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We study rare events in networks with both internal and external noise, anddevelop a general formalism for analyzing rare events that combinespair-quenched techniques and large-deviation theory. The probabilitydistribution, shape, and time scale of rare events are considered in detail forextinction in the Susceptible-Infected-Susceptible model as an illustration. Wefind that when both types of noise are present, there is a crossover region asthe network size is increased, where the probability exponent for largedeviations no longer increases linearly with the network size. We demonstratethat the form of the crossover depends on whether the endemic state islocalized near the epidemic threshold or not.

Rare events in networks with internal and external noise