  We study SIS epidemic spreading processes unfolding on a recent
generalisation of the activity-driven modelling framework. In this model of
time-varying networks each node is described by two variables: activity and
attractiveness. The first, describes the propensity to form connections. The
second, defines the propensity to attract them. We derive analytically the
epidemic threshold considering the timescale driving the evolution of contacts
and the contagion as comparable. The solutions are general and hold for any
joint distribution of activity and attractiveness. The theoretical picture is
confirmed via large-scale numerical simulations performed considering
heterogeneous distributions and different correlations between the two
variables. We find that heterogeneous distributions of attractiveness alter the
contagion process. In particular, in case of uncorrelated and positive
correlations between the two variables, heterogeneous attractiveness
facilitates the spreading. On the contrary, negative correlations between
activity and attractiveness hamper the spreading. The results presented
contribute to the understanding of the dynamical properties of time-varying
networks and their effects on contagion phenomena unfolding on their fabric.
