Gauge-Mediated Contagion: A Quantum Electrodynamics-Inspired Framework for Non-Local Epidemic Dynamics and Superdiffusion

In this paper, we introduce a gauge-mediated Epidemiological Model inspired by Quantum Electrodynamics (QED). In this model, the ``direct contact'' paradigm of classical SIR models is replaced by a gauge-mediated interaction where the environment, represented by a pathogen field $\varphi$, plays a fundamental role in the epidemic dynamics. In this model, the non-local characteristics of epidemics appear naturally by integrating out the pathogen field. Utilizing the Doi-Peliti formalism, we derive the effective action of the system and the standard Feynman rules that can be used to compute perturbatively any observables. The standard deterministic SIR equations emerge as the mean-field saddle-point approximation of this formalism. Going beyond this classical limit, we utilize 1-loop fluctuation computations to analytically derive spatial shielding effects that are inaccessible to standard compartmental models. Using standard QED techniques, we show how to relate renormalized pathogen mass, Debye screening, to epidemiological concepts and we compute at first order the effective reproductive number,$R_{eff}$, and how the condition to have an epidemic is related to a phase transition in the pathogen mass. We show that the superspreading hosts can be included easily in this formalism. We applied our model using high-resolution spatial data from the COVID-19 pandemic across 400 districts in Germany. Our analysis reveals that the gauge field provides a early warning signal, consistently anticipating surges in reported cases with a predictive lead time of approximately one week. Furthermore, the data analysis confirms a density-driven non-linear scaling in the correlation length. By linking out of equilibrium statistical physics to epidemiology, this model shows to be a predictive tool that anticipates outbreaks based on the structural instability of the network.