AEMS–One Health Mathematical & Computational Specification v2.0: A Bayesian Latent Variable Framework for Sudan Ebolavirus Spillover Prediction under Epistemic and Aleatory Uncertainty

Version 2.0 of the AEMS mathematical specification represents a paradigm shift from deterministic, complete-data surveillance models to a Hierarchical Bayesian Latent Variable Framework, specifically tailored to the epidemiological realities of Sudan ebolavirus (SUDV) in Uganda (Mubende and Kassanda ecological context). Core mathematical innovations address four critical operational bottlenecks:1. SUDV-Specific Amplification Down-weighting: Structurally decoupling domestic swine from the primary spillover pathway, correcting historical biases from Reston virus or 2012 Bundibugyo models2. Phenological Stress-Induced Shedding: Transitioning from static ground-based wildlife reports to dynamic, cloud-penetrating Remote Sensing (RS) and Synthetic Aperture Radar (SAR) covariates3. The Iceberg Phenomenon Correction: Mathematically decoupling observed clinical cases from true latent infections using community-based event proxies4. Expert-Constrained AI: Implementing informative expert priors to prevent algorithmic misclassification of seasonal anthropogenic activities The computational engine is structured as a Hierarchical Directed Acyclic Graph (DAG) with explicit separation between Latent Ecological/Epidemiological States and Observed Data Generation Processes. Inference utilizes Integrated Nested Laplace Approximations (INLA) supplemented by Hamiltonian Monte Carlo (HMC) via Stan/PyMC. The model is calibrated against the 2022 Uganda SUDV outbreak ground truth (142 confirmed cases) with validation metrics including Posterior Predictive Checks, Spatial Leave-One-Out Cross-Validation, and Continuous Rank Probability Score (CRPS).