In this paper we propose a novel algorithm which leverages models of white matter fibre dispersion to improve tractography. Tractography methods exploit directional information from diffusion weighted magnetic resonance (DW-MR) imaging to infer connectivity between different brain regions. Most tractography methods use a single direction (e.g. the principal eigenvector of the diffusion tensor) or a small set of discrete directions (e.g. from the peaks of an orientation distribution function) to guide streamline propagation. This strategy ignores the effects of within-bundle orientation dispersion, which arises from fanning or bending at the sub-voxel scale, and can lead to missing connections. Various recent DW-MR imaging techniques estimate the fibre dispersion in each bundle directly and model it as a continuous distribution. Here we introduce an algorithm to exploit this information to improve tractography. The algorithm further uses a particle filter to probe local neighbourhood structure during streamline propagation. Using information gathered from neighbourhood structure enables the algorithm to resolve ambiguities between converging and diverging fanning structures, which cannot be distinguished from isolated orientation distribution functions. We demonstrate the advantages of the new approach in synthetic experiments and in vivo data. Synthetic experiments demonstrate the effectiveness of the particle filter in gathering and exploiting neighbourhood information in recovering various canonical fibre configurations and experiments with in vivo brain data demonstrate the advantages of utilising dispersion in tractography, providing benefits in practical situations.