Recent discoveries of numerous and diverse exoplanetary systems and their debris discs have revolutionized our understanding of how planets and planetesimals form. One of the exciting recent developments is detection of a large number of young systems which appear to be hosting belts of planetesimals, yet also unexpectedly show high amounts of gas. To explain these observations novel computational models must be developed, which take into account all key physical processes shaping the distribution of dust in these systems. I propose to use a kinetic model of collisional evolution of planetesimals and dust, combined with models of dust evolution due to gas drag and radiation pressure, and models of gas structure shaped by viscous evolution and dispersal. To do this I will extend the capabilities of a kinetic model previously used in studies of gas-free debris discs to account for dynamics of small dust grains in the presence of a gaseous disc. This will allow to model the entire range of body sizes, from dust to planetesimals, in a self-consistent way. The project will require knowledge of collisional planetesimal belts as well as of the proto-planetary environment, and this knowledge will be directly drawn from the existing research experience of the candidate. The project will generate a transfer of knowledge to the host institution while developing the candidate’s theoretical and technical expertise. The results of the project will be of wide use to the planetary science community, as they will help to interpret future observations of young planetary systems, to constrain the process of protoplanetary disc dispersal, and determine properties of dust and gas that may be accreted onto planets in the last stages of their formation.