Universality classes of generalized epidemic process on random networks

TL;DR

This paper analyzes the universality classes of the generalized epidemic process on random networks, revealing complex phase transitions and confirming theoretical predictions through finite-size scaling analysis.

Contribution

It provides a comprehensive classification of phase transitions in the GEP on Poisson networks, including continuous, discontinuous, and tricritical behaviors, supported by numerical verification.

Findings

Identifies conditions for continuous and discontinuous transitions.

Confirms field-theoretical predictions with numerical simulations.

Proposes a criterion for the discontinuous transition line.

Abstract

We present a self-contained discussion of the universality classes of the generalized epidemic process (GEP) on Poisson random networks, which is a simple model of social contagions with cooperative effects. These effects lead to rich phase transitional behaviors that include continuous and discontinuous transitions with tricriticality in between. With the help of a comprehensive finite-size scaling theory, we numerically confirm static and dynamic scaling behaviors of the GEP near continuous phase transitions and at tricriticality, which verifies the field-theoretical results of previous studies. We also propose a proper criterion for the discontinuous transition line, which is shown to coincide with the bond percolation threshold.