Phase transition in the susceptible-infected model on hypernetworks
1Tel Aviv University, Tel Aviv, Israel.
Physical Review. E
|August 19, 2025
Summary
This study introduces a Susceptible-Infected (SI) model on hypernetworks with N-body interactions. It reveals a threshold for epidemic spread, driven by high-order interactions absent in pairwise models.
Area of Science:
- Epidemiology
- Network Science
- Statistical Mechanics
Background:
- The Susceptible-Infected (SI) model is a fundamental tool for understanding epidemic dynamics.
- Previous models often simplify interactions to pairwise relationships, potentially missing complex effects.
- Hypernetworks offer a more realistic framework for modeling systems with multi-agent interactions.
Purpose of the Study:
- To develop and solve master equations for the SI model on general hypernetworks with N-body interactions.
- To investigate the impact of high-order interactions on epidemic spread.
- To identify conditions for epidemic transition in complex network structures.
Main Methods:
- Derivation of master equations for the SI model on hypernetworks.
- Exact solution of these equations for infinite d-regular hypernetworks.
- Analysis of the expected infection level over time.
Main Results:
- An explicit solution for the expected infection level was obtained.
- Epidemic spread to the entire population occurs if and only if the initial infection level exceeds a positive threshold.
- This phase transition is a unique effect of high-order (N-body) interactions.
Conclusions:
- High-order interactions in hypernetworks can lead to distinct epidemic behaviors compared to pairwise interaction models.
- The identified threshold phenomenon highlights the importance of network structure and interaction multiplicity in disease transmission.
- The findings provide new insights into the dynamics of infectious diseases in complex, multi-agent systems.
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