  During an epidemic, individual nodes in a network may adapt their connections
to reduce the chance of infection. A common form of adaption is avoidance
rewiring, where a noninfected node breaks a connection to an infected neighbor
and forms a new connection to another noninfected node. Here we explore the
effects of such adaptivity on stochastic fluctuations in the
susceptible-infected-susceptible model, focusing on the largest fluctuations
that result in extinction of infection. Using techniques from large-deviation
theory, combined with a measurement of heterogeneity in the susceptible degree
distribution at the endemic state, we are able to predict and analyze large
fluctuations and extinction in adaptive networks. We find that in the limit of
small rewiring there is a sharp exponential reduction in mean extinction times
compared to the case of zero adaption. Furthermore, we find an exponential
enhancement in the probability of large fluctuations with increased rewiring
rate, even when holding the average number of infected nodes constant.
