Effect of overlap on spreading dynamics on multiplex networks

TL;DR

This paper studies how the overlap between layers in multiplex networks influences epidemic spreading, revealing that overlap can change the phase transition from continuous to discontinuous and induce bistability.

Contribution

It introduces a model for SIS epidemic spreading on multiplex networks considering layer overlap, showing how overlap affects phase transition types and bistability.

Findings

Overlap changes the epidemic phase transition from continuous to discontinuous.

Decreasing overlap enlarges the bistable region.

Results are validated by simulation and mean-field theory.

Abstract

In spite of the study of epidemic dynamics on single-layer networks has received considerable attention, the epidemic dynamics on multiplex networks is still limited and is facing many challenges. In this work, we consider the susceptible-infected-susceptible-type (SIS) epidemic model on multiplex networks and investigate the effect of overlap among layers on the spreading dynamics. To do so, we assume that the prerequisite of one $S$-node to be infected is that there is at least one infectious neighbor in each layer. A remarkable result is that the overlap can alter the nature of the phase transition for the onset of epidemic outbreak. Specifically speaking, the system undergoes a usual continuous phase transition when two layers are completely overlapped. Otherwise, a discontinuous phase transition is observed, accompanied by the occurrence of a bistable region in which a disease-free phase and an endemic phase are coexisting. As the degree of the overlap decreases, the bistable region is enlarged. The results are validated by both simulation and mean-field theory.