Modeling Hepatitis C with Piecewise Derivatives: Comparative Insights from Deterministic and Stochastic Frameworks

In this paper, we conduct a comprehensive investigation of deterministic–stochastic modeling approaches for Hepatitis C using piecewise fractional operator techniques. This novel framework captures a wide range of dynamic behaviors, from deterministic transitions to stochastic fluctuations. By constructing piecewise differential operators that switch between deterministic and stochastic regimes, we demonstrate the innovative potential of this methodology. To validate its effectiveness, we present graphical simulations of the proposed model. The results show that these operators offer a more flexible and accurate representation of the complex dynamics characteristic of real-world systems. By effectively capturing distinct behaviors over different time intervals, this approach opens new avenues for research across multiple scientific disciplines. © 2025 Abdus Salam School of mathematical Sciences. All rights reserved.