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Enhanced extinction processes in the presence of non-Gaussian controls

lora billings, Mark Dykman
We investigate stochastic extinction processes in the presence of non-Gaussian noise. Motivated by the process of natural disease extinction in epidemics, we examine the impact of random vaccinations in large populations. We show that, in the absence of vaccinations, the effective entropic barrier for extinction in an SIS model displays scaling with the distance to the bifurcation point, with an unusual critical exponent. Even a comparatively weak Poisson-distributed vaccination leads to an exponential increase in the extinction rate, with the exponent that strongly depends on the vaccination parameters. We make a direct comparison between predictions and numerical simulation in both 1 and 2 dimensional models.
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