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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.26708 |
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| _version_ | 1866914427131920384 |
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| author | Bernal-Alvarado, Jose Jesus Delepine, David |
| author_facet | Bernal-Alvarado, Jose Jesus Delepine, David |
| contents | Classical compartmental models of epidemiology rely on well-mixed, local interaction approximations that fail to capture the heavy-tailed burst dynamics and long-range spatial correlations observed in real-world outbreaks. While fractional calculus is frequently employed to model these anomalous behaviors, fractional operators are introduced phenomenologically. In this work, we demonstrate that fractional space-time epidemic dynamics emerge naturally and rigorously from first principles using a non-equilibrium quantum field theory model. By mapping the stochastic contagion process to a gauge-mediated field theory via the Doi-Peliti formalism, we go beyond the static mean-field approximation to compute the full dynamical one-loop vacuum polarization. We prove that integrating out a dynamically fluctuating host vacuum generates anomalous momentum and frequency scaling. Transitioning back to coordinate space, this derives a coupled space-time fractional integro-differential equations, where the non-linear transmission vertex is governed by parabolic Riesz potentials and Riemann-Liouville time derivatives. We show that in the anomalous regime ($α< 2$), local Debye screening is modified, facilitating Lévy flight super-spreading and temporal avalanches. Consequently, the effective reproductive number ($R_{eff}$) ceases to be a scalar, transforming into a spectral dispersion relation bounded strictly by the ultraviolet spatial cutoff. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_26708 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fractional epidemics from quantum loops Bernal-Alvarado, Jose Jesus Delepine, David Statistical Mechanics Populations and Evolution Classical compartmental models of epidemiology rely on well-mixed, local interaction approximations that fail to capture the heavy-tailed burst dynamics and long-range spatial correlations observed in real-world outbreaks. While fractional calculus is frequently employed to model these anomalous behaviors, fractional operators are introduced phenomenologically. In this work, we demonstrate that fractional space-time epidemic dynamics emerge naturally and rigorously from first principles using a non-equilibrium quantum field theory model. By mapping the stochastic contagion process to a gauge-mediated field theory via the Doi-Peliti formalism, we go beyond the static mean-field approximation to compute the full dynamical one-loop vacuum polarization. We prove that integrating out a dynamically fluctuating host vacuum generates anomalous momentum and frequency scaling. Transitioning back to coordinate space, this derives a coupled space-time fractional integro-differential equations, where the non-linear transmission vertex is governed by parabolic Riesz potentials and Riemann-Liouville time derivatives. We show that in the anomalous regime ($α< 2$), local Debye screening is modified, facilitating Lévy flight super-spreading and temporal avalanches. Consequently, the effective reproductive number ($R_{eff}$) ceases to be a scalar, transforming into a spectral dispersion relation bounded strictly by the ultraviolet spatial cutoff. |
| title | Fractional epidemics from quantum loops |
| topic | Statistical Mechanics Populations and Evolution |
| url | https://arxiv.org/abs/2603.26708 |