Developing nonlinear time-varying weighted combined prediction framework for infectious diseases: validation with respiratory infectious diseases and sexually transmitted infections
5 affiliations
- 1Key Lab of Environmental Stress and Chronic Disease Control & Prevention, China Medical University, Shenyang, 110122 PR China
- 2Department of Epidemiology & Health Statistics, School of Public Health, China Medical University, Shenyang, 110122 PR China
- 3Liaoning Provincial Center for Disease Control and Prevention, Shenyang, 110005 PR China
- 4Department of Anesthesiology & Cancer Hospital of China Medical University Liaoning Cancer Hospital & Institute, Shenyang, 110042 PR China
- 5Department of Epidemiology & Health Statistics, Key Lab of Environmental Stress and Chronic Disease Control & Prevention, School of Public Health, China Medical University, No.77 Puhe Road, Shenyang North New Area, Shenyang, Liaoning Province 110122 PR China
Abstract
Background: Traditional combined prediction models often face limitations in their ability to capture complex nonlinear relationships and weighting.
Objective: To address these challenges, we propose a nonlinear time-varying weighted combined prediction framework that integrates deep learning algorithms, optimized activation functions, and multifractal theory. This approach results in a robust combined prediction framework.
Methods: The study utilized the weekly total number of influenza cases, the daily number of confirmed cases of COVID-19, and the monthly incidence rates of HIV/AIDS and syphilis as real-world samples. Leveraging mutual information theory, combined prediction models were constructed for influenza and COVID-19 data, employing both linear and time-varying weighting methods. For HIV/AIDS and syphilis data, we applied Empirical Mode Decomposition to decompose the time series, then integrated the decomposed components via linear and time-varying weighting methods. Furthermore, multifractal theory was employed to establish an evaluation framework. The performance of individual models, linear weighted combined models, and activation function-based deep learning combined models were evaluated. This finding provides practical guidance on selecting deep learning approaches and activation functions under nonlinear time-varying weighting framework.
Results: The TCN based on Swish activation function for influenza had the best generalization and accuracy (MAE = 145.391, NMSE = 0.032, IA = 0.992). The LSTM based on Swish activation function had similar generalization and accuracy (MAE = 148.046, NMSE = 0.033, IA = 0.991). The TCN based on Swish activation function for COVID-19 had the best generalization and accuracy (MAE = 25942.744, NMSE = 0.050, IA = 0.986). The LSTM based on ELU activation function for HIV/AIDS exhibited superior predictive performance (MAE = 0.066, NMSE = 0.237, MAPE = 0.081, IA = 0.930). The LSTM based on the adjustment of ELU activation function for syphilis demonstrated superior generalization capability and accuracy (MAE = 0.096, NMSE = 0.215, MAPE = 0.037, IA = 0.931). All of them outperform linear combined prediction models.
Conclusions: The proposed nonlinear time-varying weighted combined prediction (NTVWCP) model demonstrates improved predictive accuracy, robustness, and generalization capability compared to traditional models and conventional weighting methods.
Graphical Abstract:
Supplementary Information: The online version contains supplementary material available at https://doi.org/10.1186/s12889-026-28937-2.
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BibTeX
@article{cai2026developing,
title = {{Developing nonlinear time-varying weighted combined prediction framework for infectious diseases: validation with respiratory infectious diseases and sexually transmitted infections}},
author = {Weijie Cai and Zhi Li and Yueya Chu and Yi Wang and Xueying Xu and Litao Wu and Zhouting Yao and Hongbo Liu},
journal = {BMC Public Health},
year = {2026},
month = aug,
doi = {10.1186/s12889-026-28937-2},
url = {https://doi.org/10.1186/s12889-026-28937-2},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - JOUR
TI - Developing nonlinear time-varying weighted combined prediction framework for infectious diseases: validation with respiratory infectious diseases and sexually transmitted infections
AU - Weijie Cai
AU - Zhi Li
AU - Yueya Chu
AU - Yi Wang
AU - Xueying Xu
AU - Litao Wu
AU - Zhouting Yao
AU - Hongbo Liu
PY - 2026
DA - 2026/08/08
JO - BMC Public Health
DO - 10.1186/s12889-026-28937-2
UR - https://doi.org/10.1186/s12889-026-28937-2
AB - Background: Traditional combined prediction models often face limitations in their ability to capture complex nonlinear relationships and weighting. Objective: To address these challenges, we propose a nonlinear time-varying weighted combined prediction framework that integrates deep learning algorithms, optimized activation functions, and multifractal theory. This approach results in a robust combined prediction framework. Methods: The study utilized the weekly total number of influenza cases, the daily number of confirmed cases of COVID-19, and the monthly incidence rates of HIV/AIDS and syphilis as real-world samples. Leveraging mutual information theory, combined prediction models were constructed for influenza and COVID-19 data, employing both linear and time-varying weighting methods. For HIV/AIDS and syphilis data, we applied Empirical Mode Decomposition to decompose the time series, then integrated the decomposed components via linear and time-varying weighting methods. Furthermore, multifractal theory was employed to establish an evaluation framework. The performance of individual models, linear weighted combined models, and activation function-based deep learning combined models were evaluated. This finding provides practical guidance on selecting deep learning approaches and activation functions under nonlinear time-varying weighting framework. Results: The TCN based on Swish activation function for influenza had the best generalization and accuracy (MAE = 145.391, NMSE = 0.032, IA = 0.992). The LSTM based on Swish activation function had similar generalization and accuracy (MAE = 148.046, NMSE = 0.033, IA = 0.991). The TCN based on Swish activation function for COVID-19 had the best generalization and accuracy (MAE = 25942.744, NMSE = 0.050, IA = 0.986). The LSTM based on ELU activation function for HIV/AIDS exhibited superior predictive performance (MAE = 0.066, NMSE = 0.237, MAPE = 0.081, IA = 0.930). The LSTM based on the adjustment of ELU activation function for syphilis demonstrated superior generalization capability and accuracy (MAE = 0.096, NMSE = 0.215, MAPE = 0.037, IA = 0.931). All of them outperform linear combined prediction models. Conclusions: The proposed nonlinear time-varying weighted combined prediction (NTVWCP) model demonstrates improved predictive accuracy, robustness, and generalization capability compared to traditional models and conventional weighting methods. Graphical Abstract: Supplementary Information: The online version contains supplementary material available at https://doi.org/10.1186/s12889-026-28937-2.
SN - 1471-2458
ER -