  We extend the N-Intertwined Mean-Field Approximation (NIMFA) for the
Susceptible-Infectious-Susceptible (SIS) epidemiological process to
time-varying networks. Processes on time-varying networks are often analysed
under the assumption that the process and network evolution happen on different
timescales. This approximation is called timescale separation. We investigate
timescale separation between disease spreading and topology updates of the
network. We introduce the transition times $\mathrm{\underline{T}}(r)$ and
$\mathrm{\overline{T}}(r)$ as the boundaries between the intermediate regime
and the annealed (fast changing network) and quenched (static network) regimes,
respectively, for a fixed accuracy tolerance $r$. By analysing the convergence
of static NIMFA processes, we analytically derive upper and lower bounds for
$\mathrm{\overline{T}}(r)$. Our results provide insights/bounds on the time of
convergence to the steady state of the static NIMFA SIS process. We show that,
under our assumptions, the upper-transition time $\mathrm{\overline{T}}(r)$ is
almost entirely determined by the basic reproduction number $R_0$ of the
network. The value of the upper-transition time $\mathrm{\overline{T}}(r)$
around the epidemic threshold is large, which agrees with the current
understanding that some real-world epidemics cannot be approximated with the
aforementioned timescale separation.
