Critical avalanches of Susceptible-Infected-Susceptible dynamics in finite networks

TL;DR

This paper studies the critical avalanche behavior of the SIS epidemic model on finite networks, revealing distinct dynamical regimes and scaling behaviors through simulations and theoretical analysis.

Contribution

It provides a detailed numerical and theoretical analysis of SIS avalanche dynamics on finite networks, highlighting differences between homogeneous and heterogeneous topologies.

Findings

Survival probability shows three distinct regimes.

Crossover timescales depend on network heterogeneity.

Langevin theory accurately models homogeneous networks.

Abstract

We investigate the avalanche temporal statistics of the Susceptible-Infected-Susceptible (SIS) model when the dynamics is critical and takes place on finite random networks. By considering numerical simulations on annealed topologies we show that the survival probability always exhibits three distinct dynamical regimes. Size-dependent crossover timescales separating them scale differently for homogeneous and for heterogeneous networks. The phenomenology can be qualitatively understood based on known features of the SIS dynamics on networks. A fully quantitative approach based on Langevin theory is shown to perfectly reproduce the results for homogeneous networks, while failing in the heterogeneous case. The analysis is extended to quenched random networks, which behave in agreement with the annealed case for strongly homogeneous and strongly heterogeneous networks.