Effective management strategies are needed to control expansion of invasive alien plant species and attenuate economic and ecological impacts. While previous theoretical studies have assessed optimal control strategies that balance economic costs and ecological benefits, less attention has been paid to the ways in which the spatial characteristics of individual patches may mediate the effectiveness of management strategies. We developed a spatially explicit cellular automaton model for invasive species spread, and compared the effectiveness of seven control strategies. These control strategies used different criteria to prioritize the removal of invasive species patches from the landscape. The different criteria were related to patch size, patch geometry, and patch position within the landscape. Effectiveness of strategies was assessed for both seed dispersing and clonally expanding plant species. We found that, for seed-dispersing species, removal of small patches and removal of patches that are isolated within the landscape comprised relatively effective control strategies. For clonally expanding species, removal of patches based on their degree of isolation and their geometrical properties comprised relatively effective control strategies. Subsequently, we parameterized the model to mimic the observed spatial distribution of the invasive species Antigonon leptopus on St. Eustatius (northern Caribbean). This species expands clonally and also disperses via seeds, and model simulations showed that removal strategies focusing on smaller patches that are more isolated in the landscape would be most effective and could increase the effectiveness of a 10-yr control strategy by 30-90%, as compared to random removal of patches. Our study emphasizes the potential for invasive plant species management to utilize recent advances in remote sensing, which enable mapping of invasive species at the high spatial resolution needed to quantify patch geometries. The presented results highlight how this spatial information can be used in the design of more effective invasive species control strategies.