In the Methods, we show that disease spreading in a quickly adapting network can be studied as if it took place in a well-mixed population with same average degree SkT as the original network and transmission probability l A . Since the lifetime of a link depends on its type, the average degree SkT of the network depends on the number of infected in the population, and hence becomes frequency (and time) dependent. Similarly, fast linking dynamics leads to a rescaling of the transmission probability, l?l A~g{1 l, with g depending on the particular model of disease spreading. In the SIR model, g is given by