Invasive species are significant threats to biodiversity, natural ecosystems and agriculture leading to large worldwide economic and environmental damage. Spread and control of invasive species are stochastic processes with important spatial dimensions. Most economic studies of invasive species control ignore spatial and stochastic aspects. This paper covers this gap in the previous studies by analysing a spatially explicit dynamic process of controlling invasive species in a stochastic setting. We show how stochasticity, spatial location of infestation and control can influence the spread, control efficiency and optimal control strategies. The main aim of this paper is to analyse the relationship between economic parameters and stochastic spatial characteristics of infestation and control. In the model used, there are two ways to control infestation: border control, under which the spread of invasive species from any of its infested neighbouring cell is prevented, and cell control, which removes the infestation from the existing cell. An integer optimisation model is applied to find the optimal strategies to deal with invasive species. Results show that it is optimal to eradicate or contain for a larger range of border control and cell control costs when the invasion is in the corner or on the edge as compared to the case where the initial infestation is in the middle of the landscape. Decrease in the probability of successful border control makes containment an unfavourable control option even for low border control costs. We show that decrease in the rate of spread can result in switching optimal strategies from containment to abandonment of control, or from eradication to containment. We also showed when the probability of successful cell control decreases, a lower eradication cost is required for eradication to remain the optimal strategy. In summary, this paper shows that in order to avoid providing misleading recommendations to environmental managers, it is important to include uncertainty in the spatial dynamic analysis of invasive species control.