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| Главные авторы: | , |
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| Формат: | Preprint |
| Опубликовано: |
2026
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| Предметы: | |
| Online-ссылка: | https://arxiv.org/abs/2603.26708 |
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Оглавление:
- 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.