Exact results for a simple epidemic model on a directed network: Explorations of a system in a non-equilibrium steady state

Abstract

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.

References in corpus (4)

• Epidemic dynamics and endemic states in complex networks
• Epidemics and percolation in small-world networks
• Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states
• A possible classification of nonequilibrium steady states

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