Rare-event extinction on stochastic networks
1 US Naval Research Laboratory, Code 6792, Nonlinear System Dynamics Section, Plasma Physics Division Washington, DC 20375, USA
2 College of William and Mary, Department of Applied Science - Williamsburg, VA 23187-8795, USA
Received: 31 July 2014
Accepted: 24 November 2014
We consider the problem of extinction processes on random networks with a given structure. For sufficiently large well-mixed populations, the process of extinction of one or more state variable components occurs in the tail of the quasi-stationary probability distribution, thereby making it a rare event. Here we show how to extend the theory of large deviations to random networks to predict extinction times. In particular, we use the theory to find the most probable path leading to extinction. We apply the methodology to epidemic models and discover how mean extinction times scale with epidemiological and network parameters in Erdős-Rényi networks. The results are shown to compare quite well with Monte Carlo simulations of the network in predicting both the most probable paths to extinction and mean extinction times.
PACS: 87.23.Cc – Population dynamics and ecological pattern formation / 87.10.Mn – Stochastic modeling
© EPLA, 2014