  A recently proposed density-dependent van der Waals model, with only $4$ free
parameters adjusted to fix binding energy, saturation density, symmetry energy,
and incompressibility, is analyzed under symmetric and asymmetric nuclear
matter constraints. In a previous paper, it was shown that this model is fully
consistent with the constraints related to the binary neutron star merger event
named GW170817 and reported by the LIGO and Virgo collaboration. Here, we show
that it also describes satisfactorily the low and high-density regions of
symmetric nuclear matter, with all the main constraints satisfied. We also
found a linear correlation between the incompressibility and the skewness
parameter, both at the saturation density and show how it relates to the
crossing point presented in the incompressibility as a function of the density.
In the asymmetric matter regime, other linear correlations are found, namely,
the one between the symmetry energy ($J$) and its slope ($L_0$), and other one
establishing the symmetry energy curvature as a function of the combination
given by $3J-L_0$.
