The study compiled a national monthly series of reported hepatitis B notifications in mainland China covering January 2004 through December 2025. These surveillance data formed the single input time series used for decomposition and predictive modelling. The objective was to generate reliable short- to medium-term forecasts of reported cases to inform diagnostics, care pathways, antiviral supply and targeted prevention.
To isolate multiscale temporal features from the raw notification series, the researchers applied Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN). This decomposition method separates the original signal into intrinsic mode components across different frequencies, facilitating modelling of dominant trends and seasonal patterns when used as input features for machine learning algorithms.
Four modelling approaches were trained on the CEEMDAN-derived components:
Each model used the decomposed components as features to learn temporal structure and produce multi-step forecasts.
Hyperparameters for all candidate models were tuned using the Kepler Optimization Algorithm (KOA). KOA served as the automated search strategy to identify model hyperparameters that optimized predictive performance on the validation split prior to test-set evaluation.
Models were trained with a sliding 12-month input window to capture recent temporal dynamics, then used recursively to extend forecasts up to 24 months ahead. This recursive strategy enabled production of forecasts through 2026 and 2027 based on patterns learned from the 2004–2025 training period.
Model performance was evaluated across training, validation and a held-out test split using multiple complementary metrics: R2 (coefficient of determination), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and additional regression diagnostics. These metrics quantified fit, average error magnitude, relative error and overall explanatory power.
All four modelling approaches were able to capture the major trend and seasonal structure in the notification data. On the held-out test split the Transformer encoder produced the best out-of-sample performance, with reported test metrics of MAE = 3105.508, MAPE = 0.024, RMSE = 4071.901, and R2 = 0.928.
The SVM ranked second overall; its MAE, MAPE and RMSE values were 11.317%, 11.615% and 9.964% higher than those of the Transformer on the test set. The CNN outperformed the GRU: relative to GRU on the test set, CNN achieved MAE, MAPE and RMSE reductions of 21.985%, 22.178% and 14.944%, respectively, and produced a 6.158% larger R2 than GRU.
These comparative results indicate that, for this CEEMDAN-derived feature set and national hepatitis B notification series, the Transformer encoder provided the most accurate short-term forecasts among the evaluated models, with SVM and CNN as intermediate performers and GRU ranking lowest in this comparison.
Forecasts produced from the hybrid CEEMDAN + KOA-optimised modelling framework for 2026–2027 remain elevated. The authors report little improvement in reported case counts in the forecast horizon and note the potential for resurgence. The study frames these forward projections as actionable foresight to inform allocation of diagnostic capacity, antiviral supply chains, and targeted prevention efforts.
The methodological pipeline—decomposition by CEEMDAN, supervised learning on decomposed components, and KOA-guided hyperparameter tuning—was presented as a resilient continuum connecting surveillance data to predictive modelling for public health decision making.
The authors conclude that integrating CEEMDAN decomposition with KOA-optimised machine learning models yields highly reliable short-term forecasts of reported hepatitis B cases at the national level. The Transformer encoder produced the best test-set performance in this study, followed by SVM, CNN and GRU. Forecasts through 2027 indicate sustained elevated notifications and possible resurgence, highlighting the need for continued surveillance, resource planning for diagnostics and antivirals, and targeted prevention strategies.
Notes on reporting
The abstract presents methods, key performance metrics and forecast directionality. Detailed model architectures, specific KOA hyperparameter settings, decomposition component counts, exact training/validation/test split sizes and uncertainty quantification methods are not reported in the abstract; those details would be found in the full article.