  In this paper,we present single stellar population models of intermediate age
stellar populations where dust-enshrouded AGB stars are introduced. The
formation of carbon stars is also accounted for, and is taken to be a function
of both initial mass and metallicity. The effect of the dusty envelopes around
AGB stars on the optical/near-infrared spectral energy distribution were
introduced using semi-emipirical models where the mass-loss and the
photospheric chemistry determine the spectral properties of a star along the
AGB sequence. The spectral dichotomy between O-rich stars and C-rich stars is
taken into account in the modelling. We have investigated the AGB sequence
morphology in he near-infrared CMD as a function of time and metallicity. We
show that this diaggram is characterized by three morphological features,
occupied by optically bright O-rich stars, optically bright C-rich stars, and
dust-enshrouded O-rich and C-rich stars respectively. Our models are able to
reproduce the distribution of the three AGB subtype stellar populations in
colour-colour diagrams. Effects of dusty envelopes on the luminosity function
are also investigated (Abriged).
