Rare Event Extinction on Stochastic Networks

Abstract

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 Erdos-Renyi 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.

5 pages 6 figures

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Cited by in corpus (11)

• WKB theory of large deviations in stochastic populations
• Epidemic extinction and control in heterogeneous networks
• Large deviations of random walks on random graphs
• Epidemic Extinction Paths in Complex Networks
• Enhancement of large fluctuations to extinction in adaptive networks
• Large order fluctuations, switching, and control in complex networks
• Large deviation induced phase switch in an inertial majority-vote model
• Epidemic extinction in a generalized susceptible-infected-susceptible model
• Network Inoculation: Heteroclinics and phase transitions in an epidemic model
• Extremal statistics for first-passage trajectories of drifted Brownian motion under stochastic resetting
• Epidemic extinction in a simplicial susceptible-infected-susceptible model