Competing contagion processes: Complex contagion triggered by simple contagion

TL;DR

This paper introduces a model combining simple and complex contagion processes, revealing diverse phase transitions and an intermediate phase where simple contagion spreads before complex contagion takes hold.

Contribution

It presents a novel contagion model that captures the interplay between simple and complex contagion, demonstrating complex phase behaviors including double transitions.

Findings

Identified various phase transitions including continuous, discontinuous, and hybrid types.

Discovered a double phase transition with an intermediate susceptible phase.

Mapped a phase diagram showing the conditions for different contagion regimes.

Abstract

Empirical evidence reveals that contagion processes often occur with competition of simple and complex contagion, meaning that while some agents follow simple contagion, others follow complex contagion. Simple contagion refers to spreading processes induced by a single exposure to a contagious entity while complex contagion demands multiple exposures for transmission. Inspired by this observation, we propose a model of contagion dynamics with a transmission probability that initiates a process of complex contagion. With this probability nodes subject to simple contagion get adopted and trigger a process of complex contagion. We obtain a phase diagram in the parameter space of the transmission probability and the fraction of nodes subject to complex contagion. Our contagion model exhibits a rich variety of phase transitions such as continuous, discontinuous, and hybrid phase transitions, criticality, tricriticality, and double transitions. In particular, we find a double phase transition showing a continuous transition and a following discontinuous transition in the density of adopted nodes with respect to the transmission probability. We show that the double transition occurs with an intermediate phase in which nodes following simple contagion become adopted but nodes with complex contagion remain susceptible.