shanghai from 2014 to 2022 as the training set, the SARIMA model, the Prophet model, the RF model with and without meteorological features, the XGBoost model with and without meteorological features, and the SVR model with and without meteorological features were constructed in Python to predict the monthly incidence rates from 2023 to 2024. The optimal model was selected by comparing the mean absolute error (MAE), root mean square error (RMSE) and mean absolute percentage error (MAPE) of the predicted and actual values.

Results

From 2014 to 2024, a total of 6 868 cases of other infectious diarrheal diseases were reported in Baoshan District, Shanghai, with an average annual incidence rate of 28.81 per 100 000 population. The cases exhibited a bimodal seasonal distribution (peaking in summer and winter-spring). By comparing the predictive performance of different time series models on the monthly incidence rate from 2023 to 2024, the XGBoost model without meteorological features showed the best comprehensive performance in terms of fitting accuracy indicators (MAE=5.089, RMSE=6.844, MAPE=54.646%).

Conclusion

The XGBoost model without meteorological features is the best model for short-term prediction of other infectious diarrhea diseases in Baoshan District, which can provide a scientific basis for early warning and prevention of other infectious diarrhea diseases in Baoshan District.

, authors=Lian ZONG, Jia-le ZHENG, Lun-hui XIANG, Fan HE, Xiao-feng LIU, Jiang ZHU, authorsList=Lian ZONG, Jia-le ZHENG, Lun-hui XIANG, Fan HE, Xiao-feng LIU, Jiang ZHU, authorCompany=null, correspAuthors=Jiang ZHU, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1324077484936933528, articleId=1324077480956539006, tenantId=1146029695717560320, journalId=1227665162245664772, language=CN, title=基于Python的不同时间序列模型在上海市宝山区其他感染性腹泻病预测中的比较, columnId=1228016567632462653, journalTitle=现代预防医学, columnName=流行病与统计方法, runingTitle=null, highlight=null, articleAbstract=
目的

通过比较季节性自回归滑动平均（seasonal autoregressive integrated moving awerage，SARIMA）模型、Prophet模型、随机森林模型、极端梯度提升（eXtreme gradient boosting，XGBoost）模型和支持向量回归（support vector regression，SVR）模型对上海市宝山区其他感染性腹泻病发病率的预测效果，探索最优预测模型。

方法

利用2014—2022年上海市宝山区其他感染性腹泻病月发病率作为训练集，运用Python语言分别构建SARIMA模型、Prophet模型、含与不含气象特征的随机森林模型、含与不含气象特征的XGBoost模型以及含与不含气象特征的SVR模型，对2023—2024年月发病率进行预测。通过比较预测值与实际值的平均绝对误差（mean absolute error，MAE）、均方根误差（root mean square error，RMSE）和平均绝对百分比误差（mean absolute percentage error，MAPE），遴选出最优模型。

结果

2014—2024年上海市宝山区共报告其他感染性腹泻病6 868例，年均发病率28.81/10万，病例呈双峰季节性分布（夏季和冬春季高发）。通过比较不同时间序列模型对2023—2024年月发病率的预测效果，不含气象特征的XGBoost模型拟合精度指标综合表现最优（MAE=5.089，RMSE=6.844，MAPE=54.646%）。

结论

不含气象特征的XGBoost模型为宝山区其他感染性腹泻病短期预测的最佳模型，可为宝山区其他感染性腹泻病的预警和防控提供科学依据。

, authors=宗莲, 郑家乐, 向伦辉, 何凡, 刘效峰, 朱江, authorsList=宗莲, 郑家乐, 向伦辉, 何凡, 刘效峰, 朱江, authorCompany=null, correspAuthors=朱江, authorNote=

宗莲（1990—），女，硕士，主管医师，研究方向：疾病预防控制

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朱江，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=/MYi6zMGp8EuR5YHCUg8Rw==, magXml=9FNoBMEnvqDt5w6nfItrmQ==, pdfUrl=null, pdf=4xfyIDbpqDnd7nKrWGOSFg==, pdfFileSize=1626254, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=3Cv1laLTLl67UP+7xEcuLg==, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=BqFsHVewaw8/Ciai9khN9A==, mapNumber=null, fund=null)}, authors=[Author(id=1324077485285060765, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1324077480956539006, orderNo=0, firstName=null, middleName=null, lastName=null, nameCn=null, orcid=null, stid=null, country=null, authorPic=null, dead=0, email=null, emailSecond=null, emailThird=null, correspondingAuthor=0, authorType=1, ext={EN=AuthorExt(id=1324077486962782367, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1324077480956539006, authorId=1324077485285060765, language=EN, stringName=Lian ZONG, firstName=Lian, middleName=null, lastName=ZONG, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=null, address=Shanghai Baoshan District Center for Disease Control and Prevention (Shanghai Baoshan District Health Supervision Institute), Shanghai 201901, China, bio=null, bioImg=null, bioContent=null, aboutCorrespAuthor=null), CN=AuthorExt(id=1324077487055057056, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1324077480956539006, authorId=1324077485285060765, language=CN, stringName=宗莲, firstName=null, middleName=null, lastName=null, prefix=null, suffix=null, authorComment=null, nameInitials=null, affiliation=null, department=null, xref=null, address=上海市宝山区疾病预防控制中心（上海市宝山区卫生健康监督所），上海　201901, bio={"content":"

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注：RF模型为随机森林模型。

, figureFileSmall=NHi4KVWe/ZRUvTEJd1xkzw==, figureFileBig=hjbk2zXO6MlmX2+6MV9qlg==, tableContent=null), ArticleFig(id=1324077492352463056, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1324077480956539006, language=EN, label=Table 1, caption=

Parameters grid and optimal parameters of Prophet model

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参数参数范围最优参数
changepoint_prior_scale[0.1，0.05，0.1]0.1
seasonality_prior_scale[1.0，5.0，10.0]1.0
holidays_prior_scale[10.0，15.0]10.0
seasonality_mode[‘additive’，‘multiplicative’]‘multiplicative’
), ArticleFig(id=1324077492448932049, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1324077480956539006, language=CN, label=表1, caption=

Prophet模型参数网格和最优参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数参数范围最优参数
changepoint_prior_scale[0.1，0.05，0.1]0.1
seasonality_prior_scale[1.0，5.0，10.0]1.0
holidays_prior_scale[10.0，15.0]10.0
seasonality_mode[‘additive’，‘multiplicative’]‘multiplicative’
), ArticleFig(id=1324077492537012434, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1324077480956539006, language=EN, label=Table 2, caption=

Parameters grid and optimal parameters of random forest model

, figureFileSmall=null, figureFileBig=null, tableContent=
参数参数范围最优参数
含气温和降水特征仅含气温特征仅含降水特征不含气象特征
n_estimators[100，200，300]100100100100
max_depth[None，10，20，30]10NoneNone10
min_samples_leaf[2，5，10]2222
min_samples_split[2，5，10]5552
max_features[‘sqrt’，‘log2’，None]NoneNoneNoneNone
), ArticleFig(id=1324077492620898515, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1324077480956539006, language=CN, label=表2, caption=

随机森林模型参数网格和最优参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数参数范围最优参数
含气温和降水特征仅含气温特征仅含降水特征不含气象特征
n_estimators[100，200，300]100100100100
max_depth[None，10，20，30]10NoneNone10
min_samples_leaf[2，5，10]2222
min_samples_split[2，5，10]5552
max_features[‘sqrt’，‘log2’，None]NoneNoneNoneNone
), ArticleFig(id=1324077492713173204, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1324077480956539006, language=EN, label=Table 3, caption=

Parameters grid and optimal parameters of XGBoost model

, figureFileSmall=null, figureFileBig=null, tableContent=
参数参数范围最优参数
含气温和降水特征仅含气温特征仅含降水特征不含气象特征
max_depth[3，5，7]3373
learning_rate[0.01，0.1，0.2]0.010.010.010.01
n_estimators[100，200，300]100100100100
subsample[0.7，0.9]0.70.70.70.7
colsample_bytree[0.7，0.9]0.70.90.70.9
gamma[0，0.1]000.10
min_child_weight[1，3]3333
), ArticleFig(id=1324077492813836501, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1324077480956539006, language=CN, label=表3, caption=

XGBoost模型参数网格和最优参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数参数范围最优参数
含气温和降水特征仅含气温特征仅含降水特征不含气象特征
max_depth[3，5，7]3373
learning_rate[0.01，0.1，0.2]0.010.010.010.01
n_estimators[100，200，300]100100100100
subsample[0.7，0.9]0.70.70.70.7
colsample_bytree[0.7，0.9]0.70.90.70.9
gamma[0，0.1]000.10
min_child_weight[1，3]3333
), ArticleFig(id=1324077492893528278, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1324077480956539006, language=EN, label=Table 4, caption=

Parameters grid and optimal parameters of SVR model

, figureFileSmall=null, figureFileBig=null, tableContent=
参数参数范围最优参数
含气温和降水特征仅含气温特征仅含降水特征不含气象特征
C[0.1，1，10，100]10101010
gamma[0.01，0.1，1，‘scale’，‘auto’]‘auto’‘auto’0.10.1
epsilon[0.01，0.1，0.5，1]1111
kernel[‘rbf’，‘linear’，‘poly’]‘rbf’‘rbf’‘rbf’‘rbf’
), ArticleFig(id=1324077492973220055, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1324077480956539006, language=CN, label=表4, caption=

SVR模型参数网格和最优参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数参数范围最优参数
含气温和降水特征仅含气温特征仅含降水特征不含气象特征
C[0.1，1，10，100]10101010
gamma[0.01，0.1，1，‘scale’，‘auto’]‘auto’‘auto’0.10.1
epsilon[0.01，0.1，0.5，1]1111
kernel[‘rbf’，‘linear’，‘poly’]‘rbf’‘rbf’‘rbf’‘rbf’
), ArticleFig(id=1324077493061300440, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1324077480956539006, language=EN, label=Table 5, caption=

Comparison of accuracy coefficients of different time series models

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模型MAERMSEMAPE（%）
SARIMA模型11.02312.63771.253
Prophet模型16.73618.64393.961
随机森林模型5.3937.39034.417
XGBoost模型5.0896.84454.646
SVR模型6.9779.10841.782
), ArticleFig(id=1324077493136797913, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1324077480956539006, language=CN, label=表5, caption=

不同时间序列模型精度系数比较

, figureFileSmall=null, figureFileBig=null, tableContent=
模型MAERMSEMAPE（%）
SARIMA模型11.02312.63771.253
Prophet模型16.73618.64393.961
随机森林模型5.3937.39034.417
XGBoost模型5.0896.84454.646
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基于Python的不同时间序列模型在上海市宝山区其他感染性腹泻病预测中的比较
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宗莲 , 郑家乐 , 向伦辉 , 何凡 , 刘效峰 , 朱江
现代预防医学 | 流行病与统计方法 2026,53(7): 1172-1179
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现代预防医学 |流行病与统计方法 2026 , 53 (7) : 1172 -1179
基于Python的不同时间序列模型在上海市宝山区其他感染性腹泻病预测中的比较
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宗莲, 郑家乐, 向伦辉, 何凡, 刘效峰, 朱江
作者信息
  • 上海市宝山区疾病预防控制中心（上海市宝山区卫生健康监督所），上海　201901
通讯作者:
朱江，E-mail：
作者简介:

宗莲（1990—），女，硕士，主管医师，研究方向：疾病预防控制

Comparison of different Python-based time series models in the prediction of other infectious diarrhea diseases in Baoshan District, Shanghai
Lian ZONG, Jia-le ZHENG, Lun-hui XIANG, Fan HE, Xiao-feng LIU, Jiang ZHU
Affiliations
  • Shanghai Baoshan District Center for Disease Control and Prevention (Shanghai Baoshan District Health Supervision Institute), Shanghai 201901, China
出版时间: 2026-04-10 doi: 10.20043/j.cnki.MPM.202507165
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摘要
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目的

通过比较季节性自回归滑动平均（seasonal autoregressive integrated moving awerage，SARIMA）模型、Prophet模型、随机森林模型、极端梯度提升（eXtreme gradient boosting，XGBoost）模型和支持向量回归（support vector regression，SVR）模型对上海市宝山区其他感染性腹泻病发病率的预测效果，探索最优预测模型。

方法

利用2014—2022年上海市宝山区其他感染性腹泻病月发病率作为训练集，运用Python语言分别构建SARIMA模型、Prophet模型、含与不含气象特征的随机森林模型、含与不含气象特征的XGBoost模型以及含与不含气象特征的SVR模型，对2023—2024年月发病率进行预测。通过比较预测值与实际值的平均绝对误差（mean absolute error，MAE）、均方根误差（root mean square error，RMSE）和平均绝对百分比误差（mean absolute percentage error，MAPE），遴选出最优模型。

结果

2014—2024年上海市宝山区共报告其他感染性腹泻病6 868例，年均发病率28.81/10万，病例呈双峰季节性分布（夏季和冬春季高发）。通过比较不同时间序列模型对2023—2024年月发病率的预测效果，不含气象特征的XGBoost模型拟合精度指标综合表现最优（MAE=5.089，RMSE=6.844，MAPE=54.646%）。

结论

不含气象特征的XGBoost模型为宝山区其他感染性腹泻病短期预测的最佳模型，可为宝山区其他感染性腹泻病的预警和防控提供科学依据。

Python  /  时间序列模型  /  其他感染性腹泻病  /  预测
Objective

To compare the predictive performance of seasonal autoregressive integrated moving average (SARIMA) model, Prophet model, random forest (RF) model, extreme gradient boosting (XGBoost) model, and support vector regression (SVR) model on the incidence of other infectious diarrhea diseases in Baoshan District, Shanghai, and to explore the optimal forecasting model.

Methods

Using the monthly incidence rates of other infectious diarrhea diseases in Baoshan District, Shanghai from 2014 to 2022 as the training set, the SARIMA model, the Prophet model, the RF model with and without meteorological features, the XGBoost model with and without meteorological features, and the SVR model with and without meteorological features were constructed in Python to predict the monthly incidence rates from 2023 to 2024. The optimal model was selected by comparing the mean absolute error (MAE), root mean square error (RMSE) and mean absolute percentage error (MAPE) of the predicted and actual values.

Results

From 2014 to 2024, a total of 6 868 cases of other infectious diarrheal diseases were reported in Baoshan District, Shanghai, with an average annual incidence rate of 28.81 per 100 000 population. The cases exhibited a bimodal seasonal distribution (peaking in summer and winter-spring). By comparing the predictive performance of different time series models on the monthly incidence rate from 2023 to 2024, the XGBoost model without meteorological features showed the best comprehensive performance in terms of fitting accuracy indicators (MAE=5.089, RMSE=6.844, MAPE=54.646%).

Conclusion

The XGBoost model without meteorological features is the best model for short-term prediction of other infectious diarrhea diseases in Baoshan District, which can provide a scientific basis for early warning and prevention of other infectious diarrhea diseases in Baoshan District.

Python  /  Time series model  /  Other infectious diarrhea diseases  /  Forecast
宗莲, 郑家乐, 向伦辉, 何凡, 刘效峰, 朱江. 基于Python的不同时间序列模型在上海市宝山区其他感染性腹泻病预测中的比较. 现代预防医学, 2026 , 53 (7) : 1172 -1179 . DOI: 10.20043/j.cnki.MPM.202507165
Lian ZONG, Jia-le ZHENG, Lun-hui XIANG, Fan HE, Xiao-feng LIU, Jiang ZHU. Comparison of different Python-based time series models in the prediction of other infectious diarrhea diseases in Baoshan District, Shanghai[J]. Modern Preventive Medicine, 2026 , 53 (7) : 1172 -1179 . DOI: 10.20043/j.cnki.MPM.202507165
正文
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其他感染性腹泻病是由多种病原体引起的，除霍乱、细菌性或阿米巴性痢疾、伤寒及副伤寒外以腹泻为主要症状的法定丙类传染病[1]。监测数据显示，2024年上海市其他感染性腹泻病已超越手足口病跃居丙类传染病发病数第二位。因此，寻求有效的时间序列模型对其他感染性腹泻病进行早期预警具有重要的现实意义。时间序列模型作为分析和预测时序数据的一类统计或机器学习方法[2]，已被广泛应用于其他感染性腹泻病发病的预测研究[3-4]，但针对不同模型预测效果比较的系统性研究较为有限。本研究利用上海市宝山区2014年1月—2024年12月其他感染性腹泻病的报告信息分别建立季节性自回归滑动平均（seasonal autoregressive integrated moving average，SARIMA）模型、Prophet模型、随机森林模型、极端梯度提升（eXtreme gradient boosting，XGBoost）模型和支持向量回归（support vector regression，SVR）模型，通过评估在测试集上的预测效果，遴选出最适合宝山区其他感染性腹泻病发病趋势预测的模型，从而为本地疫情的早期预警、动态监测和防控处置提供科学依据。
1　资料与方法
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1.1　资料来源
其他感染性腹泻病发病资料来自中国疾病预防控制信息系统，为2014年1月—2024年12月报告、现住址为上海市宝山区的所有已审核个案。气温和降水量数据来源于美国国家海洋和大气管理局下设的国家环境信息中心；人口资料来源于上海市宝山区统计年鉴。
1.2　研究方法
1.2.1　SARIMA模型
SARIMA模型在自回归滑动平均（autoregressive integrated moving average，ARIMA）模型基础上，增加了季节性参数，专门用于分析预测具有季节性等周期规律的时间序列数据，是一种在气象、经济、医疗卫生领域广泛应用的经典时间序列模型。该模型一般为ARIMA（p，d，q）（P，D，Q）s的形式，p为自回归阶数，d为非季节性差分阶数，q为滑动平均阶数；P为季节性自回归阶数，D为季节性差分阶数，Q为季节性滑动平均阶数，s为周期长度。本研究使用的为其他感染性腹泻病月发病数据，因此s=12。建模步骤一般如下：（1）平稳化序列：观察原始时间序列的趋势和周期变化，对时间序列进行单位根（augmented Dickey-Fuller，ADF）检验，判断序列的平稳性，对不平稳序列采取差分使其平稳化；（2）模型参数选取：对参数p、q、P、Q建立参数网格进行搜索，依据赤池信息准则（Akaike information criterion，AIC）、贝叶斯信息准则（Bayesian information criterion，BIC）等，筛选出模型最优参数；（3）效果评估：对选出模型的残差进行Ljung-Box白噪声检验和正态性检验。
1.2.2　Prophet模型
该模型是由Facebook开发的一个开源时间序列预测模型，于2017年发布，适合用于处理具有趋势性、季节性和节假日效应的数据[5]，其核心采用加法模型分解时间序列为趋势项、季节项和节假日项，表达式可写为：
其中g（t）为趋势项，用于拟合非周期的趋势变化；s（t）为周期项，用傅里叶级数建立周期模型，以拟合季、月、周、日等周期性变化规律；h（t）为节假日项，用于处理节假日因素对预测的影响；ε（t）为噪声项，表示未预测到的随机扰动。本研究通过网格搜索方式调整参数组合，得到最佳的模型预测效果。
1.2.3　随机森林模型
随机森林模型为一种基于Bagging集成学习方法的机器学习模型，其本质是一个包含多个决策树的分类器。决策树是一个基本的分类或回归模型，可以通过系列特征将数据分割成不同类别或预测一个连续的数值[6]。随机森林模型通过构建多个决策树提高准确性和鲁棒性，可不受多重共线性特征影响，对非线性关系数据处理结果较好。模型算法主要是对每个决策树，进行有放回的随机抽样获得样本集，从所有的M个特征中随机选取m个特征（m≤M，默认），在树的每个分裂点，根据所选特征进行最佳分裂，直到得到最终结果。在树的构建过程中，每棵树都会完整生长而不被剪枝。最后根据所有决策树的预测结果，进行投票或回归得到最终结果。本研究通过网格搜索方式遍历超参数组合，对每种组合进行训练和评估，选取性能指标最优的参数组合构建模型。
1.2.4　XGBoost模型
XGBoost模型基于梯度提升框架进行集成学习。它通过构建一系列决策树等弱预测模型，然后加权平均这些模型的预测结果来学习复杂的非线性关系，提高整体的预测性能[7]。模型将损失函数进行二阶泰勒展开，通过L1和L2正则化优化模型性能，防止过拟合。XGBoost模型在每棵树的构建过程中使用了更精细的剪枝策略，在分裂点可并行评估所有分割方式。其目标函数表示为：
其中第一部分表示误差损失，用以衡量实际值和预测值的差异；第二部分Ω（ft）表示正则化项，通过叶子节点数和叶子节点权重等限制模型的复杂度。
1.2.5　SVR模型
SVR模型是机器学习领域用于回归问题的一种监督学习模型，相较于传统线性回归，SVR模型可通过核方法捕捉非线性关系，常用的核函数包括线性核、高斯核、多项式核等。模型的核心目标是试图找到一个最优的超平面，使所有输入的数据点到这个平面的距离尽可能小，同时也引入正则化项控制模型的复杂度避免过拟合。其原理是在线性函数两侧设置一个间距为ε的间隔带，对所有落入间隔带内的样本不计算损失，最后通过最小化损失和最大化间隔来优化模型[8]。其目标函数为：
其中w、b为超平面参数，C为正则化参数，控制模型的复杂度和误差；ξi、i为松弛变量，表示允许超出ε带的范围。本研究通过网格搜索和交叉验证方法来寻求最佳参数来构建最适合预测发病率的模型。
1.2.6　模型评价和选取
本研究利用2014年1月—2022年12月上海市宝山区其他感染性腹泻病月发病率作为训练集，并用2023年1月—2024年12月的月发病率作为测试集，通过比较不同时间序列模型的预测值和实际值的平均绝对误差（mean absolute error，MAE）、均方根误差（root mean square error，RMSE）、平均绝对百分比误差（mean absolute percentage error，MAPE），最后遴选出最适合预测上海市宝山区其他感染性腹泻病发病率趋势的模型。
1.3　统计学分析
应用Microsoft Excel 2019进行数据处理和描述性统计，分别使用Python 3.9中的statsmodels库进行数据平稳性检验、SARIMA模型构建和互相关函数（cross-correlation function，CCF）分析，scikit-learn库进行网格搜索、随机森林模型和SVR模型的构建以及精度指标的计算，prophet库进行Prophet模型构建、xgboost库进行XGBoost模型的构建、matplotlib库进行数据可视化。检验水准α=0.05。
2　结果
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2.1　原始序列分析
2014—2024年，宝山区共报告其他感染性腹泻病6 868例，年发病率在10.21/10万（2022年）~48.56/10万（2019年）间波动，年均报告发病率为28.81/10万。月份分布上看，整体呈现双峰分布，两个高峰分别出现在6—9月（37.57%）及12月—次年3月（35.06%）。分别绘制2014年1月—2024年12月宝山区月平均气温、降水量与其他感染性腹泻病发病率关系的散点图，见图1。Spearman相关性分析显示，月平均气温与发病率的相关系数ρ=0.109（95%CI：-0.072~0.289，P=0.212），降水量与发病率的相关系数ρ=0.075（95%CI：-0.105~0.248，P=0.391），均呈微弱正相关，但无显著统计学意义。
2.2　时间序列模型构建
2.2.1　SARIMA模型构建
利用seasonal_decompose函数对2014—2024年上海市宝山区其他感染性腹泻病月度发病率时间序列进行季节性分解，绘制分解序列图，观察其总体趋势、季节波动和残差分布情况，2020年之前宝山区其他感染性腹泻病发病率总体较为平稳，2020和2022年有明显的降低。月度发病率存在明显季节性，发病率时间序列的残差在一定范围内波动。见图2。
划分2014年1月—2022年12月数据为训练集，2023年1月—2024年12月数据为测试集。利用adfuller函数对发病率时间序列进行平稳性检验，Dickey-Fuller统计量为-3.232（P=0.018），为平稳序列，无需差分。考虑到数据有明显的季节性周期，对序列进行一阶季节性差分，因此选取模型参数d=0，D=1。为寻找最优的p、q、P、Q参数，利用网格搜索方法并结合SARIMAX函数构建模型，根据AIC准则，最终选取p=1，q=4，P=2，Q=0。ARIMA（1，0，4）（2，1，0）12模型AIC值为564.936。对模型残差绘制密度直方图、正态Q-Q图和自相关图进行可视化诊断，同时进行Ljung-Box白噪声检验（χ2=0.211，P=0.646），差异无统计学意义，残差为白噪声序列。见图3。
2.2.2　Prophet模型构建
对Prophet模型的参数建立网格，由于发病率为月度数据，且有明显季节性，因此yearly_seasonality参数选择为True。利用训练集数据通过网格搜索用Prophet函数构建模型，进行交叉验证，并根据精度指标MAE最小的原则选取最优参数，见表1。用最佳参数重新训练模型，用add_country_holidays方法加入中国法定节假日作为节假日参数，对2023—2024年月发病率进行预测和效果评价。对最优模型的残差进行Ljung-Box检验（χ2=31.491，P<0.001），残差仍存在显著自相关。
2.2.3　随机森林模型构建
通过CCF分别检测上海市宝山区的月平均气温、降水量与其他感染性腹泻病月发病率之间的滞后相关性，显示月均气温的1~3阶滞后与发病率均未呈现统计学显著相关性（P>0.05），降水量的1阶滞后与发病率之间的相关系数达到显著性水平（P=0.046）。分别构建含气温和降水特征、仅含气温特征、仅含降水特征和不含气象特征的随机森林模型，对模型参数建立网格，使用Random Forest Regressor方法初始化模型，设置交叉验证参数cv=5，使用GridSearchCV函数分别进行网格搜索并选取最优参数，见表2。通过比较各个模型的MAE，不含气象特征的随机森林模型预测效果更佳，见图4。对最佳随机森林模型的残差进行Ljung-Box检验（χ2=0.356，P=0.551），差异无统计学意义，残差为白噪声序列。
2.2.4　XGBoost模型构建
对上海市宝山区其他感染性腹泻病的月发病率序列分别构建含气温和降水特征、仅含气温特征、仅含降水特征和不含气象特征的XGBoost模型，对模型的参数建立网格，使用XGBRegressor方法初始化模型，设置交叉验证参数cv=5，用GridSearchCV函数进行网格搜索并选取最优参数，见表3。通过比较各个模型的MAE，不含气象特征的XGBoost模型预测效果更佳，见图5。对最佳XGBoost模型的残差进行Ljung-Box检验（χ2=12.878，P<0.001），残差仍存在显著自相关。
2.2.5　SVR模型构建
对上海市宝山区其他感染性腹泻病的月发病率序列分别构建含气温和降水特征、仅含气温特征、仅含降水特征和不含气象特征的SVR模型，使用Standard Scaler方法对特征进行标准化。对SVR模型的参数建立网格，使用SVR函数初始化模型，设置交叉验证参数cv=5，用GridSearchCV函数进行网格搜索并选取最优参数，见表4。通过比较各个模型的MAE，不含气象特征的SVR模型预测效果更佳，见图6。对最佳SVR模型的残差进行Ljung-Box检验（χ2=34.017，P<0.001），残差仍存在显著自相关。
2.2.6　最佳预测模型选取
分别选取上述不同类型的最优时间序列模型预测2023年1月—2024年12月上海市宝山区其他感染性腹泻病的月发病率情况，并与实际值进行比较，通过计算MAE、RMSE和MAPE，综合比较可见不含气象特征的XGBoost模型预测效果较其他模型更为优秀（MAE=5.089，RMSE=6.844，MAPE=54.646%）。见表5和图7。
3　讨论
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研究显示，随机森林、XGBoost和SVR模型的预测性能总体优于SARIMA模型和Prophet模型，这可能与机器学习模型在处理非线性关系和特征交互上的固有优势有关，这也与诸多研究的结果一致[9-10]。SARIMA模型虽然能捕捉时间序列的趋势和季节性，但是对复杂的非线性关系建模能力有限，Prophet模型能灵活处理趋势变化、周期规律和节假日效应，但在处理非线性效应和外部变量关系时稍逊一筹，导致了在测试集上表现欠拟合[11]。相比之下，随机森林模型和XGBoost模型可通过决策树的递归分割，对变量间的非线性交互效应自动建模；SVR模型则通过核函数将数据映射到高维空间，拟合复杂的非线性边界[12]。本研究中，XGBoost模型较随机森林模型和SVR模型表现出更低的MAE与RMSE值，预测精度更为优秀，这可能与模型的固有机制相关。XGBoost模型采用梯度提升框架，通过序列化地构建决策树并专注于修正前序模型的残差，使其更擅长捕捉时间序列中复杂的非线性模式，其内置的正则化项有效控制了模型复杂度，避免了过拟合，从而获得了更好的泛化性能。而随机森林模型的Bagging策略虽能有效降低方差，但其精度上限可能不如Boosting策略；而SVR的性能则更依赖于核函数与超参数的精细调优[13]。
SARIMA模型作为传统时间序列模型，进行残差诊断是模型构建的必要步骤，其目标是验证模型是否完全提取了数据中的线性依赖关系；而机器学习模型更关注预测精度，将残差分析视为一种辅助诊断工具而非强制性步骤，其通过正则化、交叉验证、集成学习等不同机制来控制过拟合，而非完全依赖残差的独立性假设。为了体现研究的严谨性，对所有采用模型的残差进行了Ljung-Box检验，显示SARIMA、随机森林模型的残差序列为白噪声，而Prophet、XGBoost和SVR模型的残差序列均还存在自相关。但基于机器学习模型显著更低的MAE值和RMSE值，它们仍然是更优秀的预测模型，残差中剩余的自相关信息对预测精度的提升潜力已非常有限。
本研究在构建不同类型的时间序列模型时，用网格搜索的方法选取超参数，存在着一定的局限性[14]。一是，网格搜索本质是在预设的离散参数组合下进行穷举搜索，参数组合的数量会随着参数数量和预设值数量呈指数级增长，计算成本会因为参数组合爆炸和时序重新训练验证急剧升高，因此需在搜索效率和模型性能之间做出平衡；二是，参数网格为离散化采样，当最优参数位于网格点之间时，易遗漏连续参数的最优解，且无法捕捉到有些关键参数之间的协同和交互作用；另外网格搜索对参数的静态优化，难以捕捉其他感染性腹泻病在真实世界中存在的局部暴发和波动特征，虽然在测试集上表现较好，但对长期预测的泛化能力仍存在不足。
尽管Spearman相关性分析显示月平均气温、降水量与其他感染性腹泻发病率之间均无显著的统计学关联，但也未排除可能存在复杂的非线性关联。基于CCF分析，本研究在特征工程中引入了平均气温、降水量及降水量的1阶滞后项，通过构建不同特征组合的模型，评估并对比其精度指标，以确定最优特征集。虽然大量文献证实了气温与降水对感染性腹泻发病存在相关性[15-16]，但本研究发现在引入这些气象特征后，所有机器学习模型的预测性能均未得到改善，反而有所下降。这一的结果可能由以下原因导致：首先，时间特征是气象季节性的强代理变量，模型已通过月份特征间接学习到了气象的季节性变化信号，引入的气温和降水特征反而成为了冗余信息；其次，气象因素的影响可能存在滞后效应与非线性的复杂机制，简单的月均气温可能掩盖了短期的气温波动对其他感染性腹泻病发病率的影响，而未能有效刻画这一关系；最后，其他感染性腹泻病的发病可能还会受到更多因素的影响，如病原谱变化、新冠疫情、公众健康行为改变等因素，可能掩盖了气象因素的独立贡献。这一发现提示，在利用机器学习模型进行流行病学预测时，应审慎使用依赖于固定特征的预测模型。未来的预警系统应着眼于动态和自适应型，能够定期评估各预测因子的效用，并在信号减弱时自动降权或剔除该因子。在今后的研究中，也可尝试构建混合模型[17]，采用随机搜索、贝叶斯优化等方法寻找最佳参数[18]，并引入更多的环境因子和社会特征[19]，来提高模型的精准性和鲁棒性，为宝山区其他感染性腹泻病提供更可靠有效的预警参考。
基金
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  • 上海市加强公共卫生体系建设三年行动计划（2023—2025年）重点学科(GWVI-11.1-06)
  • 上海市宝山区科学技术委员会医学卫生项目(2025-E-11)
  • 宝山区传染病流行病学重点学科项目(BSZK-2023-A20)
  • 宝山区卫生健康委优青（育才）计划(BSWSYC-2023-21)
文献
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2026年第53卷第7期
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doi: 10.20043/j.cnki.MPM.202507165
  • 接收时间：2025-07-13
  • 首发时间：2026-11-02
  • 出版时间：2026-04-10
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  • 收稿日期：2025-07-13
基金
上海市加强公共卫生体系建设三年行动计划（2023—2025年）重点学科(GWVI-11.1-06)
上海市宝山区科学技术委员会医学卫生项目(2025-E-11)
宝山区传染病流行病学重点学科项目(BSZK-2023-A20)
宝山区卫生健康委优青（育才）计划(BSWSYC-2023-21)
作者信息
    上海市宝山区疾病预防控制中心（上海市宝山区卫生健康监督所），上海　201901

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Number of
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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
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