Fractional-order mathematical modelling of Polycystic Ovarian Syndrome disease transmission dynamics: A comparative analysis of Caputo and modified Mittag-Leffler kernel approaches

Abstract

 This study presents a fractional-order compartmental model for the transmission dynamics of Polycystic Ovary Syndrome ($\p$), structured around four clinically meaningful states: susceptible-at-risk ($\S$), diagnosed individuals ($\P$), those under active treatment ($\T$), and recovered ($\R$). To capture the memory-dependent nature of disease progression, we formulate the model using two distinct fractional operators: the Caputo $(\c$) and modified Mittag-Leffler kernel $(\m)$ derivatives. The mathematical properties of the system, including non-negativity, boundedness, existence, uniqueness, and stability of solutions, are rigorously established to ensure the well-posedness of the model. Numerical simulations are performed using a suitably adapted Runge--Kutta (RK) method to explore the impact of fractional differentiation on disease progression, treatment efficacy, and recovery trends. The results reveal notable differences in trajectory sensitivity and stability profiles between the $\c$ and $\m$ approaches, offering deeper insight into the role of fractional calculus in modelling complex biomedical phenomena.