Universal behavior in a generalized model of contagion

TL;DR

This paper introduces a comprehensive contagion model incorporating memory effects, revealing three main dynamic classes and providing insights into contagion susceptibility and control strategies across biological and social systems.

Contribution

It presents a unified model of contagion that interpolates between existing models and classifies collective dynamics into three main types based on measurable parameters.

Findings

Three classes of collective dynamics identified

Exact solutions for a simplified model derived

Parameters determining system behavior are measurable

Abstract

Models of contagion arise broadly both in the biological and social sciences, with applications ranging from the transmission of infectious diseases to the diffusion of innovations and the spread of cultural fads. In this Letter, we introduce a general model of contagion which, by explicitly incorporating memory of past exposures to, for example, an infectious agent, rumor, or new product, includes the main features of existing contagion models and interpolates between them. We obtain exact solutions for a simple version of the model, finding that under general conditions only three classes of collective dynamics exist, two of which correspond to familiar epidemic threshold and critical mass dynamics, while the third is a distinct intermediate case. We find that for a given length of memory, the class into which a particular system falls is determined by two parameters, each of which ought to be measurable empirically. Our model suggests novel measures for assessing the susceptibility of a population to large contagion events, and also a possible strategy for inhibiting or facilitating them.