Chang-Hoon Lee, Suresh Manian

In the field of Fuzzy Mathematics, Computational Logic and Applied Analysis, deterministic epidemiological models fail to capture stochastic transmission variability and fuzzy diagnostic reporting uncertainty. This empirical investigation systematically examines Stochastic Differential Equation Modeling of Epidemic Propagation with Fuzzy Environmental Parameter Fluctuations through a multi-stage experimental methodology and rigorous quantitative analytical framework. Utilizing Itô stochastic calculus coupled with fuzzy parameter membership functions modeling variable transmission contact rates, data were gathered across multiple operational cycles and validated against established international benchmarks. The statistical and computational results reveal that the stochastic fuzzy model accurately bounded epidemic wave peaks and extinction thresholds under volatile contact rate scenarios. Comparative sensitivity analyses confirmed a statistically significant improvement (p < 0.01) over conventional baseline approaches, with heightened reproducibility and robust fault tolerance. These comprehensive findings provide actionable theoretical insights and practical implementation guidelines for computational epidemiologists and public health mathematical modeling groups. Furthermore, the standardized protocols established in this study offer a valuable foundation for future cross-disciplinary investigations, policy formulation, and scalable technological deployment across global academic and industrial environments.