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arXiv · 1409.0149

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

Maxim S. Shkarayev·R. K. P. Zia
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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.

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Maxim S. Shkarayev, R. K. P. Zia. 2014-08-30. Exact results for a simple epidemic model on a directed network: Explorations of a system in a non-equilibrium steady state. https://doi.org/10.1103/physreve.90.032107

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