Simplicial contagion in temporal higher-order networks

Abstract

Complex networks represent the natural backbone to study epidemic processes in populations of interacting individuals. Such a modeling framework, however, is naturally limited to pairwise interactions, making it less suitable to properly describe social contagion, where individuals acquire new norms or ideas after simultaneous exposure to multiple sources of infections. Simplicial contagion has been proposed as an alternative framework where simplices are used to encode group interactions of any order. The presence of higher-order interactions leads to explosive epidemic transitions and bistability which cannot be obtained when only dyadic ties are considered. In particular, critical mass effects can emerge even for infectivity values below the standard pairwise epidemic threshold, where the size of the initial seed of infectious nodes determines whether the system would eventually fall in the endemic or the healthy state. Here we extend simplicial contagion to time-varying networks, where pairwise and higher-order simplices can be created or destroyed over time. By following a microscopic Markov chain approach, we find that the same seed of infectious nodes might or might not lead to an endemic stationary state, depending on the temporal properties of the underlying network structure, and show that persistent temporal interactions anticipate the onset of the endemic state in finite-size systems. We characterize this behavior on higher-order networks with a prescribed temporal correlation between consecutive interactions and on heterogeneous simplicial complexes, showing that temporality again limits the effect of higher-order spreading, but in a less pronounced way than for homogeneous structures. Our work suggests the importance of incorporating temporality, a realistic feature of many real-world systems, into the investigation of dynamical processes beyond pairwise interactions.

arXiv comment9 pages, 5 figures

References in corpus (33)

• Statistical mechanics of complex networks
• Epidemic spreading in scale-free networks
• Epidemic processes in complex networks
• Temporal Networks
• Networks beyond pairwise interactions: structure and dynamics
• Simplicial models of social contagion
• Activity driven modeling of time varying networks
• Small But Slow World: How Network Topology and Burstiness Slow Down Spreading
• Discrete-time Markov chain approach to contact-based disease spreading in complex networks
• Evolutionary dynamics of higher-order interactions in social networks
• What are higher-order networks?
• Explosive higher-order Kuramoto dynamics on simplicial complexes
• Evidence of Complex Contagion of Information in Social Media: An Experiment Using Twitter Bots
• Abrupt Desynchronization and Extensive Multistability in Globally Coupled Oscillator Simplices
• Social contagion models on hypergraphs
• Fundamentals of spreading processes in single and multilayer complex networks
• Random walks on hypergraphs
• Random Walks on Simplicial Complexes and the normalized Hodge 1-Laplacian
• Generalized network structures: The configuration model and the canonical ensemble of simplicial complexes
• Multiorder Laplacian for synchronization in higher-order networks
• Analytical computation of the epidemic threshold on temporal networks
• The effect of heterogeneity on hypergraph contagion models
• Abrupt phase transition of epidemic spreading in simplicial complexes
• Multi-body Interactions and Non-Linear Consensus Dynamics on Networked Systems
• Complex contagion process in spreading of online innovation
• Chaos in generically coupled phase oscillator networks with nonpairwise interactions
• A Universal Route to Explosive Phenomena
• Fundamental properties of cooperative contagion processes
• Growing scale-free simplices
• Network clique cover approximation to analyze complex contagions through group interactions
• Contact-based model for epidemic spreading on temporal networks
• Explosive transitions induced by interdependent contagion-consensus dynamics in multiplex networks
• Markovian approach to tackle the interaction of simultaneous diseases

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• Group interactions modulate critical mass dynamics in social convention
• Effective epidemic containment strategy in hypergraphs
• Synchronization in temporal simplicial complexes
• A framework to generate hypergraphs with community structure
• Simplicial cascades are orchestrated by the multidimensional geometry of neuronal complexes
• Inference of time-ordered multibody interactions
• Consensus dynamics on temporal hypergraphs