From Stochastic Shocks to Macroscopic Tails: The Moyal Distribution as a Unified Framework for Epidemic Dynamics
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912888612978688 |
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| author | Bernal-Alvarado, Jose de Jesus Delepine, David |
| author_facet | Bernal-Alvarado, Jose de Jesus Delepine, David |
| contents | Traditional epidemiological models often fail to characterize the extreme volatility and heavy-tailed "Dragon King" events observed in real-world outbreaks. We propose a unified framework that bridges microscopic agent-based simulations with macroscopic wave decomposition using the Moyal probability density function. By treating viral transmission as a stochastic collision process, we derive a Moyal-Poisson mixture that describes secondary case distributions. Our model successfully recovers the extreme ``superspreading'' events in SARS, MERS, and COVID-19 data that standard Negative Binomial models systematically miss. Furthermore, we apply spectral decomposition to pandemic waves in Germany, demonstrating that the macroscopic "Social Friction" ($β$) is a direct emergent property of microscopic "Collision Shocks". This framework provides a useful descriptive tool for public health planning, emphasizing the need to manage extreme volatility rather than deterministic averages. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08101 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | From Stochastic Shocks to Macroscopic Tails: The Moyal Distribution as a Unified Framework for Epidemic Dynamics Bernal-Alvarado, Jose de Jesus Delepine, David Populations and Evolution Traditional epidemiological models often fail to characterize the extreme volatility and heavy-tailed "Dragon King" events observed in real-world outbreaks. We propose a unified framework that bridges microscopic agent-based simulations with macroscopic wave decomposition using the Moyal probability density function. By treating viral transmission as a stochastic collision process, we derive a Moyal-Poisson mixture that describes secondary case distributions. Our model successfully recovers the extreme ``superspreading'' events in SARS, MERS, and COVID-19 data that standard Negative Binomial models systematically miss. Furthermore, we apply spectral decomposition to pandemic waves in Germany, demonstrating that the macroscopic "Social Friction" ($β$) is a direct emergent property of microscopic "Collision Shocks". This framework provides a useful descriptive tool for public health planning, emphasizing the need to manage extreme volatility rather than deterministic averages. |
| title | From Stochastic Shocks to Macroscopic Tails: The Moyal Distribution as a Unified Framework for Epidemic Dynamics |
| topic | Populations and Evolution |
| url | https://arxiv.org/abs/2602.08101 |