  We estimate the abundance of Compton-thick (CT) active galactic nuclei (AGN)
based on our joint model of X-ray and infrared backgrounds. At L_{rest 2-10
keV} > 10^42 erg/s, the CT AGN density predicted by our model is a few 10^-4
Mpc^-3 from z=0 up to z=3. CT AGN with higher luminosity cuts (> 10^43, 10^44 &
10^45 erg/s) peak at higher z and show a rapid increase in the number density
from z=0 to z~2-3. The CT to all AGN ratio appears to be low (2-5%) at
f_{2-10keV} > 10^-15 erg/s/cm^2 but rises rapidly toward fainter flux levels.
The CT AGN account for ~ 38% of the total accreted SMBH mass and contribute ~
25% of the cosmic X-ray background spectrum at 20 keV. Our model predicts that
the majority (90%) of luminous and bright CT AGN (L_{rest 2-10 keV} > 10^44
erg/s or f_{2-10keV} > 10^-15 erg/s/cm^2) have detectable hot dust 5-10 um
emission which we associate with a dusty torus. The fraction drops for fainter
objects, to around 30% at L_{rest 2-10 keV} > 10^42 erg/s or f_{2-10keV} >
10^-17 erg/s/cm^2. Our model confirms that heavily-obscured AGN (N_HI > 10^23
cm^-2) can be separated from unobscured and mildly-obscured ones (N_HI < 10^23
cm^-2) in the plane of observed-frame X-ray hardness vs. mid-IR/X-ray ratio.
