Neurogenic Rosacea as a Lyapunov‑Stabilisable System: A Control‑Theoretic Framework for Rogue Neuroimmune Loops

Abstract

Rosacea affects roughly $5\%$ of adults worldwide [1, 2], yet patients with prominent neurogenic features often remain refractory to standard anti‑inflammatory or vasomotor therapies [5, 6]. We propose that this recalcitrant subset is best understood through a control‑theoretic lens: the neurogenic cascade constitutes a positive‑feedback loop whose stability is governed by a Lyapunov‑style criterion. The core architecture comprises a state variable (neuronal excitability), an output (Substance P release), a feedback branch (PAR‑2‑mediated sensitisation) [15, 16, 17], and a transcriptional amplifier (CREB) [13]. We formalise this as a two‑dimensional dynamical system and derive an explicit closed‑form stability condition: dimensional stability requires $G \cdot S < \beta_x \beta_y$, which after nondimensionalisation becomes $(G \cdot S) - \beta < 1$. When this condition is violated, the loop becomes self‑sustaining. We synthesise three convergent lines of evidence: (i) disulfiram‑zinc inhibits CREB DNA binding, reducing loop gain [25]; (ii) GABA derivatives (gabapentin, pregabalin) and baclofen modulate the physiological brake [38, 39, 40]; (iii) independent work in oncology neuroimmunology (PMC12652726 [1]) describes analogous self‑sustaining regulatory architectures, while the EMN‑S framework [52] has previously invoked Lyapunov stability in narrative terms. Crucially, homologous loop architectures appear in migraine, chronic pain, asthma, and atopic dermatitis [53, 54, 55, 56]. We therefore present neurogenic rosacea not as a dermatological curiosity, but as the initial proof‑of‑concept for a potentially generalisable theory of Lyapunov‑stabilisable neuroimmune loops. The framework yields specific, testable cross‑domain predictions and outlines a translational roadmap from in vitro validation to biomarker‑guided clinical trials. This work provides the first explicit closed‑form Lyapunov stability criterion for a dermatological neuroimmune loop and outlines a translational pathway for operator‑guided stabilisation in rosacea and beyond.