Tuberculosis (TB) is a growing problem worldwide, especially with the emergence and high prevalence of multidrug-resistant strains. We develop a metapopulation model for TB spread, which is particularly suited to investigating transmission between areas of high and low prevalence. A case study of cross-border transmission in the Torres Strait region of Australia and Papua New Guinea (PNG) is considered and a sensitivity analysis is conducted. We find that only 6 of the 50 parameters analysed are important to the cumulative number of clinically active TB patients in the entire region. Of these, only the detection rate in PNG is found to be an important intervention parameter. We therefore give insight into the extent the area with the high burden of TB (PNG in the case study) is dominating the TB dynamics of the entire region. Furthermore, the sensitivity analysis results give insight into the data that most important to collect and refine, which is found to be data relating to the PNG parameters.