# Co-Contagion Diffusion on Multilayer Networks

## TL;DR

This paper models co-contagion diffusion on multilayer networks, revealing how contagion speed, network topology, and dormancy influence diffusion dynamics and interdependence between contagions.

## Contribution

It extends threshold models to multilayer networks, analyzing the effects of synergy, dormancy, and topology on co-contagion diffusion with novel insights.

## Key findings

- Faster contagions induce branching on slower ones.
- Shorter path lengths reduce dormancy impact.
- Long-range graphs cause contagion dependence on dormancy rates.

## Abstract

This study examines the interface of three elements during co-contagion diffusion: the \textbf{synergy} between contagions, the \textbf{dormancy} rate of each individual contagion, and the \textbf{multiplex network topology}. Dormancy is defined as a weaker form of "immunity," where dormant nodes no longer actively participate in diffusion, but are still susceptible to infection. The proposed model extends the literature on threshold models, and demonstrates intricate interdependencies between different graph structures. Our simulations show that first, the faster contagion induces branching on the slower contagion; second, shorter characteristic path lengths diminish the impact of dormancy in lowering diffusion. Third, when two long-range graphs are paired, the faster contagion depends on both dormancy rates, whereas the slower contagion depends only on its own; fourth, synergistic contagions are less sensitive to dormancy, and have a wider window to diffuse. Furthermore, when long-range and spatially constrained graphs are paired, ring vaccination occurs on the spatial graph and produces partial diffusion, due to dormant, surrounding nodes. The spatial contagion depends on both dormancy rates whereas the long-range contagion depends on only its own.