Fuzzy logic provides a powerful framework for handling uncertainty in epidemiological modeling, while fractional calculus and stochastic processes capture long-memory effects and randomness in disease dynamics. In this study, we formulate a fuzzy fractional stochastic epidemic model for sugarcane smut disease. The model’s parameters are represented as triangular fuzzy numbers using an \(\alpha\) -cut approach to capture the parametric uncertainty. The disease transmission dynamics are governed by fractional-order differential equations with Caputo derivatives to capture the memory effects. Stochastic fluctuations are incorporated via a fractional Brownian motion term with a specified Hurst index. We derive the model basic reproduction number and perform a stability analysis using Matignon’s fractional stability criterion, establishing threshold conditions for disease outbreak or eradication. Numerical simulations implemented with the Adams-Bashforth-Moulton scheme validate the theoritical results. The fuzzy fractional model demonstrates an enhanced capacity to capture the disease dynamics as compared to its integer-order counterpart. Furthermore, the inclusion of fuzzy parameters and fractional Brownian motion-driven noise offers a more comprehensive view of the epidemic trajectory. This study highlights the improved predictive capability of integrating fuzzy logic and fractional stochastic modeling in epidemiology, providing deeper insights for understanding and controlling disease spread under uncertainty and long-memory effects.
