Modelling of intermediate-age stellar populations: III Effects of dust-shells around AGB stars

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).