Biological invasions are nowadays an important challenge to biodiversity and human welfare. This paper deals with the control of an invasive species, void of market value, and acting as a space competitor for a valuable native harvested species. It presents a theoretical bioeconomic model describing the interacting dynamics of the two species and accounting for the undesirable consequences of native stock harvesters' behaviour on the spread of invasion. Dynamic optimisation of the model displays the existence of a time-path leading to an optimal stationary steady-state solution where the native species is sustainably harvested and the invasive species is kept under control, provided unit costs of native species harvesting and of invaded areas cleaning are quite low, natural and anthropogenic dispersal coefficients of invasion, and time-discount rate are moderate. Moreover, the problem should be addressed early enough. The model is applied to the Bay of Saint-Brieuc scallop fishery invaded by slipper-limpet. We show that it is nearly always optimal to control the invasion in that case study.