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

Jose de Jesus Bernal-Alvarado, David Delepine

TL;DR

A gauge-mediated Epidemiological Model inspired by Quantum Electrodynamics, where the ``direct contact''paradigm of classical SIR models is replaced by a gauge-mediated interaction where the environment plays a fundamental role in the epidemic dynamics.

Abstract

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.

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

TL;DR

A gauge-mediated Epidemiological Model inspired by Quantum Electrodynamics, where the ``direct contact''paradigm of classical SIR models is replaced by a gauge-mediated interaction where the environment plays a fundamental role in the epidemic dynamics.

Abstract

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 , 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,, 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.
Paper Structure (15 sections, 43 equations, 3 figures, 2 tables)

This paper contains 15 sections, 43 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Theoretical framework
  3. The Action and Field Definitions
  4. Generating Functional of the gauge mediated SIR Model
  5. Feynman Rules and Diagrammatic Representation
  6. Vacuum Polarization (the self-energy $\Pi$ of the pathogen field)
  7. $R_0$ in QED-SIR model
  8. Debye screening and $R_0$
  9. $R_{eff}$ Computation
  10. Superspreading hosts
  11. Results and discussion
  12. Operational Framework and Practical Application
  13. Calibration of Field Operators
  14. Operational Workflow
  15. Conclusion and Future Perspectives

Figures (3)

  • Figure 1: Vacuum Polarization of the Pathogen Field. The one-loop self-energy diagram $\Pi(q)$ for the gauge mediator $\varphi$. The incoming pathogen (wavy line) fluctuates into a virtual pair of Susceptible ($\phi_S$) and Infected ($\phi_I$) matter fields before recombining. This process is responsible for the renormalization of the pathogen mass $m_R$ and the emergence of the Debye screening length $\lambda_D$ in the effective potential.
  • Figure 2: 1-Loop Vertex Correction. The Feynman diagram representing the renormalization of the infection rate $\beta$. The main interaction (center vertex) is "dressed" by a virtual pathogen loop (wavy line) carrying momentum $k$. This loop integral generates the logarithmic correction $\ln(\Lambda/m_R)$ in two dimensions, effectively screening the coupling constant at large distances.
  • Figure 3: Workflow for the practical application of the QED-SIR model. The process translates biological data into field-theoretic variables to assess the stability of the epidemiological vacuum.