  We aim at modeling the infrared galaxy evolution in an as simple as possible
way and reproduce statistical properties among which the number counts between
15 microns and 1.1 mm, the luminosity functions, and the redshift
distributions. We then aim at using this model to interpret the recent
observations (Spitzer, Akari, BLAST, LABOCA, AzTEC, SPT and Herschel), and make
predictions for future experiments like CCAT or SPICA.
  This model uses an evolution in density and luminosity of the luminosity
function with two breaks at redshift ~0.9 and 2 and contains the two
populations of the Lagache et al. (2004) model: normal and starburst galaxies.
We also take into account the effect of the strong lensing of high-redshift
sub-millimeter galaxies. It has 13 free parameters and 8 additional calibration
parameters. We fit the parameters to the IRAS, Spitzer, Herschel and AzTEC
measurements with a Monte-Carlo Markov chain.
  The model ajusted on deep counts at key wavelengths reproduces the counts
from the mid-infrared to the millimeter wavelengths, as well as the
mid-infrared luminosity functions. We discuss the contribution to the cosmic
infrared background (CIB) and to the infrared luminosity density of the
different populations. We also estimate the effect of the lensing on the number
counts, and discuss the recent discovery by the South Pole Telescope (SPT) of a
very bright population lying at high-redshift. We predict confusion level for
future missions using a P(D) formalism, and the Universe opacity to TeV photons
due to the CIB.
