A Multi-Scale Integrative Framework for Age-Related MacularDegeneration:Stochastic Dynamics, Bayesian Inference, Global Sensitivity, and TranslationalTherapeutics

Age-related macular degeneration (AMD) is the leading cause of irreversible central vision loss in adults aged 50 and older, affecting approximately 196 million individuals globally and projected to exceed 288 million by 2040. Despite substantial mechanistic knowledge, to the best of our knowledge, no published mathematical framework has simultaneously achieved multi-scale mechanistic fidelity, formal dynamical systems analysis, stochastic embedding, hierarchical Bayesian calibration, global sensitivity analysis, and Popperian falsifiability. We formulate a five-compartment nonlinear stochastic dynamical system governing retinal pigment epithelium (RPE) cell density $R$, lipofuscin load $L$, drusen volume $D$, oxidative stress $O$, and inflammatory activity $I$. The system is derived from first principles---Michaelis–Menten lysosomal kinetics, A2E photo-oxidation spectroscopy, complement cascade ordinary differential equations, and demographic birth–death noise---via systematic multi-scale reduction. It\^{o}-calculus foundations with Milstein strong-order-1 discretisation underpin numerical integration. Lyapunov stability and saddle-node bifurcation are rigorously proven. The model is embedded in a hierarchical Bayesian framework with No-U-Turn Sampler (NUTS), Beta-Binomial likelihood, and formal WAIC/LOO-CV model selection. Global sensitivity is quantified via Sobol' variance decomposition (131\,072 evaluations), Morris elementary effects, and partial rank correlation coefficients. A composite early molecular diagnostic index $\mathcal{I}_{\mathrm{diag}}$ combines fundus autofluorescence and drusen volume with sensitivity-derived weights. Model validation against clinical data from Rein et al.\(2022) JAMA Ophthalmology and CDC VEHSS (2024) prevalence strata achieves $R^2 = 0.944$, RMSE $= 0.71\%$, MAE $= 0.53\%$, and 95\% CI coverage $\geq 97\%$ across all age groups. A saddle-node bifurcation at $\Lcrit = 0.682 \pm 0.021$ marks a mathematically proven irreversibility threshold. Sobol' analysis identifies lysosomal clearance $\varepsilon$ as the dominant therapeutic target ($S_1 = 0.471$, $S_T = 0.523$), 2.6$\times$ more influential than A2E–ROS coupling $\pi$ ($S_1 = 0.181$). The diagnostic index achieves AUC-ROC $= 0.951$ (95\% CI: 0.931–0.968), sensitivity 93.5\%, and specificity 89.2\% at age 55, exceeding all published clinical prediction tools. This framework represents, to the best of our knowledge, an integrative approach that simultaneously contributes formal proof of disease-commitment bifurcation, mechanistic parameter inheritance from spectroscopy to population prevalence, Sobol' therapeutic target ranking, a composite diagnostic index with high cross-validated performance, a Milstein SDE formulation for RPE dynamics, a hierarchical Bayesian model with formal model selection, and explicit Popperian falsifiability conditions. A WHO-aligned translational roadmap spanning 2027--2035 and fully reproducible Python code accompany all results.