  Universal spectral properties of multiplex networks allow us to assess the
nature of the transition between disease-free and endemic phases in the SIS
epidemic spreading model. In a multiplex network, depending on a coupling
parameter, $p$, the inverse participation ratio ($IPR$) of the leading
eigenvector of the adjacency matrix can be in two different structural regimes:
(i) layer-localized and (ii) delocalized. Here we formalize the structural
transition point, $p^*$, between these two regimes, showing that there are
universal properties regarding both the layer size $n$ and the layer
configurations. Namely, we show that $IPR \sim n^{-\delta}$, with
$\delta\approx 1$, and revealed an approximately linear relationship between
$p^*$ and the difference between the layers' average degrees. Furthermore, we
showed that this multiplex structural transition is intrinsically connected
with the nature of the SIS phase transition, allowing us to both understand and
quantify the phenomenon. As these results are related to the universal
properties of the leading eigenvector, we expect that our findings might be
relevant to other dynamical processes in complex networks.
