Phase-Synchronized Dual-Target Modulation Rescues Long COVID In Silico: A Langevin Dynamics and Pontryagin Optimal Control Approach

Abstract

Background: Long COVID (Post-Acute Sequelae of SARS-CoV-2, PASC) presents as a heterogeneous, treatment-resistant chronic syndrome. Conventional anti-inflammatory monotherapies frequently fail in clinical trials, exhibiting post-treatment rebound oscillations. We hypothesize that Long COVID represents a non-equilibrium bi-stable dynamical system where inflammatory pathology (I) and regulatory repair kinetics (R) form a persistent attractor state, requiring phase-synchronized dual modulation to traverse the separatrix into permanent remission. Methods: We formulated a 2D stochastic Langevin dynamical system describing non-linear auto-amplifying inflammation I(t) coupled with regulatory repair R(t), parameterized by an HLA-DRB1*13:02 genetic risk coefficient (χ) derived from epidemiological odds ratios (OR = 6.74, β_H = 1.908). An in silico randomized clinical trial was conducted on a virtual cohort (N = 1,000) over 12 weeks across three primary arms: Arm A (Control / Natural History), Arm B (Empirical Periodic Anti-Inflammatory Pulse, u_I), and Arm C (Phase-Synchronized Model Predictive Control Dual-Target Modulation, u_I + u_R). We further benchmarked a heuristic fixed-window controller (v1.0) against a Pontryagin's Minimum Principle (PMP) costate-guided, HLA-adaptive controller (v2.0). Results: Natural recovery was completely absent in Arm A (0.0% remission, mean disease AUC: 232.39). Empirical anti-inflammatory monotherapy (Arm B) yielded negligible efficacy (1.3% remission, AUC: 172.02) due to depletion of repair feedback and subsequent rebound. Controller v1.0 achieved 63.4% remission. Controller v2.0 achieved a 69.7% remission rate (p < 0.001, Log-rank test), reduced mean disease AUC to 29.42 (87.3% reduction vs control), cut post-exertional flare-ups by 51.3%, and shortened median time-to-remission from 42.1 days to 32.4 days (Hazard Ratio = 1.34, 95% CI: 1.20–1.50). Conclusions: Phase-synchronized dual-target modulation successfully destabilizes the chronic Long COVID attractor and steers state trajectories into the recovery basin. These findings provide a mathematical foundation for digital biomarker-guided, wearable-driven personalized therapies in post-viral syndromes.