Lumping Reductions for Multispread in Multi-Layer Networks

Spreading phenomena arise from simple local interaction among a large number of actors through different networks of interactions. Computational modelling and analysis of such phenomena is challenging due to the combinatorial explosion of possible network configurations. Traditional (single layer) networks are commonly used to encode the heterogeneous relationships among agents but are limited to a single type of interaction. Multiplex Multi-Layer networks (MLNs) have been introduced to allow the modeler to compactly and naturally describe multiple types of interactions and multiple simultaneous spreading phenomena. The downside is an increase in the complexity of the already challenging task of the analysis and simulation of such spreading processes. In this paper we explore the use of lumping techniques that preserve dynamics, previously applied to Continuous Time Markov Chains (CTMC) and single layer networks to multiple spreading processes on MLNs.