Double transitions and hysteresis in heterogeneous contagion processes

TL;DR

This paper investigates how heterogeneity in individual adoption thresholds affects contagion dynamics, revealing double phase transitions and hysteresis effects in the spread process.

Contribution

It introduces a mean-field model for heterogeneous contagion thresholds and uncovers novel phenomena like double phase transitions and hysteresis in the contagion process.

Findings

Identification of a double phase transition in contagion dynamics.

Observation of hysteresis curves due to network core effects.

Derivation of phase diagrams based on transmission probability and threshold fraction.

Abstract

In many real-world contagion phenomena, the number of contacts to spreading entities for adoption varies for different individuals. Therefore, we study a model of contagion dynamics with heterogeneous adoption thresholds. We derive mean-field equations for the fraction of adopted nodes and obtain phase diagrams in terms of the transmission probability and fraction of nodes requiring multiple contacts for adoption. We find a double phase transition exhibiting a continuous transition and a subsequent discontinuous jump in the fraction of adopted nodes because of the heterogeneity in adoption thresholds. Additionally, we observe hysteresis curves in the fraction of adopted nodes owing to adopted nodes in the densely connected core in a network.