A Deterministic Limit for Pandemic Escape: Deriving the Critical Outbreak Radius via Spatial Containment Diffusivity

The forecasting of wildland fire behavior relies heavily on empirical probability models, such as the Rothermel surface fire spread equation, which evaluates fuel moisture, wind, and topography to estimate transmission rates. While these classical thermodynamics models effectively describe linear fire spread, they fail to deterministically define the exact spatial boundary where a controllable surface fire transitions into a self-sustaining, convective firestorm (megafire). This paper introduces a strict continuum framework for macroscopic combustion scaling. By modeling the atmospheric canopy as a thermodynamic balance between ambient thermal diffusivity and localized combustion intensity at the flame front, we derive a universal critical flashpoint radius (Rflashpoint). We demonstrate that the onset of a megafire is not a statistical anomaly governed by extreme weather, but an exact deterministic limit where localized exothermic heat release strictly overpowers the advective cooling capacity of the surrounding atmosphere. We contrast this geometric invariant with traditional spread-rate probability matrices and propose a blueprint for Active Canopy Monitoring (ACM) using real-time infrared drone telemetry.