  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.
