An Integrative Eight-Dimensional Nonlinear Dynamical Model for Polycystic Ovary Syndrome Management: First-Principles Derivation, Global Asymptotic Stability Analysis, Optimal Control, Bayesian Inference, Sensitivity Analysis, and Translational Framework
Abstract
Polycystic ovary syndrome (PCOS) is the most prevalent heterogeneous endocrine-metabolic-reproductive disorder among reproductive-age women, with a global prevalence of 8--13\% and substantial phenotypic variability across ethnic groups and diagnostic criteria (Rotterdam, NIH, AES) \citep{Teede2018, Teede2023, Azziz2016}. The syndrome is mechanistically driven by intertwined hyperandrogenism, insulin resistance (affecting 50--90\% of patients), ovulatory dysfunction, polycystic ovarian morphology, chronic low-grade systemic inflammation, hypothalamic-pituitary-ovarian axis dysregulation, and gut microbiome dysbiosis characterized by reduced Shannon diversity, depleted SCFA-producing taxa, and altered bile-acid metabolism \citep{Teede2018, Qi2019, Torres2018, Lindheim2017}. Conventional mono-therapeutic or dual-axis strategies (lifestyle modification, metformin, clomiphene citrate, letrozole, oral contraceptives) achieve remission rates of 40--66\% and fertility restoration below 60\%, with high relapse upon discontinuation and limited impact on long-term cardiometabolic risk \citep{Teede2018, Legro2014, Thessaloniki2008}. Recent causal evidence from fecal microbiota transplantation (FMT) in germ-free and antibiotic-treated rodent models demonstrates that transplantation of PCOS-patient-derived microbiota can induce metabolic dysfunction and ovarian abnormalities, while healthy microbiota transplantation shows therapeutic potential \citep{Qi2019, Torres2018, Lindheim2017}.…
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