  In this paper we study a model of interacting dark energy -- dark matter
where the ratio between these components is supposed to change from early to
late times in such a way that the model can solve or alleviate the cosmic
coincidence problem (CP). The interaction arises from an assumed relation
$\rho_x\propto\rho_d^\alpha$, where $\alpha$ is a free parameter. For a dark
energy equation of state parameter $\omega=-1$, if $\alpha=0$, the standard
$\Lambda$CDM model is recovered, where the coincidence problem is unsolved. For
$0<\alpha<1$, the CP would be alleviated and for $\alpha\sim1$, the CP would be
solved. The dark energy component is analyzed both with $\omega=-1$ and
$\omega\neq -1$ equation of state parameter. In the case of $\omega=-1$, from
SNe Ia+$H(z)$ data constraints, we found $\alpha=0.109^{+0.062}_{-0.072}$ at
68\% c.l. and the CP is alleviated. For $\omega\neq-1$, a degeneracy arises on
the $\omega$ -- $\alpha$ plane, we added cosmic microwave background distance
priors and BAO to the constraints, which yielded $\alpha=-0.075\pm0.046$ at
68\% c.l. and the CP is not alleviated even for 2$\sigma$ superior limit for
$\alpha$.
