  The modeling of the spreading of communicable diseases has experienced
significant advances in the last two decades or so. This has been possible due
to the proliferation of data and the development of new methods to gather, mine
and analyze it. A key role has also been played by the latest advances in new
disciplines like network science. Nonetheless, current models still lack a
faithful representation of all possible heterogeneities and features that can
be extracted from data. Here, we bridge a current gap in the mathematical
modeling of infectious diseases and develop a framework that allows to account
simultaneously for both the connectivity of individuals and the age-structure
of the population. We compare different scenarios, namely, i) the homogeneous
mixing setting, ii) one in which only the social mixing is taken into account,
iii) a setting that considers the connectivity of individuals alone, and
finally, iv) a multilayer representation in which both the social mixing and
the number of contacts are included in the model. We analytically show that the
thresholds obtained for these four scenarios are different. In addition, we
conduct extensive numerical simulations and conclude that heterogeneities in
the contact network are important for a proper determination of the epidemic
threshold, whereas the age-structure plays a bigger role beyond the onset of
the outbreak. Altogether, when it comes to evaluate interventions such as
vaccination, both sources of individual heterogeneity are important and should
be concurrently considered. Our results also provide an indication of the
errors incurred in situations in which one cannot access all needed information
in terms of connectivity and age of the population.
