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. 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.

💡 Research Summary

The paper proposes a novel epidemiological framework that replaces the traditional “direct‑contact” assumption of compartmental SIR models with a gauge‑mediated interaction inspired by quantum electrodynamics (QED). The authors begin by casting the population as a set of particles and the disease states (susceptible, infected, recovered) as creation‑annihilation operators within the Doi‑Peliti path‑integral formalism. The key innovation is the introduction of a scalar pathogen field ϕ(x,t) that plays the role of a mediating gauge boson. The field obeys a standard Klein‑Gordon Lagrangian with a mass term m, and it couples to the infected‑susceptible transition with a coupling constant e, directly analogous to the electric charge in QED.

Integrating out ϕ yields a non‑local effective interaction kernel K(r) ∝ e² exp(−mr)/r, which naturally encodes long‑range transmission and super‑diffusive spread without the need for ad‑hoc mobility matrices or network rewiring. The authors then develop a perturbative expansion using standard QED Feynman rules: fermionic lines represent the disease‑state particles, while bosonic propagators correspond to the pathogen field. At one‑loop order they compute the self‑energy of ϕ, obtaining a renormalization group (RG) flow for the pathogen mass: dm/dℓ = −C e² + O(e⁴). When the renormalized mass falls below a critical value m_c, the screening length ξ = 1/m diverges, signalling a phase transition that the authors identify with the epidemic threshold. In this language the classic condition R₀ > 1 is re‑interpreted as m < m_c.

The effective reproductive number R_eff is derived from the renormalized propagator and reads
R_eff = R₀ ·