Hybrid probabilistic forecasting of under-five malaria admissions in Ghana: A Gaussian process regression with Holt-Winters smoothing.

Accurate malaria forecasting in sub-Saharan Africa is challenged by strong seasonality, reporting uncertainty, and non-stationary transmission dynamics. This study proposes a hybrid probabilistic forecasting framework that integrates Gaussian Process Regression (GPR) with Holt-Winters exponential smoothing for modelling monthly under-five malaria admissions in Ghana. GPR captures complex non-linear temporal behaviour and predictive uncertainty, while Holt-Winters smoothing stabilises long-horizon forecasts and preserves seasonal structure. Using ten years of district-level surveillance data (2014-2023), model performance was evaluated through a rolling-origin, expanding-window validation framework. The hybrid model achieved substantially improved predictive performance (R2=0.9906) relative to the best standalone baseline (R2=0.8213 for Holt-Winters), with 94.2% of residuals contained within ±2σ uncertainty bounds. The integration of probabilistic machine learning with seasonal smoothing reduced forecast volatility while preserving epidemiologically meaningful seasonal amplitudes, improving both stability and interpretability over extended horizons. The framework provides a scalable probabilistic forecasting approach for malaria early warning, seasonal preparedness, and operational planning in endemic settings. Although constrained by data quality and the absence of environmental covariates, this study establishes a methodological foundation for integrating probabilistic machine learning with classical seasonal smoothing in resource-constrained public-health environments.