AEMS-One Health Mathematical and Computational Specification v1.0: Adaptive Environmental Modeling System for Bayesian Spillover Risk Prediction in Data-Scarce Environments

This document presents the initial mathematical and computational specification of the Adaptive Environmental Modeling System (AEMS-One Health), a probabilistic framework for zoonotic spillover risk prediction in data-scarce environments. The AEMS architecture is structured as a hierarchical Bayesian Directed Acyclic Graph (DAG) integrating five major domains:• Environmental Drivers (flood persistence, moisture anomaly, forest fragmentation, land use change)• Ecological Reservoir Dynamics (bat displacement processes)• Livestock Amplification Processes (pig amplification intensity)• Wildlife Sentinel Signals (mortality events with detection probability)• Human Exposure Processes (market connectivity, population density, mobility) The framework employs:• Hierarchical Bayesian inference with spatial and temporal random effects• Multivariate normal distributions for environmental state vectors• Negative binomial models for wildlife mortality signals (accounting for overdispersion)• Gamma distributions for human exposure intensity• Bayesian environmental reconstruction for missing data under cloud-obstructed conditions• Expert knowledge assimilation through structured prior distributions• Explicit uncertainty quantification with 95% credible intervals Computational implementation utilizes PyMC, Stan, and TensorFlow Probability for model layer, with GeoPandas, Rasterio, and PostGIS for spatial operations. Historical validation is planned for the 2022 Sudan ebolavirus outbreak in Mubende and Kasanda districts, Uganda (142 confirmed cases). NOTE: This is version 1.0 of the mathematical specification, representing the initial conceptual framework. For the refined operational version addressing SUDV-specific epidemiological realities (including down-weighting of livestock amplification, SAR-optical fusion for cloud-penetrating monitoring, and explicit Iceberg Phenomenon correction), please refer to version 2.0.