🤖 AI Summary
This work proposes a unified framework for modeling the coupling between epidemic dynamics and spontaneous behavioral responses by starting from microscopic stochastic transmission mechanisms. Building on the Doi–Peliti stochastic field theory, pathogens are represented as gauge-mediated fields, while a reactive immunity field capable of spontaneous symmetry breaking is introduced. Macroscopic reaction–diffusion equations are derived via a saddle-point approximation of the effective action. The study innovatively maps concepts from quantum field theory—such as the Coleman–Weinberg mechanism, Debye screening, and vacuum polarization—onto epidemiological contexts, revealing how fear-induced drift and cubic screening dynamically suppress the effective reproduction number. The model is validated against high-resolution COVID-19 data from Germany, accurately reproducing both the susceptibility-density-squared dependence of the free energy and the behaviorally induced cubic nonlinear suppression term.
📝 Abstract
We present a unified theoretical model relating stochastic microscopic epidemic dynamics with macroscopic non-linear population behavior. Utilizing the Doi-Peliti formalism, we model the pathogen as a gauge mediator field coupled to susceptible and infected host populations, and introduce a Reactive Immunity Field capable of spontaneous symmetry breaking. We demonstrate that the naive epidemic vacuum is destabilized by radiative loop corrections via the Coleman-Weinberg mechanism, generating a dynamic herd immunity threshold. By extracting the classical saddle-point limit of the Effective Action, we derive the macroscopic reaction-diffusion equations governing the host population. We show that integrating out the gauge mediator inherently generates a thermodynamic Free Energy dependent on the square of the susceptible density. This non-linearity produces a macroscopic spatial ``Fear Drift'' proportional to the magnitude of the immunity field, and a cubic shielding penalty in the effective reproductive number ($R_{eff}$). In this work, we establish a mapping between fundamental field-theoretic mechanisms and specific terms in the macroscopic behavioral equations. We demonstrate that Debye screening is physically executed by the spatial cross-diffusion fluxes driving host evacuation. Simultaneously, vacuum polarization manifests as a non-linear cubic penalty ($-S^3 I$) in the dressed reaction rate that dynamically suppresses the effective reproductive number. As a validation of our model, we apply the formalism to high-resolution spatiotemporal COVID-19 data from Germany.