  We use subhalo abundance and age distribution matching to create
magnitude-limited mock galaxy catalogs at $z\sim0.43$, $0.52$, and $0.63$ with
$z$-band and $3.4$ micron $W1$-band absolute magnitudes and ${r-z}$ and
${r-W1}$ colors. From these magnitude-limited mocks we select mock luminous red
galaxy (LRG) samples according to the $(r-z)$-based (optical) and
$(r-W1)$-based (infrared) selection criteria for the LRG sample of the Dark
Energy Spectroscopic Instrument (DESI) Survey. Our models reproduce the number
densities, luminosity functions, color distributions, and projected clustering
of the DESI Legacy Surveys that are the basis for DESI LRG target selection. We
predict the halo occupation statistics of both optical and IR DESI LRGs at
fixed cosmology, and assess the differences between the two LRG samples. We
find that IR-based SHAM modeling represents the differences between the optical
and IR LRG populations better than using the $z$-band, and that age
distribution matching overpredicts the clustering of LRGs, implying that galaxy
color is uncorrelated with halo age in the LRG regime. Both the optical and IR
DESI LRG target selections exclude some of the most luminous galaxies that
would appear to be LRGs based on their position on the red sequence in optical
color-magnitude space. Both selections also yield populations with a
non-trivial LRG-halo connection that does not reach unity for the most massive
halos. We find the IR selection achieves greater completeness ($\gtrsim 90\%$)
than the optical selection across all redshift bins studied.
