We present the first single-burst stellar population models in the infrared wavelength range between 2.5 and 5 {mu}m which are exclusively based on empirical stellar spectra. Our models take as input 180 spectra from the stellar IRTF (Infrared Telescope Facility) library. Our final single-burst stellar population models are calculated based on two different sets of isochrones and various types of initial mass functions of different slopes, ages larger than 1 Gyr and metallicities between [Fe/H] = -0.70 and 0.26. They are made available online to the scientific community on the MILES web page. We analyse the behaviour of the Spitzer [3.6]-[4.5] colour calculated from our single stellar population models and find only slight dependences on both metallicity and age. When comparing to the colours of observed early-type galaxies, we find a good agreement for older, more massive galaxies that resemble a single-burst population. Younger, less massive and more metal-poor galaxies show redder colours with respect to our models. This mismatch can be explained by a more extended star formation history of these galaxies which includes a metal-poor or/and young population. Moreover, the colours derived from our models agree very well with most other models available in this wavelength range. We confirm that the mass-to-light ratio determined in the Spitzer [3.6] {mu}m band changes much less as a function of both age and metallicity than in the optical bands.
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