Up to now we have assumed that the network dynamics proceeds much faster than disease spreading. This may not always be the case, and hence it is important to assess the domain of validity of this limit. In the following, we discuss the particular case of the SIS model. An analogous study for both SIR and SI yields qualitatively similar results, as discussed in the Text S1. Figure 3 shows the average SIT of the quasi-stationary distributions (circles) obtained via computer simulations (see Methods for details) as a function of the relative time scale t of network update (taking as unit time scale that associated with disease dynamics). Whenever t??, we can characterize the disease dynamics analytically, assuming a well-mixed population (complete graph), whereas for t?0 we recover the analytical results obtained in the fast linking limit. At intermediate time scales, Figure 3 shows that as long as t is smaller than 10, network dynamics contributes to inhibit disease spreading by effectively increasing the critical spreading rate. Overall, the validity of the time scale separation extends well beyond the limits one might anticipate based solely on the time separation ansatz. As long as the time scale for network update is smaller than the one for disease spreading (tv1), the analytical prediction for the limit t?0, indicated by the lower dashed line in Figure 3 , remains valid. The analytical result in the extreme opposite limit (t??), indicated by the upper dashed line in Figure 3 , holds as long as tw10 5 . Moreover, it is noteworthy that the network dynamics influences the disease dynamics both by reducing the frequency of interactions between susceptible and infected, but also by reducing the average degree of the network. These complementary effects are disentangled for intermediate regimes, in which the network dynamics is too slow to warrant sustained protection of susceptible individuals from contacts with infected, despite managing to reduce the average degree (shown by crosses). In fact, for tw10 the disease dynamics is mostly controlled by the average degree, as shown by the solid lines in Figure 3 . Here, the average stationary distribution was determined by replacing, in the analytic expression for static networks, SkT by the timedependent average connectivity SkT Ã computed numerically.