Directionality reduces the impact of epidemics in multilayer networks

Our understanding of how diseases spread has greatly benefited from advances in network modeling. However, despite of its importance for disease contagion, the directionality of edges has rarely been taken into account. On the other hand, the introduction of the multilayer framework has made it possible to deal with more complex scenarios in epidemiology such as the interaction between different pathogens or multiple strains of the same disease. In this work, we study in depth the dynamics of disease spreading in directed multilayer networks. Using the generating function approach and numerical simulations of a stochastic susceptible-infected-susceptible model, we calculate the epidemic threshold of synthetic and real-world multilayer systems and show that it is mainly determined by the directionality of the links connecting different layers, regardless of the degree distribution chosen for the layers. Our findings are of utmost interest given the ubiquitous presence of directed multilayer networks and the widespread use of disease-like spreading processes in abroad range of phenomena such as diffusion processes in social and transportation systems.