A phase transition in the Susceptible-Infected model on hypernetworks

2025/04/16 by Gadi Fibich, Fibich, Gadi, Guy Rothmann +1
Physics and Astronomy · Mathematics · #Theoretical and Computational Physics #Mathematical Biology Tumor Growth #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2504.11818

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 → ∞ 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.

Citations

• Explicit solutions of the SI and Bass models on sparse Erdős-Rényi and regular networks
• What Are Higher-Order Networks?
• Networks beyond pairwise interactions: structure and dynamics
• Social contagion models on hypergraphs
• Simplicial models of social contagion
• A Sharp Threshold for Bootstrap Percolation in a Random Hypergraph
• Simplicial Activity Driven Model
• Boundary Effects in the Discrete Bass Model
• Epidemic processes in complex networks
• Epidemic outbreaks in complex heterogeneous networks
• Epidemic Spreading in Scale-Free Networks

Related

• Explicit solutions of the Bass and SI models on hypernetworks
• The spread of infections on evolving scale-free networks
• Epidemic threshold and localization of the SIS model on directed complex networks
• SIR Epidemics in Interconnected Networks: threshold curve and phase transition
• Epidemic Thresholds with External Agents