The protection of threatened native species, and control of invasive species, requires the implementation of well-developed management policies. Mathematical models are a key tool that can be used to test, develop and optimise strategies to manage invasive and protect native species. The work outlined in this study represents a long-standing research programme to use mathematical models to inform policy and practice to protect native red squirrels in the UK that are threatened with replacement by the introduced, invasive, grey squirrel. We show how classical deterministic models of interacting species and infectious disease can be extended to spatial, stochastic models that represent the dynamics and habitat of the UK squirrel system. Working with stakeholders, the research has helped shape red squirrel conservation policy and had a direct impact on current and future forest management practice in the UK that balances timber production and red squirrel conservation.