This paper presents a Lagrangian stochastic model to simulate colloid resuspension from rough surfaces. For that purpose, the extension of a recent proposition is discussed as well as the details of its numerical implementation. The basis of this model is a dynamical approach which reproduces explicitly the different steps involved in a three-stage scenario of particle resuspension where particles are set in motion (first stage); roll/slide along a rough surface due to varying force moments (second stage); and can be detached when a large-scale asperity is hit (third stage). The model treats separately hydrodynamic forces (drag force), adhesion forces (mainly due to interface chemical effects) and surface roughness through a two-level description (small-scale asperities and large-scale asperities) within a unified approach that combines the effects of fluid mechanics, interface chemistry and material properties. A description of the key points of the model brings forward the important role played by the number of small-scale asperities in contact with each particle; the pivot point around which particles can roll; the streamwise kinetic energy acquired as particles roll/slide along the surface; the probability to hit a large-scale asperity and the prediction of the actual detachment. Specific methods to simulate the trajectories of these stochastic processes are detailed and validated in a step-by-step manner with a specific emphasis put on the interplay between adhesion forces and particle dynamics. Finally, once each step has been separately assessed, the complete model is evaluated by comparing predictions to a realistic resuspension test-case for airborne colloids, showing that good and consistent numerical predictions are obtained with reasonable time steps. (C) 2014 Elsevier Ltd. All rights reserved.