tetano
Editor, Senior Moderator
Front Public Health
. 2026 May 5:14:1806095.
doi: 10.3389/fpubh.2026.1806095. eCollection 2026.
A stacked ensemble model with NNLS-based weighting for influenza forecasting: a case study of Anhui Province, China
Qingqing Zhu[SUP] #[/SUP][SUP] 1 2 [/SUP], Minglei Zhu[SUP] #[/SUP][SUP] 2 [/SUP], Yuhang Cai[SUP] 3 [/SUP], Junwei Xiang[SUP] 3 [/SUP], Shuwen Li[SUP] 1 [/SUP], Biao Zhu[SUP] 1 [/SUP], Meng Zhu[SUP] 1 [/SUP], Lei Gong[SUP] 1 [/SUP], Sai Hou[SUP] 1 [/SUP], Jun He[SUP] 1 [/SUP], Junling Yu[SUP] 1 [/SUP], Jiabing Wu[SUP] 1 [/SUP]
Affiliations
Background: Influenza poses a significant global public health threat, with its pandemic potential and seasonal variability presenting formidable challenges to prediction accuracy. This study leverages high-quality weekly data (incidence rates, viral subtypes, and meteorological indicators) from the provincial influenza surveillance system in Anhui Province, eastern China, spanning 2015-2025. A multi-source data fusion model was developed to overcome the limitations of traditional methods in modeling nonlinear transmission dynamics and multi-factor synergistic effects.
Methods: Single models were constructed using ARIMA, Prophet, and XGBoost, then stacked into an interpretable ensemble model (Stacked-NNLS) using non-negative least squares (NNLS). Performance was comprehensively evaluated using R [SUP]2[/SUP] (explained variance), RMSE (root mean square error), MAE (mean absolute error), and MAPE (mean absolute percentage error).
Results: ARIMA exhibits poor fit for non-stationary sequences (training set R [SUP]2[/SUP] = -3.66; test set R [SUP]2[/SUP] = 0.03). Prophet effectively captures long-term trends (training/test set R [SUP]2[/SUP] = 0.38/0.88). XGBoost shows overfitting (training/test set R [SUP]2[/SUP] = 0.99/0.74). The Stacked-NNLS model demonstrated significantly superior robustness (training/test R [SUP]2[/SUP] = 0.94/0.94), outperforming baseline models across all metrics.
Conclusion: By integrating statistical, seasonal, and nonlinear modeling approaches, Stacked-NNLS demonstrated robust predictive performance in capturing influenza trends, seasonal fluctuations, and complex interactions among multiple factors, suggesting its potential utility for infectious disease early warning and public health decision-making.
Keywords: ARIMA; Prophet; XGBoost; ensemble learning; influenza forecasting; influenza surveillance; stacking (NNLS); time series modeling.
. 2026 May 5:14:1806095.
doi: 10.3389/fpubh.2026.1806095. eCollection 2026.
A stacked ensemble model with NNLS-based weighting for influenza forecasting: a case study of Anhui Province, China
Qingqing Zhu[SUP] #[/SUP][SUP] 1 2 [/SUP], Minglei Zhu[SUP] #[/SUP][SUP] 2 [/SUP], Yuhang Cai[SUP] 3 [/SUP], Junwei Xiang[SUP] 3 [/SUP], Shuwen Li[SUP] 1 [/SUP], Biao Zhu[SUP] 1 [/SUP], Meng Zhu[SUP] 1 [/SUP], Lei Gong[SUP] 1 [/SUP], Sai Hou[SUP] 1 [/SUP], Jun He[SUP] 1 [/SUP], Junling Yu[SUP] 1 [/SUP], Jiabing Wu[SUP] 1 [/SUP]
Affiliations
- PMID: 42163928
- PMCID: PMC13183840
- DOI: 10.3389/fpubh.2026.1806095
Background: Influenza poses a significant global public health threat, with its pandemic potential and seasonal variability presenting formidable challenges to prediction accuracy. This study leverages high-quality weekly data (incidence rates, viral subtypes, and meteorological indicators) from the provincial influenza surveillance system in Anhui Province, eastern China, spanning 2015-2025. A multi-source data fusion model was developed to overcome the limitations of traditional methods in modeling nonlinear transmission dynamics and multi-factor synergistic effects.
Methods: Single models were constructed using ARIMA, Prophet, and XGBoost, then stacked into an interpretable ensemble model (Stacked-NNLS) using non-negative least squares (NNLS). Performance was comprehensively evaluated using R [SUP]2[/SUP] (explained variance), RMSE (root mean square error), MAE (mean absolute error), and MAPE (mean absolute percentage error).
Results: ARIMA exhibits poor fit for non-stationary sequences (training set R [SUP]2[/SUP] = -3.66; test set R [SUP]2[/SUP] = 0.03). Prophet effectively captures long-term trends (training/test set R [SUP]2[/SUP] = 0.38/0.88). XGBoost shows overfitting (training/test set R [SUP]2[/SUP] = 0.99/0.74). The Stacked-NNLS model demonstrated significantly superior robustness (training/test R [SUP]2[/SUP] = 0.94/0.94), outperforming baseline models across all metrics.
Conclusion: By integrating statistical, seasonal, and nonlinear modeling approaches, Stacked-NNLS demonstrated robust predictive performance in capturing influenza trends, seasonal fluctuations, and complex interactions among multiple factors, suggesting its potential utility for infectious disease early warning and public health decision-making.
Keywords: ARIMA; Prophet; XGBoost; ensemble learning; influenza forecasting; influenza surveillance; stacking (NNLS); time series modeling.