A Four-Process Digital Twin for Chronic Insomnia: Insomnia as a Dynamical Trap, Sleep as an Attractor, and AI as the Stabilising Controller that Reshapes the Landscape

This paper presents a mathematically rigorous digital-twin framework for chronic insomnia designed for AI-driven closed-loop sleep intervention using consumer wearables. Extending the classical Borbély two-process model, the framework introduces two additional physiologically and psychologically grounded state variables: a fast arousal variable A(t)A(t)A(t) and a slow sleep-confidence variable T(t)T(t)T(t), capturing the long-term conditioning dynamics characteristic of chronic insomnia. The model integrates four interacting processes: circadian rhythm dynamics, homeostatic sleep pressure, somatic-cognitive hyperarousal, and conditioned sleep confidence. The framework is formulated as a nonlinear low-dimensional state-space system suitable for personalised digital twins implemented through modern wearable sensors. The paper derives measurement equations linking latent states to observable physiological signals including heart-rate variability (HRV), skin temperature, actigraphy, electrodermal activity (EDA), and ambient light exposure. A central contribution is the introduction of the sleep-confidence variable T(t)T(t)T(t), representing the learned expectation that bed will or will not lead to sleep. The paper formalises chronic insomnia as a feedback loop in which bedtime itself becomes a conditioned hyperarousal cue after years or decades of failed sleep experiences. The framework further incorporates: Bayesian state estimation using an unscented Kalman filter (UKF), model-predictive AI control, personalised parameter adaptation, and constrained intervention policies explicitly designed to avoid iatrogenic reductions in sleep confidence. The AI intervention architecture specifies timing, modality, and psychological framing of feedback, including: circadian light scheduling, wind-down anchoring, stimulus control, paradoxical intention, and post-failure cognitive reframing. The paper additionally identifies several clinically invisible “pre-clinical” trend signals detectable only through continuous wearable telemetry and model-based inference, including: baseline HRV drift, circadian phase drift, micro-erosion of sleep confidence, arousal–sleep-pressure decoupling, and personalised light-hygiene drift. Analytically, the paper proves existence and local exponential stability of a high-confidence equilibrium state and derives quantitative asymmetries between the rapid collapse and slow recovery of sleep confidence under chronic insomnia dynamics. The work positions chronic insomnia not merely as a disturbance of circadian or homeostatic regulation, but as a dynamically reinforced conditioning disorder requiring long-timescale confidence restoration. The proposed framework is intended as a foundation for interpretable, wearable-based AI sleep systems and future digital therapeutics. Suggested Keywords / Bullet Points Digital twin Chronic insomnia Sleep dynamics Circadian rhythm Homeostatic sleep pressure Hyperarousal Sleep confidence AI-driven healthcare Closed-loop intervention Wearable sensors Model-predictive control Pavlovian conditioning Unscented Kalman filter Personalised medicine Computational neuroscience Nonlinear dynamical systems CBT-I Sleep regulation HRV analysis Consumer wearables Bayesian state estimation Circadian entrainment Physiological modelling AI for sleep medicine Preventive sleep analytics