Bayesian inference of nonlinear malaria dynamics in Ghana via an ensemble Markov chain Monte Carlo sampler

Reliable quantification of malaria dynamics in sub-Saharan Africa remains hindered by short, noisy, and spatially heterogeneous surveillance records that challenge the assumptions of conventional deterministic models. In Ghana, health-facility data between 2014 and 2023 reveal highly non-linear and age-specific fluctuations in hospital admissions, yet existing approaches struggle to capture such stochastic variability or provide credible uncertainty bounds. This study develops a Bayesian nonlinear inference framework that integrates a cubic deterministic baseline with a damped oscillatory kernel, estimated via an affine-invariant ensemble Markov Chain Monte Carlo sampler. The framework accommodates limited data, explicitly models parameter uncertainty, and generates probabilistic forecasts of malaria admissions for children under five years and individuals aged five years or more. Results demonstrate that the proposed hybrid cubic-damped oscillatory kernel model achieves strong empirical adequacy ((Formula presented) for  < 5 years; (Formula presented) for  ≥ 5 years) with residual errors below 2% and unimodal, well-mixed posterior distributions confirming robust convergence. District-level analysis reveals pronounced spatial heterogeneity, with coefficients of variation ranging from  < 0.07 in stable urban centres such as Kumasi to  > 3.3 in peripheral districts including Mpohor and Bia East. Forecasts for 2024–2026 indicate a gradual resurgence in admissions, increasing from approximately 137,000 to 149,000 cases among children under five and from 348,000 to 375,000 among older individuals, with uncertainty widening modestly over time. By producing interpretable probabilistic forecasts, this Bayesian framework provides a principled tool for anticipating short-term malaria fluctuations, guiding resource allocation, and strengthening data-driven decision-making within Ghana’s national malaria control strategy.