Modeling Disease-State Transitions Through Stochastic Delay Dynamics: A Computational Framework for Neurological Risk Stratification

This paper proposes a candidate mapping between a mathematically established delay-induced variance-divergence phenomenon (derived in a companion theoretical study of linear stochastic delay-differential equations) and longitudinal neurological biomarker trajectories. Rather than presenting validated clinical results, the paper specifies a falsification-oriented framework: an explicit scheme for estimating latent delay and feedback parameters from biomarker time series (e.g., p-tau217, NfL, structural MRI), a pre-specified definition of what would constitute a positive versus negative result, and a concrete validation protocol against established baselines (Cox proportional hazards, gradient-boosted trees) using public longitudinal cohorts such as ADNI, OASIS, or NACC. No patient-level data, clinical results, or diagnostic/prognostic claims are made in this paper; its contribution is a testable hypothesis and a pre-registerable study design intended to guide a future validation study.