Fig. 3.

SCM of order D = 2 on a synthetic random simplicial complex (RSC). The RSC is generated with the procedure described in this manuscript, with parameters N = 2000, p₁ and p_Δ tuned in order to produce a simplicial complex with 〈k〉 ∼ 20 and 〈k_Δ〉 ∼ 6. a The average fraction of infected obtained by means of numerical simulations is plotted against the rescaled infectivity λ = β〈k〉/μ for λ_Δ = 0.8 (white squares) and λ_Δ = 2.5 (filled blue circles). The light blue circles give the numerical results for the standard SIS model (λ_Δ = 0) that does not consider higher-order effects. The red lines correspond to the analytical mean field solution described by Eq. (3). For λ_Δ = 2.5 we observe a discontinuous transition with the formation of a bistable region where healthy and endemic states co-exist. b Effect of the initial density of infected nodes, shown by the temporal evolution of the densities of infectious nodes (a single realization is shown for each value of the initial density). The infectivity parameters are set within the range in which we observe a bistable region (λ = β〈k〉/μ = 0.75, λ_Δ = β_Δ〈k_Δ〉/μ = 2.5). Different curves—and different colors—correspond to different values for the initial density of infectious nodes ρ₀ ≡ ρ(0). The dashed horizontal line corresponds to the unstable branch ${\rho }_{2-}^{*}$ of the mean field solution given by Eq. 4, which separates the two basins of attraction