We propose new types of density dependent contact pairing interaction which reproduce the pairing gaps in symmetric and neutron matter obtained by a microscopic treatment based on the nucleon-nucleon interaction. 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 the density power law function usually introduced together with the contact interaction and require the introduction of another isoscalar term. The BCS-BEC crossover of neutrons pairs in symmetric and symmetric nuclear matter 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 $\rho_n/\rho_0\sim 10^{-3}$). Contrary the bare interaction does not form the BEC state at any neutron density.