A Hybrid Reciprocal Adaptive Ventilation with Passive Thermal Recovery (RAV-PTR) System: Mathematical Modeling, Monte Carlo Uncertainty Quantification, Physiological Safety Assessment, and Low-Cost Implementation for Reducing Domestic Carbon Monoxide Poisoning Risk

Carbon monoxide (CO) poisoning from domestic heating and combustion appliances is a largely preventable cause of death, with an estimated 28,900 deaths worldwide in 2021 (95% uncertainty interval 21,700–32,800) [1]. We present RAV-PTR, a low-cost (≤ 45 USD bill-of-materials) sensor-driven hybrid ventilation system that combines reciprocal counter-flow ventilation, passive porous-media heat recovery (ηrec ∈ [0.65, 0.82]), and hysteresis control (activation at CO > 9 ppm, deactivation at CO < 7 ppm). The system is governed by a coupled set of mass- and energy-balance ordinary differential equations (ODEs), solved with an event-driven stiff integrator and validated against an exact analytical solution for the sealed-room limit (relative error < 10⁻¹⁵). A Monte Carlo uncertainty quantification (10,000 realizations; source strength S ∼ Uniform(800, 900) ppm·m³/h; recovery efficiency ηrec ∼ N(0.72, 0.05), truncated to [0.65, 0.82]) confirms a median peak CO reduction of approximately 87% relative to sealed conditions, while simultaneously reducing thermal loss by approximately 3% and fan electrical energy consumption by approximately 13% relative to continuous constant ventilation, at the cost of a marginally higher peak CO than constant ventilation (9.0 ppm vs. 8.4 ppm, both far below internationally recognized short-term exposure thresholds). Physiological safety is assessed with both the classical Haldane equilibrium relation [17] and the Coburn–Forster–Kane (CFK) dynamic model [18, 19]: applying the concentration-dependent CFK closed-form solution to every Monte Carlo CO trajectory gives a peak carboxyhemoglobin (COHb) of under 1% at 4 hours (sedentary activity), and the Haldane equilibrium bound applied to the highest sustained CO level in the ensemble remains below 2%, both comfortably under the 10% WHO chronic-exposure threshold. A rank-based multi-parameter sensitivity analysis identifies source strength S as the dominant driver of peak CO and CO dose, and recovery efficiency ηrec as the dominant driver of thermal loss. All numerical results, tables, and the figure in this manuscript are reproduced directly by the open-source Python code in Appendix A (fixed seed 42). Grounded in representative winter climate data for Ta'if, Saudi Arabia (∆T ≈ 11.5 K), the framework is immediately deployable in low-resource settings and, at even modest adoption, could plausibly prevent a substantial number of otherwise-preventable CO deaths per year in high-risk households — a projection whose assumptions and uncertainty are made explicit in Section 6.