Exact results for a simple epidemic model on a directed network: Explorations of a system in a non-equilibrium steady state
Statistical Mechanics
2015-06-22 v1
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.
Keywords
Cite
@article{arxiv.1409.0149,
title = {Exact results for a simple epidemic model on a directed network: Explorations of a system in a non-equilibrium steady state},
author = {Maxim S. Shkarayev and R. K. P. Zia},
journal= {arXiv preprint arXiv:1409.0149},
year = {2015}
}