Epidemic spreading in multiplex networks with Markov and memory based inter-layer dynamics

Many spreading processes of information and diseases take place over complex networks that are composed of multiple interconnection layers. The relationship between network structure, nodes' activity and spreading dynamics impose a threshold above which an epidemic endures. The network structure of individual layers can take different forms, such as scale-free or random, which significantly impacts the epidemic threshold. Similarly, the nodes' inter-layer transition dynamics largely influences the threshold as well. In this study we consider an inter-layer dynamics following: a Markov process, and a memory based activity creating inter-event times with a heavy-tail distribution, which are typically observed in human behavior. It is shown that by introducing a layer of inactivity the epidemic threshold can be closely predicted with our previously derived expression for multiplex networks.