Fig. 1.

Simplicial contagion model (SCM). The underlying structure of a social system is made of simplices, representing d-dimensional group interactions (a), organized in a simplicial complex (b). c–h Different channels of infection for a susceptible node i in the simplicial contagion model (SCM) of order D = 2. Susceptible and infected nodes are colored in blue and red, respectively. Node i is in contact with one (c, e) or more (d, f) infected nodes through links (1-simplices), and it becomes infected with probability β at each timestep through each of these links. g, h Node i belongs to a 2-simplex (triangle). In g one of the nodes of the 2-simplex is not infected, so i can only receive the infection from the (red) link, with probability β. In h the two other nodes of the 2-simplex are infected, so i can get the infection from each of the two 1-faces (links) of the simplex with probability β, and also from the 2-face with probability β₂ = β_Δ. i Infected nodes recover with probability μ at each timestep, as in the standard SIS model