High tuberculosis (TB) prevalence in Papua New Guinea (PNG) is a serious public health concern. The epidemic in this region is exacerbated by the presence of drug-resistant TB strains as well as HIV infection. This presents a public health threat not only locally but also to Australia due to the high potential for cross-border transmission between PNG’s Western Province and the Australian Torres Strait Islands. We present two mathematical models of TB in the Western Province: a simple model of the underlying TB dynamics, and a detailed model which accounts for the additional effects of HIV and drug resistance. The detailed model is used to make quantitative predictions about the impact of expanding the TB case detection rate under the Directly Observed Treatment, Short-course treatment regimen. This paper provides a framework for future investigation into the economic costs and public health benefits of potential TB interventions in this region, with the eventual aim of providing recommendations to guide policy makers in both PNG and Australia.