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.

5 pages, 4 figures. To appear in Physical Review Research

References in corpus (6)

• Synchronization in complex networks
• 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
• Emergent Complex Network Geometry

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• Tiered synchronization in coupled oscillator populations with interaction delays and higher-order interactions
• Influence of Asymmetric Parameters in Higher-Order Coupling With Bimodal Frequency Distribution
• Effective vaccination strategy using graph neural network ansatz
• Competing spreading dynamics in simplicial complex