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Radicalisation is a developmental process involving a complex interaction of individual, environmental and systemic factors. A good understanding of how radicalisation happens is essential in the fight against terrorism, as it enables interventions to be devised that will interrupt the process and prevent people potentially becoming terrorists. The purpose of this research is to build a mathematical model describing the radicalisation process, and then to use this model as an aid to understanding. The methodology is in two phases: the first phase is to construct a basic initial model and to parameterise it using secondary data. This phase highlights where knowledge is still lacking. The second phase uses these knowledge gaps as a guide to prioritise the collection of further empirical data, which is then used to refine the model. This improved model could then be used to predict the spread of radicalisation in an area, to compare different areas, or to identify further knowledge gaps. The model could also be used to assess the likely effectiveness of an intervention before it is trialled in the field.