A Control-Theoretic Framework for Dynamic Heat Risk Assessment: Modeling Acclimatization, Cumulative Strain, and Stability Thresholds During Multi-Day Heat Exposure

Heat-related mortality during extreme heat events exhibits delayed, non-linear dynamics that cannot be explained by static environmental thresholds or simple cumulative exposure metrics alone. This paper introduces PYROX (Populational Yield for Relative Outdoor eXposure), a control-theory-inspired framework that models human heat stress response as a cascaded dual-process system with bidirectional feedback . The model formalizes the dynamic interaction between short-term physiological acclimatization (α) and cumulative physiological strain (Σ) , coupling them through a closed loop in which accumulated strain progressively suppresses acclimatization capacity, and diminished acclimatization in turn increases the rate of strain accumulation. This mutual feedback creates a non-linear instability mechanism. Using a discrete-time formulation, I demonstrate the existence of a critical strain threshold (Σ_critical) beyond which adaptation collapses and the system becomes unstable, leading to runaway decompensation under continued exposure. Analytical stability analysis shows this threshold emerges as a mathematical property of the feedback structure. The framework provides a mechanistic explanation for delayed mortality peaks and abrupt health deterioration during prolonged heatwaves. It enables explicit prediction of intervention windows , time-to-critical transitions , and population-specific vulnerability , offering a dynamic alternative to current heat-health warning systems.