We analyse the connection between the star formation quenching of galaxies and their location in the outskirts of clusters in the redshift range z = [0, 2] by estimating the fraction of red galaxies. More specifically, we focus on galaxies that infall isotropically from those that are infalling alongside filaments. We use a sample of galaxies obtained from the semi-analytical model of galaxy formation sag applied to the MultiDark simulation, mdpl2. In agreement with observational results, we find that the infall regions show levels of star formation that are intermediate between those of galaxies in clusters and in the field. Moreover, we show that, in the redshift range [0-0.85], the quenching of the star formation is stronger in the filamentary region than in the isotropic infall region. We also study the fraction of red galaxies as a function of the normalized distance to the cluster centre and find that, for radii R/R-200 > 3, the fraction of red galaxies in the filamentary region is considerably larger than in the isotropic infall region. From the analysis of properties of the main progenitors of galaxies identified at z = 0, we find that they have different evolutionary behaviours depending on the stellar mass and environment. Our results confirm the observational findings that suggest that the infall regions of clusters play an important role in the pre-processing of galaxies along most of the evolutionary history of galaxies.