A Bounded Multi-Scale Stochastic Model of RPE Attrition in Age-Related Macular Degeneration: Mechanistic Derivation, Constrained Calibration to Population Prevalence, Global Sensitivity Analysis, and Structural Robustness

Background. Age-related macular degeneration (AMD) is the leading cause of irreversible central vision loss in adults aged 50 and older. Mechanistic mathematical models that link molecular kinetics to population level prevalence remain scarce, and published multi scale frameworks are rarely subjected to independent numerical verification of their own internal consistency.Methods. We formulate a five compartment stochastic dynamical system for retinal pigment epithelium (RPE) density R, lipofuscin load L, drusen volume D, oxidative stress O, and inflammatory activity I, derived from Michaelis Menten lysosomal kinetics, A2E photo oxidation, complement activation, and demographic birth death noise. Consistent with the post mitotic nature of RPE cells, the RPE equation is formulated as a pure attrition process with no compensatory proliferation term. The oxidative inflammatory feedback loop is regularised with saturating (Hill type) coupling terms to guarantee boundedness, a property we verify numerically and prove analytically. Model parameters were held at literature sourced point estimates where available; a small subset of parameters lacking a single well established point estimate were calibrated by constrained optimisation within their literature reported 95% ranges against age stratified AMD prevalence data. Every statistic, sensitivity index, and figure reported below is regenerated by direct execution of the accompanying code (Section 7).Results. The bounded stochastic system, combined with population level heterogeneity in lipofuscin toxicity, A2E ROS coupling, lysosomal clearance, and CFH Y402H genotype, reproduces the reported age stratified prevalence pattern with R squared equal to 0.912, RMSE equal to 2.67 percentage points, MAE equal to 2.46 percentage points (four age strata, 50 to 80+ years). Global variance based sensitivity analysis (Sobol, N equal to 30,000 model evaluations) identifies lipofuscin mediated RPE toxicity (alpha) as the overwhelmingly dominant driver of RPE loss (S1 equal to 0.990, ST equal to 0.996), with all other calibrated parameters, including lysosomal clearance and CFH genotype, contributing negligible variance individually. A candidate composite diagnostic index, combining age matched lipofuscin and drusen measures, shows only a weak and counter intuitively signed association with subsequent RPE loss (Spearman rho equal to minus 0.37, p equal to 3.4 times 10 to the minus 14, N equal to 400 simulated individuals), indicating that, in its present linear form, it is not a reliable early diagnostic construct within this model and requires re derivation before any clinical interpretation is attempted.Conclusions. This bounded stochastic compartmental model is internally consistent, numerically reproducible, and modestly but genuinely predictive of reported epidemiological trends, with lipofuscin mediated RPE toxicity identified as the dominant lever for progression risk. We report explicitly where the model's predictions remain weak, namely the composite diagnostic index, CFH genotype sensitivity, and the absence of a genuine disease commitment bifurcation under literature consistent parameters, and identify the specific structural, data, and computational limitations that any follow up study must address before results of this kind can be considered clinically actionable. An exploratory structural extension (bounded density threshold RPE regeneration, an explicit Bruch's membrane compartment, and continuous CFH kinetics) does not produce genuine bistability, but points to bounded drusen and debris clearance, rather than RPE self renewal, as a more plausible candidate mechanism for any true disease commitment threshold, a specific, falsifiable direction for future work.