Macroscopic Signatures of Gauge-Mediated Contagion: Deriving Behavioral Shielding from Stochastic Field Theory
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908927879282688 |
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| author | Bernal-Alvarado, Jose de Jesus Delepine, David |
| author_facet | Bernal-Alvarado, Jose de Jesus Delepine, David |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00153 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Macroscopic Signatures of Gauge-Mediated Contagion: Deriving Behavioral Shielding from Stochastic Field Theory Bernal-Alvarado, Jose de Jesus Delepine, David Populations and Evolution Applications 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. |
| title | Macroscopic Signatures of Gauge-Mediated Contagion: Deriving Behavioral Shielding from Stochastic Field Theory |
| topic | Populations and Evolution Applications |
| url | https://arxiv.org/abs/2604.00153 |