Epidemics on multilayer simplicial complexes

Simplicial complexes describe the simple fact that in social networks a link can connect more than two individuals. As we show here, this has far-reaching consequences for epidemic spreading, in particular in the context of a multilayer network model, where one layer is a virtual social network and the other one is a physical contact network. The social network layer is responsible for the transmission of information via pairwise or higher order 2-simplex interactions among individuals, while the physical layer is responsible for the epidemic spreading. We use the microscopic Markov chain approach to derive the probability transition equations and to determine epidemic outbreak thresholds. We further support these results with Monte Carlo simulations, which are in good agreement, thus confirming the analytical tractability of the proposed model. We find that information transmission rates are frequently low when actual disease transmission rates in the physical network are low or medium, and we show that this can be mitigated effectively by introducing 2-simplex interactions in the social network. The relative ease of introducing higher-order interactions in virtual social networks means that this could be exploited to inhibit epidemic outbreaks.