We propose new types of density dependent contact pairing interaction which reproduce the pairing gaps in symmetric and neutron matters obtained by the Brueckner G-matrix theory. These interactions are able to simulate the pairing gaps of either the bare interaction or the interaction screened by the medium polarization effects. It is shown that the medium polarization effects cannot be cast into a usual density power law function of the contact interaction and require the introduction of another isoscalar term. The BCS-BEC crossover of neutrons pairs in symmetric and asymmetric nuclear matters is studied by using these contact interactions. It is shown that the bare and screened pairing interactions lead to different features of the BCS-BEC crossover in symmetric nuclear matter. For the screened pairing interaction, a two-neutron BEC state is formed in symmetric matter at $k_{Fn}\sim 0.2$~fm$^{-1}$ (neutron density $\rho_n/\rho_0\sim 10^{-3}$). Contrarily the bare interaction does not form the BEC state at any neutron densities.