Abrupt phase transition of epidemic spreading in simplicial complexes

Abstract

Recent studies on network geometry, a way of describing network structures as geometrical objects, are revolutionizing our way to understand dynamical processes on networked systems. Here, we cope with the problem of epidemic spreading, using the Susceptible-Infected-Susceptible (SIS) model, in simplicial complexes. In particular, we analyze the dynamics of SIS in complex networks characterized by pairwise interactions (links), and three-body interactions (filled triangles, also known as 2-simplices). This higher-order description of the epidemic spreading is analytically formulated using a microscopic Markov chain approximation. The analysis of the fixed point solutions of the model, reveal an interesting phase transition that becomes abrupt with the infectivity parameter of the 2-simplices. Our results pave the way for network theorists to advance in our physical understanding of epidemic spreading in real scenarios where diseases are transmitted among groups as well as among pairs, and to better understand the behaviour of dynamical processes in simplicial complexes.

arXiv comment5 pages, 4 figures. To appear in Physical Review Research

References in corpus (22)

• Epidemic processes in complex networks
• Synchronization in complex networks
• Dynamical interplay between awareness and epidemic spreading in multiplex networks
• Simplicial models of social contagion
• A roadmap for the computation of persistent homology
• Discrete-time Markov chain approach to contact-based disease spreading in complex networks
• Simplicial Closure and higher-order link prediction
• Pseudofractal Scale-free Web
• Competing spreading processes on multiplex networks: awareness and epidemics
• Abrupt Desynchronization and Extensive Multistability in Globally Coupled Oscillator Simplices
• Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of numerical and theoretical results
• Persistent Homology of Complex Networks
• Explosive Phenomena in Complex Networks
• Simplicial complexes and complex systems
• Topological analysis of the connectome of digital reconstructions of neural microcircuits
• Pair quenched mean-field theory for the susceptible-infected-susceptible model on complex networks
• A framework for epidemic spreading in multiplex networks of metapopulations
• Effective approach to epidemic containment using link equations in complex networks
• Non-perturbative heterogeneous mean-field approach to epidemic spreading in complex networks
• Emergent Complex Network Geometry
• Hopf normal form with $S_N$ symmetry and reduction to systems of nonlinearly coupled phase oscillators
• Synchronization in Network Geometries with Finite Spectral Dimension

Cited by in corpus (43)

• Networks beyond pairwise interactions: structure and dynamics
• The physics of higher-order interactions in complex systems
• Explosive higher-order Kuramoto dynamics on simplicial complexes
• Higher-order interactions in complex networks of phase oscillators promote abrupt synchronization switching
• Random walks on hypergraphs
• The effect of heterogeneity on hypergraph contagion models
• Coupled Dynamics on Hypergraphs: Master Stability of Steady States and Synchronization
• Higher-order percolation processes on multiplex hypergraphs
• Simplicial contagion in temporal higher-order networks
• Unified treatment of synchronization patterns in generalized networks with higher-order, multilayer, and temporal interactions
• Contagion in simplicial complexes
• Evolution of Cooperation in the Presence of Higher-Order Interactions: from Networks to Hypergraphs
• Network clique cover approximation to analyze complex contagions through group interactions
• Hyperedge overlap drives explosive collective behaviors in systems with higher-order interactions
• Expectation-Maximizing Network Reconstruction and MostApplicable Network Types Based on Binary Time Series Data
• Effective epidemic containment strategy in hypergraphs
• Homological percolation transitions in growing simplicial complexes
• Balanced Hodge Laplacians Optimize Consensus Dynamics over Simplicial Complexes
• Contagion dynamics on hypergraphs with nested hyperedges
• Social contagion on higher-order structures
• Simplicially driven simple contagion
• Hypergraph assortativity: a dynamical systems perspective
• Multistability in coupled oscillator systems with higher-order interactions and community structure
• $(k,q)$-core decomposition of hypergraphs
• Self-organized explosive synchronization in complex networks: Emergence of synchronization bombs
• Stochastic epidemic model on a simplicial complex
• Prediction and mitigation of nonlocal cascading failures using graph neural networks
• Nonlinear bias toward complex contagion in uncertain transmission settings
• Infection percolation: A dynamic network model of disease spreading
• Tiered synchronization in coupled oscillator populations with interaction delays and higher-order interactions
• Simplicial cascades are orchestrated by the multidimensional geometry of neuronal complexes
• The universality of physical images at relative timescales on multiplex networks
• Influence of Asymmetric Parameters in Higher-Order Coupling With Bimodal Frequency Distribution
• Higher-order temporal network effects through triplet evolution
• Topological estimation of the latent geometry of a complex network
• Tricritical behavior in epidemic dynamics with vaccination
• Adaptive Epidemic Dynamics on Hypergraphs with Group-Level Immunization and Rewiring
• Local topological moves determine global diffusion properties of hyperbolic higher-order networks
• Extremal statistics for first-passage trajectories of drifted Brownian motion under stochastic resetting
• Epidemic extinction in a simplicial susceptible-infected-susceptible model
• Combinatorial Properties for a Class of Simplicial Complexes Extended from Pseudo-fractal Scale-free Web
• Effective vaccination strategy using graph neural network ansatz
• Competing spreading dynamics in simplicial complex