DBSCAN Clustering and Entropy Optimization for Geospatial Analysis of Urban–Rural Healthcare Inequities in Latin America

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Abstract
Healthcare access in Latin America is highly unequal, with rural and peri-urban populations disproportionately excluded from essential and specialized services. To address the persistent gaps often obscured by conventional urban–rural classifications, this study developed a machine learning framework integrating the Functional Urban Area (FUA) model with Density-Based Spatial Clustering of Applications with Noise (DBSCAN) and Shannon entropy optimization to refine urbanization gradients and quantify inequities across 11 countries. High-resolution population density data from the Meta High Resolution Settlement Layer (HRSL, 2020) and CIESIN’s Gridded Population of the World (GPWv4, rev. 11), combined with healthcare facility locations from Healthsites.io, were processed in R to generate population-facility networks. Entropy optimization dynamically determined country-specific DBSCAN distance thresholds, ensuring representative clustering of functional urban and rural areas. Facilities were categorized by care level, and per-capita densities were compared across clusters. Results showed that entropy-optimized DBSCAN improved spatial precision over traditional approaches and revealed systemic urban bias: Peru, Chile, and Venezuela had the lowest hospital densities, while Ecuador, Bolivia, and Paraguay displayed the strongest rural deficits in primary care. Specialized services were overwhelmingly concentrated in urban clusters. This reproducible framework establishes a quantitative baseline for healthcare inequities, providing data-driven insights to inform the design of decentralized strategies to improve equitable access to care across Latin America.

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