  An effective two-dimensional two-band model for infinite-layer nickelates
consists of bands obtained from $d_{x^2-y^2}$ and $s$--like orbitals. We
investigate whether it could be mapped onto a single-band Hubbard model and the
filling of Hubbard bands. We find that both one-band physics and a
Kondo-lattice regime emerge from the same two-orbital model, depending on the
strength of electronic correlations and the filling of the itinerant $s$-band.
Next we investigate one-particle excitations by changing the screening. First,
for weak screening the strong correlations push electrons out of the $s$-band
so that the undoped nickelate is similar to a cuprate. Second, for strong
screening the $s$ and $d_{x^2-y^2}$ bands are both partly filled and weakly
couple. Particularly in this latter regime mapping to a one-band model gives
significant spectral weight transfer between the Hubbard subbands. Finally we
point out that the superconducting phases may have either $d$-wave or $s$-wave
symmetry.
