Exact results for a simple epidemic model on a directed network: explorations of a system in a nonequilibrium steady state.

Motivated by fundamental issues in nonequilibrium statistical mechanics, we study the venerable susceptible-infected-susceptible (SIS) model of disease spreading in an idealized, simple setting. Using Monte Carlo and analytic techniques, we consider a fully connected, unidirectional network of odd number of nodes, each having an equal number of in- and out-degrees. With the standard SIS dynamics at high infection rates, this system settles into an active nonequilibrium steady state. We find the exact probability distribution and explore its implications for nonequilibrium statistical mechanics, such as the presence of persistent probability currents.