A phase transition in the Susceptible-Infected model on hypernetworks
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915245832798208 |
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| author | Fibich, Gadi Rothmann, Guy |
| author_facet | Fibich, Gadi Rothmann, Guy |
| contents | We derive the master equations for the Susceptible-Infected (SI) model on general hypernetworks with~$N$-body interactions. We solve these equations exactly for infinite~$d$-regular hypernetworks, and obtain an explicit solution for the expected infection level as a function of time. The solution shows that the epidemic spreads out to the entire population as~$t \to \infty$ if and only if the initial infection level exceeds a positive threshold value. This phase transition is a high-order interactions effect, which is absent with pairwise interactions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11818 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A phase transition in the Susceptible-Infected model on hypernetworks Fibich, Gadi Rothmann, Guy Physics and Society We derive the master equations for the Susceptible-Infected (SI) model on general hypernetworks with~$N$-body interactions. We solve these equations exactly for infinite~$d$-regular hypernetworks, and obtain an explicit solution for the expected infection level as a function of time. The solution shows that the epidemic spreads out to the entire population as~$t \to \infty$ if and only if the initial infection level exceeds a positive threshold value. This phase transition is a high-order interactions effect, which is absent with pairwise interactions. |
| title | A phase transition in the Susceptible-Infected model on hypernetworks |
| topic | Physics and Society |
| url | https://arxiv.org/abs/2504.11818 |