Effects of memory on spreading processes in non-Markovian temporal networks based on simplicial complex

Abstract

Most real-world networks are complex and highly dynamic, especially biological and social networks. The interactions among nodes of this type of network tend to involve more than two nodes and change over time, and the simplicial complex structures are more adequate to describe the processes of multi-node interactions in temporal networks. However, existing models ignore the effects of memory, which has been proved to be important to affect network’ evolution and dynamic processes unfolding on the networks. Therefore, to bridge the gap, we propose a novel Simplicial Activity Driven (SADM) model with Memory, in which the simplicial structures can accurately represent multi-node interactions, and the memory can precisely describe the repeated interaction patterns. In addition, to explore how dynamical processes are impacted by SADM model, we consider the susceptible–infected–recovered (SIR) model, and adopt the temporal heterogeneous mean-field approach to calculate the SIR epidemic threshold for SADM model. We show analytically and numerically that memory in nodes’ connection patterns can shift the epidemic threshold to a larger value and decrease the density of infected nodes by confining spreading processes among nodes with recurrent communication patterns, which can make the systems less vulnerable to disease spreading. The SADM model yields new insights to elucidate the effects of social dynamics on spreading processes.