  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.
