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arXiv · 2504.11818

A phase transition in the Susceptible-Infected model on hypernetworks

Gadi Fibich·Guy Rothmann
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Abstract

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.

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Gadi Fibich, Guy Rothmann. 2025-04-16. A phase transition in the Susceptible-Infected model on hypernetworks. https://arxiv.org/abs/2504.11818

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