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<p>Polycystic Ovary Syndrome (PCOS) is a prevalent endocrine and metabolic condition in reproductive-age women, characterized by anovulation, infertility, and insulin resistance. Traditional mathematical models do not fully capture the disorder’s complicated, non-local, and memory-dependent processes. This paper proposes a new mathematical model for PCOS based on an extended fractal-fractional derivative operator, which improves the depiction of complicated scaling behaviors and memory effects in biological systems. Well-known theorems are used to demonstrate the existence, uniqueness, positivity, and boundedness of system solutions. The proposed model focuses on disease-free and disease-endemic equilibrium points, with reproduction number as a key indicator. Furthermore, a strength number, which is an extension of the reproductive number, is calculated. The sensitivity analysis of both reproductive and strength numbers is covered in detail. The Lyapunov function’s global stability of equilibrium points is assessed through first and second derivative tests. Numerical simulations are employed in the study to investigate the effects of the fractional operator on women’s health. The Newton polynomial interpolation method is used to estimate solutions to the generalized fractal fractional system. The fractal-fractional operator enhances the simulation of PCOS dynamics, providing critical insights for clinicians and policymakers in crafting effective treatment and management strategies.</p>

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Modeling and biological feasibility of polycystic ovarian syndrome treatment in women to enhance infertility rate with fractional operator

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月3日

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  • Muhammad Farman

摘要

Polycystic Ovary Syndrome (PCOS) is a prevalent endocrine and metabolic condition in reproductive-age women, characterized by anovulation, infertility, and insulin resistance. Traditional mathematical models do not fully capture the disorder’s complicated, non-local, and memory-dependent processes. This paper proposes a new mathematical model for PCOS based on an extended fractal-fractional derivative operator, which improves the depiction of complicated scaling behaviors and memory effects in biological systems. Well-known theorems are used to demonstrate the existence, uniqueness, positivity, and boundedness of system solutions. The proposed model focuses on disease-free and disease-endemic equilibrium points, with reproduction number as a key indicator. Furthermore, a strength number, which is an extension of the reproductive number, is calculated. The sensitivity analysis of both reproductive and strength numbers is covered in detail. The Lyapunov function’s global stability of equilibrium points is assessed through first and second derivative tests. Numerical simulations are employed in the study to investigate the effects of the fractional operator on women’s health. The Newton polynomial interpolation method is used to estimate solutions to the generalized fractal fractional system. The fractal-fractional operator enhances the simulation of PCOS dynamics, providing critical insights for clinicians and policymakers in crafting effective treatment and management strategies.