Modeling the evolution of infrared galaxies: a parametric backward evolution model

International audience Aims: We attempt to model the infrared galaxy evolution in as simple a way as possible and reproduce statistical properties such as the number counts between 15 μm and 1.1 mm, the luminosity functions, and the redshift distributions. We then use the fitted model to interpret observations from Spitzer, AKARI, BLAST, LABOCA, AzTEC, SPT, and Herschel, and make predictions for Planck and future experiments such as CCAT or SPICA. Methods: This model uses an evolution in density and luminosity of the luminosity function parametrized by broken power-laws with two breaks at redshift ~0.9 and 2, and contains the two populations of the Lagache model: normal and starburst galaxies. We also take into account the effect of the strong lensing of high-redshift sub-millimeter galaxies. This effect is significant in the sub-mm and mm range near 50 mJy. It has 13 free parameters and eight additional calibration parameters. We fit the parameters to the IRAS, Spitzer, Herschel, and AzTEC measurements with a Monte Carlo Markov chain. Results: The model adjusted to deep counts at key wavelengths reproduces the counts from mid-infrared to millimeter wavelengths, as well as the mid-infrared luminosity functions. We discuss the contribution to both the cosmic infrared background (CIB) and the infrared luminosity density of the different populations. We also estimate the effect of the lensing on the number counts, and discuss the discovery by the South Pole Telescope (SPT) of a very bright population lying at high redshift. We predict the contribution of the lensed sources to the Planck number counts, the confusion level for future missions using a P(D) formalism, and the Universe opacity to TeV photons caused by the CIB. Material of the model (software, tables and predictions) is available online