Quasi-stationary analysis of the contact process on annealed scale-free networks

TL;DR

This paper analyzes the quasi-stationary state of the contact process on annealed scale-free networks, combining analytical and numerical methods to understand critical behavior and corrections to scaling.

Contribution

It introduces a mapping of the contact process to a one-step process and provides an accurate analytical approach to study its quasi-stationary state on annealed networks.

Findings

Excellent agreement between master equation solutions and stochastic simulations.

Identification of strong corrections to scaling in critical and supercritical regions.

Analytical finite size scaling results obtained via heterogeneous mean-field approach.

Abstract

We present an analysis of the quasi-stationary (QS) state of the contact process (CP) on annealed scale-free networks using a mapping of the CP dynamics in a one-step processes and analyzing numerically and analytically the corresponding master equation. The relevant QS quantities determined via the master equation exhibit an excellent agreement with direct QS stochastic simulations of the CP. The high accuracy of the resulting data allows to probe the strong corrections to scaling present in both the critical and supercritical regions, corrections that mask the correct finite size scaling obtained analytically by applying an exact heterogeneous mean-field approach. {Our results represent a promising starting point for a deeper understanding of the contact process and absorbing phase transitions on real (quenched) complex networks