The impact of cross-layer movement on epidemic spreading in time-varying multiplex networks

Abstract In the context of real-world multiplex networks, the movement of individuals across different layers introduced interlayer coupling, which significantly affected diffusion processes within each layer. Additionally, the relationships among individuals undergo changes over time. Despite the abundant literature on the dynamics of propagation in complex networks, the impact of interlayer transitions (or interlayer jumps, interlayer shifts) on the spread of epidemics in activity-driven time-varying multiplex networks remains a relatively unexplored area. In this study, we introduced a time-varying two-layer network model that incorporated a subset of nodes known as inter-layer travelers, allowing them to move between different layers. We developed a theoretical framework based on the quenched mean-field approximation, which yielded precise estimations of epidemic thresholds and final states in both layers. Our findings indicated that the hopping behavior of interlayer travelers and the time-varying nature of the network impeded the disease transmission process. Furthermore, stronger heterogeneity in the individual activities could promote epidemic spread. However, the hopping behavior of interlayer travelers enhanced epidemic transmission in sub-networks with lower node activity heterogeneity while inhibiting it in sub-networks with higher node activity heterogeneity. Additionally, stronger contact capacity of nodes promoted disease spread, and interlayer traveler hopping promoted epidemic spreading in the sparse layer while suppressing it in the dense layer. Notably, an enhanced positive correlation between activities in the two layers can greatly suppress the spreading dynamics, suggesting a practical and effective approach to controlling epidemics in the real world.