1. A metapopulation neighbourhood model of the seed bank of an annual plant, that included the effects of heterogeneity in space and time, of stochastic local extinction and of dispersal, was modified using data reported previously, to examine control of the arable weed Avena sterilis. 2. In the absence of herbicide, for spatially homogeneous environments, few differences were found in the modelled mean predicted population for two levels of dispersal (strong and moderate), although the rate of spread and the variance of the number of seeds per cell were greater for the higher level of dispersal. For spatially heterogeneous environments, with strong dispersal, an increase of the spatial scale of patchiness increased the variance, whereas moderate dispersal had the opposite effect. The introduction of temporal heterogeneity did not affect the results greatly; nor did the inclusion of variation in the fecundity parameter. 3. With the introduction of a herbicide with spatially variable efficacy, the modelled metapopulation in all cases declined exponentially and became globally extinct in approximately 20 years; strongly dispersed populations with large-scale spatial heterogeneity were slightly more persistent. However, in all cases, it was usually possible to decrease the population within the model to acceptable levels (<10 seedlings m^-2) within a period of between 3 and 5 years. Spatial variability was considerable and extreme patch persistence was occasionally observed.