
==== Front
Chin Med J (Engl)
Chin Med J (Engl)
CM9
Chinese Medical Journal
0366-6999
2542-5641
Lippincott Williams & Wilkins Hagerstown, MD

CMJ-2022-3491
10.1097/CM9.0000000000003238
00013
3
Correspondence
Influenza time series prediction models in a megacity from 2010 to 2019: Based on seasonal autoregressive integrated moving average and deep learning hybrid prediction model
Yang Jin 1 2
Yang Liuyang 2 3
Li Gang 4
Du Jing 4
Ma Libing 2 5
Zhang Ting 2
Zhang Xingxing 2
Yang Jiao 2
Feng Luzhao 2
Yang Weizhong 2
Wang Chen 2 6
Ni Jing
1 Department of Epidemiology, School of Public Health, Southern Medical University, Guangzhou, Guangdong 510515, China
2 School of Population Medicine and Public Health, Chinese Academy of Medical Sciences & Peking Union Medical College, Beijing 100730, China
3 The Third Affiliated Hospital of Kunming Medical University, Yunnan Cancer Hospital, Kunming, Yunnan 650106, China
4 Beijing Centre for Disease Prevention and Control, Beijing 100013, China
5 Department of Respiratory and Critical Care Medicine, Affiliated Hospital of Guilin Medical University, Guilin, Guizhou 561113, China
6 National Clinical Research Center for Respiratory Diseases, China-Japan Friendship Hospital, Beijing 100029, China
Correspondence to: Weizhong Yang, School of Population Medicine and Public Health, Chinese Academy of Medical Sciences & Peking Union Medical College, Beijing 100730, China E-Mail: yangweizhong@cams.cn;
Chen Wang, School of Population Medicine and Public Health, Chinese Academy of Medical Sciences & Peking Union Medical College, Beijing 100730, China;National Clinical Research Center for Respiratory Diseases, China-Japan Friendship Hospital, Beijing 100029, China E-Mail: wangchen@pumc.edu.cn
09 8 2024
20 9 2024
137 18 22422244
23 12 2023
Copyright © 2024 The Chinese Medical Association, produced by Wolters Kluwer, Inc. under the CC-BY-NC-ND license.
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives License 4.0 (CCBY-NC-ND), where it is permissible to download and share the work provided it is properly cited. The work cannot be changed in any way or used commercially without permission from the journal. http://creativecommons.org/licenses/by-nc-nd/4.0

OPEN-ACCESSTRUE
SDCT
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pmcTo the Editor: Influenza viruses are constantly evolving and have the ability to infect a wide range of hosts, leading to recurrent infections and ongoing morbidity.[1] In China, the surveillance for respiratory infectious diseases has been specifically performed for influenza and other respiratory infectious diseases. However, the current surveillance system relies heavily on the analysis of clinically confirmed influenza cases, which has lagged behind the times.[2] It is very important to establish a more accurate influenza prediction model, particularly in densely populated megacities. Our research aims to explore and develop more accurate and sensitive models for predicting influenza outbreaks.

The data of this study were provided by Beijing infectious disease surveillance and early warning system for medical institutions and have been anonymized. We selected the influenza-like illness (ILI) patients and influenza polymerase chain reaction-positivity patients from the 26th week of 2010 to the 25th week of 2019 for modeling. We considered ILI%, influenza positive rate, and the product of ILI% and influenza positive rate (ILI% × influenza positive rate) as independent variables.

We established seasonal autoregressive integrated moving average (SARIMA) models for ILI%, influenza positive rate, and ILI% × influenza positive rate respectively, starting from the summer point, the peak bottom point, and the peak rising point [Supplementary Method, http://links.lww.com/CM9/C91]. After selecting the best prediction point by R square (R2) and Akaike information criterion (AIC), we compared the model performances of different parameters at that point using the SARIMA model.

We established a hybrid model based on the long short-term memory (LSTM) architecture. For supervised learning, we implemented a “slider” mechanism with a period of 52 and a step size of 1 along the time axis. As the “slider” progressed along the timeline, features and labels were dynamically defined. In Path 1, the data directly interfaced with a Self-Attention block, enabling the model to focus on pivotal features while disregarding less influential ones. Path 2 involved routing the data through ZeroPadding, Convolution, and Globalpooling layers before linking with a ReSNet block. Path 3 incorporated data into an LSTM layer, then merged the outcomes of Path 1 and Path 2. The data then passed through the Dense, Dropout, and GlobalPooling layers after concatenation. A Linear activation function was applied to the final Dense layer to yield prediction results [Supplementary Figure 1, http://links.lww.com/CM9/C91].

Finally, R-square (R2) and expected variance were applied to compare the hybrid LSTM prediction model with the best model selected by SARIMA.

Between the 26th week of 2010 and the 25th week of 2019, there were 542,602,473 outpatient and emergency department visits, of which 6,753,116 met the ILI criteria, and the ILI% was 1.24%. Of all the ILI patients, 94,813 samples were tested and 15,883 (16.75%) were positive for influenza [Supplementary Table 1, http://links.lww.com/CM9/C91]. Time series decomposition of ILI%, influenza positive rate, and ILI% × influenza positive rate revealed seasonal and periodic patterns [Supplementary Figure 2, http://links.lww.com/CM9/C91]. The trends and peak times exhibited a consistent alignment across ILI%, influenza positive rate, and ILI% × influenza positive rate [Supplementary Figure 3, http://links.lww.com/CM9/C91].

SARIMA models were initially constructed for the summer point, the peak bottom point, and the peak rising point. R2 and AIC were used to compare the fitting effects of the models. The results suggested that modeling at the peak rising point was better than those at the other two forecast points, and the prediction model of influenza positive rate showed the best effect [Supplementary Figure 4, http://links.lww.com/CM9/C91]. According to the comparison of models at different forecast points, the peak rising point was finally selected to establish the SARIMA model. The data were stable after the first order difference [Supplementary Figure 5, http://links.lww.com/CM9/C91]. The best SARIMA model for ILI% was (1,1,1) (1,1,1)52 with the R2 of 0.590 and the expected variance of 0.596. The model for influenza positive rate was (2,1,3) (1,1,1)52 with the R2 of 0.836 and the expected variance of 0.840. The model for ILI% × influenza positive rate was (5,1,7) (1,1,1)52, the R2 was 0.754, and the expected variance was 0.760. We further constructed hybrid LSTM model for ILI% (R2 was 0.781 and expected variance was 0.782), influenza positive rate (R2 was 0.945 and expected variance was 0.945), and ILI% × influenza positive rate (R2 was 0.868 and expected variance was 0.868). The results showed that the hybrid LSTM model performed better than the SARIMA model in terms of ILI%, influenza positive rate, and ILI% × influenza positive rate [Figure 1].

Figure 1 Comparison of the SARIMA and LSTM models. The peak rising point was set as the 52nd week of 2018 (abbreviated as 201852). Modeling was conducted from 201026 to 201851 to predict the influenza trend from 201852 to 201925. The vertical coordinates of LSTM method were normalized. CI: Confidence interval. EX: Expected variance; ILI: Influenza-like illness; LSTM: Long short-term memory; SARIMA: Seasonal autoregressive integrated moving average.

To further compare the two models for different prediction periods, we incrementally extended the prediction window from the 1st week to the 26th week. The values for R2 and expected variance of the hybrid LSTM model were higher than those of SARIMA model for ILI%, influenza positive rate, and ILI% × influenza positive rate. This suggested that the hybrid LSTM model could maintain a good prediction effect with the extension of the prediction period. On the contrary, the prediction effect of SARIMA model decreased with the extension of the prediction period [Supplementary Figure 6, http://links.lww.com/CM9/C91].

In megacities, characterized by dense populations and numerous public spaces, local or regional outbreaks and epidemics of influenza can occur with ease. This study applies time series forecasting and deep learning techniques to construct prediction models for influenza during non-pandemic periods in such settings. By comparing the model effects at different prediction points, we found optimal predictive efficacy when models were developed during the peak rise period of influenza. Both the SARIMA and the hybrid LSTM models showed good prediction effects in terms of ILI%, influenza positive rate, and ILI% × influenza positive rate. Furthermore, our findings highlight the superior predictive performance of the influenza positivity rate. Notably, the hybrid LSTM model, boasting higher R2 and expected variance values, outperformed the SARIMA model, indicating its suitability for long-term forecasting.

Previous studies have extensively documented the effectiveness of SARIMA models in influenza prediction.[3] However, these studies have often overlooked a crucial aspect: determining the most accurate prediction time point. Therefore, we conducted a comprehensive comparison of results across various prediction points. Our results showed that the model at the peak rising point performed better than those at the summer point and the peak bottom point for ILI%, influenza positive rate, and ILI% × influenza positive rate. This suggested that the SARIMA model displayed the best prediction effect at the peak rising point when predicting the trend of influenza in megacities.

While the application of deep learning models in infectious disease research is gaining attention, its utilization remains relatively limited.[4] In our study, we incorporated parallel Self-Attention block and RESNET block based on LSTM, resulting in a novel hybrid LSTM model. This enhanced model demonstrated greater robustness and comprehensive data feature extraction capabilities. The results showed that the effect of the hybrid LSTM model was better than that of the SARIMA model. Additionally, we evaluated both models across various prediction periods ranging from 1st week to 26th weeks. Remarkably, the hybrid LSTM model maintained strong predictive efficacy even with extended prediction periods, whereas the performance of the SARIMA model notably declined with longer forecast horizons. This indicated that the hybrid LSTM model had a good prediction effect and was more suitable for long-term prediction of influenza, while SARIMA performed well in short-term prediction. Despite the increased complexity of the hybrid LSTM model, measures were taken to mitigate potential issues such as gradient disappearance. The implementation of short-circuit connections effectively addressed this concern, while the utilization of high-performance graphics processing units facilitated efficient model training, overcoming challenges associated with increased computational demand.

In conclusion, enhancing the timeliness and sensitivity of influenza and other respiratory infectious disease predictions holds significant importance. Our findings highlight the efficacy of combining ILI% data with the hybrid LSTM model to accurately forecast influenza epidemic trends. Influenza-like cases and influenza positive rate played complementary roles in the prediction process. In addition, the hybrid LSTM model also showed good prediction effect for ILI% × influenza positive rate, which was generally used to estimate the activity intensity of influenza.

Acknowledgement

We thank staff members at the Beijing Centre for Disease Prevention and Control, and staff members at the Chinese Center for Disease Control and Prevention.

Fundings

This work was supported by grants from the Chinese Academy of Medical Sciences (CAMS) Innovation Fund for Medical Sciences (No.2021-I2M-1-044); the High-level Public Health Talent Development Program of Beijing (Discipline Leader-01-09); and the Postdoctoral Fellowship Program of CPSF (No.GZC20231052).

Conflicts of interest

None.

Supplementary Material

How to cite this article: Yang J, Yang LY, Li G, Du J, Ma LB, Zhang T, Zhang XX, Yang J, Feng LZ, Yang WZ, Wang C. Influenza time series prediction models in a megacity from 2010 to 2019: Based on seasonal autoregressive integrated moving average and deep learning hybrid prediction model. Chin Med J 2024;137:2242–2244. doi: 10.1097/CM9.0000000000003238
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