A stochastic simplicial SIS model for complex networks

Abstract

We propose a stochastic epidemiological model for simplicial complex networks by means of a stochastic differential equation (SDE) that extends the mean field approach of the simplicial social contagion model. We show that, under appropriate conditions, if the stochastic basic reproductive number is smaller than one, then the disease dies out with probability one; otherwise the solution of the SDE oscillates infinitely often around a point which can be explicitly computed. We perform numerical experiments which illustrate the theoretical results. In addition, we carry out simulations on a real simplicial network and on a synthetic network, which show good agreement with the theoretical and numerical predictions of the SDE.