HiBASIL: Hierarchical Bayesian Source Inference and Localization for Spatial Epidemiology

O_LIIdentifying spatial origins of biological invasions, disease outbreaks, or environmental contaminants is critical for timely intervention. However, existing methods struggle to resolve overlapping signals from multiple sources or account for extreme zero/one inflation in bounded data. C_LIO_LIWe developed HiBASIL (Hierarchical BAyesian Source Inference and Localization), a Bayesian framework that jointly infers source coordinates and mechanistic dispersal kernels from zero-one-inflated spatial observations. We systematically tested HiBASIL across 2,500 simulations spanning localized to long-distance dispersal regimes, various foci weight mixtures (0.5/0.5 to 0.95/0.05), and varying sample sizes (N = 50 to 500) to evaluate geometric sensitivity, spatial robustness, parameter recovery capability, and multi-focal resolution. We applied HiBASIL in tracking cucurbit downy mildew dispersal in field experiments including non-inoculated control, single-focus, and two-foci treatments arranged in a randomized complete block design. To demonstrate broad applicability, we validated HiBASIL with historical London cholera epidemic data to determine whether it could accurately localize the epicenter. C_LIO_LIHiBASIL achieved 100% accuracy in kernel identification under correct model specification, 100% and 98% (2% predictive equivalence) in under- and over-parameterization scenarios, and maintained appropriate parsimony in null scenarios. Source localization was highly precise, with a median bias of 0.11 m, successfully resolving minority sources contributing only 5% of the observations. Importantly, the framework provides intrinsic self-diagnostics, signaling model complexity mismatch through posterior bimodality (under-parameterization) or parameter collapse (over-parameterization). HiBASIL is applicable in various epidemic scenarios, including diffused long-distance dispersal. Under an isotropic process, HiBASIL achieved sub-meter mean errors on two-source localization in cucurbit downy mildew field tests, effectively isolating transmission signals from landscape noise despite sparse sampling. Despite confounding influence of underlying network processes in the historical cholera data, the posterior localized the epicenter to within [~] 33m, demonstrating portability beyond plant disease epidemiology. C_LIO_LIIn summary, HiBASIL can accurately localize multiple sources across various epidemic scenarios, extremely unbalanced foci mixtures, and sparse sampling conditions. HiBASIL also demonstrates wide applicability across agricultural and human disease epidemic systems. By providing an open-source Python implementation, HiBASIL enables rigorous inverse spatial inference for ecology, epidemiology, and environmental monitoring, transforming how discrete transmission sources are identified in complex landscapes. C_LI