Abrupt phase transition of epidemic spreading in simplicial complexes

TL;DR

This paper investigates epidemic spreading in simplicial complexes, revealing an abrupt phase transition influenced by higher-order interactions, which enhances understanding of disease transmission in group-based networks.

Contribution

It introduces an analytical framework for SIS epidemic dynamics in simplicial complexes, highlighting a novel abrupt phase transition due to three-body interactions.

Findings

Discovered an abrupt phase transition in epidemic spreading.

Higher-order interactions significantly affect epidemic dynamics.

Provided an analytical model for SIS 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.