A unified framework of interplay between two spreading processes in multiplex networks

¹ School of Mathematics and Statistics, Wuhan University - Wuhan, China
² School of Engineering, Honghe University - Honghe, China
³ Computational Science Hubei Key Laboratory, Wuhan University - Wuhan, China
⁴ College of Mathematics and Statistics, Shenzhen University - Shenzhen, China

^(a) shcheng@whu.edu.cn (corresponding author)
^(b) xqwu@whu.edu.cn (corresponding author)

Received: 6 January 2016
Accepted: 29 April 2016

Abstract

Different spreading processes may interplay and display rich intertwined effects in multiplex networks. In this study, a model is proposed that consists of a two-layer network and two spreading processes respectively spread by each layer. The proposed framework can unify three scenarios for various mutual influences between the two spreading processes. The epidemic thresholds of interacting networks are contrasted and proven using the corresponding isolated networks for three scenarios: competing spreading processes, cooperative spreading processes and the combination of the two. The following conclusions resulted from this work with these three scenarios. First, the epidemic threshold of the interacting two-layer networks can be increased for two competing spreading processes; second, the epidemic threshold of the interacting two-layer networks can be decreased for two cooperative spreading processes; third, when the spreading process in one layer restrains the spreading process in the other layer, and the spreading process in the latter reinforces that in the former, the epidemic threshold of the former layer can be increased and that of the latter layer can be decreased for the interacting networks in comparison to the corresponding isolated networks. Simulations accurately verified the stated results.