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

12 pages, 8 figures

References in corpus (6)

• Critical phenomena in complex networks
• Thresholds for epidemic spreading in networks
• Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of numerical and theoretical results
• Sandpile on Scale-Free Networks
• Langevin approach for the dynamics of the contact process on annealed scale-free networks
• A simple unified view of branching process statistics: random walks in balanced logarithmic potentials