Phase transitions for polyadic epidemic and voter models with multiscale groups

TL;DR

This paper investigates how multiscale polyadic interactions influence phase transitions in epidemic and voter models, revealing bistability and stabilization effects that differ from classical pairwise interaction assumptions.

Contribution

It introduces the analysis of multiscale polyadic group interactions in epidemic and voter models, highlighting their effects on stability and phase transitions.

Findings

Bistability region protects the disease-free state beyond classical thresholds.

Multiscale interactions stabilize networks and accelerate convergence.

Polyadic interactions significantly alter equilibrium dynamics.

Abstract

Polyadic (or higher-order) interactions can significantly impact the dynamics of interacting particle systems. However, previous studies have often assumed group sizes to be relatively small. In this work, we examine the influence of multiscale polyadic group interactions, where some groups are small and others are very large. We consider two paradigmatic examples, an SIS-epidemic and the adaptive voter model. On the level of the mean field, we specifically discuss the impact of the multiscale polyadic interactions on equilibrium dynamics and phase transitions. For the SIS-epidemic model, we find a region of bistability that protects the disease-free state over a wide range beyond the classical epidemic threshold from a significant outbreak. For the adaptive voter model, we show that multiscale polyadic interactions can stabilize the network or increase the convergence rate to an unbiased equilibrium.