  Epidemic-like spreading processes on top of multilayered interconnected
complex networks reveal a rich phase diagram of intertwined competition
effects. A recent study by the authors [Granell et al. Phys. Rev. Lett. 111,
128701 (2013)] presented the analysis of the interrelation between two
processes accounting for the spreading of an epidemics, and the spreading of
information awareness to prevent its infection, on top of multiplex networks.
The results in the case in which awareness implies total immunization to the
disease, revealed the existence of a metacritical point at which the critical
onset of the epidemics starts depending on the reaching of the awareness
process. Here we present a full analysis of these critical properties in the
more general scenario where the awareness spreading does not imply total
immunization, and where infection does not imply immediate awareness of it. We
find the critical relation between both competing processes for a wide spectrum
of parameters representing the interaction between them. We also analyze the
consequences of a massive broadcast of awareness (mass media) on the final
outcome of the epidemic incidence. Importantly enough, the mass media makes the
metacritical point to disappear. The results reveal that the main finding i.e.
existence of a metacritical point, is rooted on the competition principle and
holds for a large set of scenarios.
