The control of invasive species and protection of threatened native species requires well-developed policy and species management strategies. Mathematical models provide a key tool that can be used to test, develop and optimise strategies to manage invasive species. We use the native red squirrel and invasive grey squirrel system on the Island of Anglesey, UK, as a case study system in which to parameterise a mathematical model that includes the control of grey squirrels. We develop a stochastic, spatial model that represents the real habitat structure, distribution and linkage on Anglesey and the neighbouring mainland and includes the key population and epidemiological dynamics of the red-grey-squirrelpox system. The model also includes a representation of the trapping and removal of grey squirrels which is parameterised from field data on Anglesey in which grey squirrel were removed and red squirrels reintroduced between 1998-2013. The model is used to assess different management procedures to protect red squirrels from island re-invasion by grey squirrels; including the threat of squirrelpox spread posed by endemic mainland grey populations. The findings have important implications for the conservation of threatened red squirrels throughout the UK and in Europe. Moreover, the modelling framework is based on well-understood, classical models of competitive and epidemiological interactions and therefore the techniques can be adapted and applied more generally to manage the threat of invasive species in a wide range of natural systems.