Efficient Detection of Rare Disease Hotspots Using Fuzzy Adaptive Cluster Sampling under Inhomogeneous Spatial Point Processes

Reliable detection and estimation of rare disease hotspots are fundamentally hindered by low prevalence, weak spatial signals, and severe operational constraints in surveillance systems. Classical adaptive cluster sampling, although theoretically suitable for rare events, often suffers from sharp instability due to rigid threshold-based triggering and uncontrolled cluster expansion. This study develops a novel fuzzy adaptive cluster sampling framework for hotspot detection and inference under inhomogeneous spatial point processes by replacing binary triggering with probabilistic, membershipdriven adaptive expansion. A complete design-based inferential structure is established through defuzzified Horvitz–Thompson type estimators, Monte Carlo approximation of inclusion probabilities, and network-level variance estimation, with formal proofs of design unbiasedness, consistency, and variance stabilization. Extensive simulation experiments based on inhomogeneous Poisson spatial point process models with embedded rare disease hotspots demonstrate that the proposed fuzzy adaptive design consistently achieves higher detection sensitivity under weak and diffuse clustering while maintaining controlled false alarm rates and stable sampling effort. Comprehensive sensitivity analyses with respect to fuzziness level, hotspot-to-background intensity contrast, spatial neighborhood structure, and disease rarity further confirm the robustness and operational reliability of the framework. The results establish fuzzy adaptive cluster sampling as a statistically principled, operationally stable, and practically implementable methodology for modern rare disease surveillance under spatial uncertainty.