  Motivated by fundamental issues in non-equilibrium statistical mechanics
(NESM), we study the venerable susceptible-infected (SIS) model of disease
spreading in an idealized, simple setting. Using Monte Carlo and analytic
techniques, we consider a fully connected, uni-directional 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 non-equilibrium steady state. We find the exact probability distribution
and explore its implications for NESM, such as the presence of persistent
probability currents.
