Kinetics of Social Contagion

TL;DR

This paper analyzes a comprehensive model of social contagion incorporating peer pressure, immune nodes, and external influence, revealing complex spreading dynamics and phase transitions in adoption behavior.

Contribution

It introduces an analytical and simulation-based study of social contagion dynamics with immune nodes and external influence, highlighting a transition in spreading speed related to immune node density.

Findings

Spontaneous adopters lead to global spreading.

A transition from fast to slow spreading occurs as immune node density increases.

The transition is linked to a percolation of induced clusters.

Abstract

Diffusion of information, behavioral patterns or innovations follows diverse pathways depending on a number of conditions, including the structure of the underlying social network, the sensitivity to peer pressure and the influence of media. Here we study analytically and by simulations a general model that incorporates threshold mechanism capturing sensitivity to peer pressure, the effect of `immune' nodes who never adopt, and a perpetual flow of external information. While any constant, non-zero rate of dynamically-introduced spontaneous adopters leads to global spreading, the kinetics by which the asymptotic state is approached shows rich behavior. In particular we find that, as a function of the immune node density, there is a transition from fast to slow spreading governed by entirely different mechanisms. This transition happens below the percolation threshold of network fragmentation, and has its origin in the competition between cascading behavior induced by adopters and blocking due to immune nodes. This change is accompanied by a percolation transition of the induced clusters.