Context. Dusty discs detected around main-sequence stars are thought to be signs of planetesimal belts in which the dust distribution is shaped by collisional and dynamical processes, including interactions with gas if present. The debris disc around the young A-type star HD 131835 is composed of two dust rings at ∼65 au and ∼100 au, a third unconstrained innermost component, and a gaseous component centred at ∼65 au. New ALMA observations show that the inner of the two dust rings is brighter than the outer one, in contrast with previous observations in scattered light. Aims. We explore two scenarios that could explain these observations: the two dust rings might represent distinct planetesimal belts with different collisional properties, or only the inner ring might contain planetesimals while the outer ring consists entirely of dust that has migrated outwards due to gas drag. Methods. To explore the first scenario, we employed a state-of-the-art collisional evolution code. To test the second scenario, we used a simple dynamical model of dust grain evolution in an optically thin gaseous disc. In each case we identified the parameters of the planetesimal and the gaseous disc that best reproduce the observational constraints. Results. Collisional models of two planetesimal belts cannot fully reproduce the observations by only varying their dynamical excitation, and matching the data through a different material strength requires an extreme difference in dust composition. The gas-driven scenario can reproduce the location of the outer ring and the brightness ratio of the two rings from scattered light observations, but the resulting outer ring is too faint overall in both scattered light and sub-millimetre emission. Conclusions. The dust rings in HD 131835 could be produced from two planetesimal belts, although how these belts would attain the required extremely different properties needs to be explained. The dust-gas interaction is a plausible alternative explanation and deserves further study using a more comprehensive model.