  Social interactions are stratified in multiple contexts and are subject to
complex temporal dynamics. The systematic study of these two features of social
systems has started only very recently mainly thanks to the development of
multiplex and time-varying networks. However, these two advancements have
progressed almost in parallel with very little overlap. Thus, the interplay
between multiplexity and the temporal nature of connectivity patterns is poorly
understood. Here, we aim to tackle this limitation by introducing a
time-varying model of multiplex networks. We are interested in characterizing
how these two properties affect contagion processes. To this end, we study SIS
epidemic models unfolding at comparable time-scale respect to the evolution of
the multiplex network. We study both analytically and numerically the epidemic
threshold as a function of the overlap between, and the features of, each
layer. We found that, the overlap between layers significantly reduces the
epidemic threshold especially when the temporal activation patterns of
overlapping nodes are positively correlated. Furthermore, when the average
connectivity across layers is very different, the contagion dynamics are driven
by the features of the more densely connected layer. Here, the epidemic
threshold is equivalent to that of a single layered graph and the impact of the
disease, in the layer driving the contagion, is independent of the overlap.
However, this is not the case in the other layers where the spreading dynamics
are sharply influenced by it. The results presented provide another step
towards the characterization of the properties of real networks and their
effects on contagion phenomena
