In the Text S1 we derive an analytical expression for the average recovery time (t i ) of a population with i infected individuals. Figure 4A shows the recovery time t 1 in adaptive networks for different levels of information, illustrating the spectacular effect brought about by the network dynamics on the recovery time. While on networks without information (b I = b H ) the recovery time rapidly increases with the rate of infection l, adding information moves the fraction of infected individuals rapidly to the absorbing state, and, therefore, to the disappearance of the disease. Moreover, as shown in the Text S1, the size of the population can have a profound effect on the recovery times. With increasing population size, the population spends most of the time in the vicinity of the state associated with the interior root of G(i). For large populations, this acts to reduce the intrinsic stochasticity of the dynamics, dictating a very slow extinction of the disease.