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.
Highlights
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
The network science community has turned its attention to network geometry [6,7,8,9] to better represent the kinds of interactions that one can find beyond typical pairwise interactions
The most accurate approximation when compared with the Monte Carlo simulation of the system, is provided by the epidemic link equations ELE
Summary
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. These higher-order interactions are encoded in geometrical structures that describe the different kinds of simplex structure present in the network: a filled clique of m + 1 nodes is known as an m-simplex, and together a set of 1-simplexes (links), 2simplexes (filled triangles), etc., comprise the simplicial complex.
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