Understanding airborne infectious disease transmission on public transport is essential to reducing the risk of infection of passengers and crew members. We propose a new one-dimensional (1D) model that predicts the longitudinal dispersion of airborne contaminants and the risk of disease transmission inside a railway carriage. We compare the results of this 1D-model to the predictions of a model that assumes the carriage is fully mixed. The 1D-model is validated using measurements of controlled carbon-dioxide experiments conducted in a full-scale railway carriage. We use our results to provide novel insights into the impact of various strategies to reduce the risk of airborne transmission on public transport.