A new host-pathogen model is described that simulates HIV-MTB co-infection and treatment, with the objective of testing treatment strategies. The model includes CD4+ and CD8+ T cells, resting and activated macrophages, HIV and Mycobacterium tuberculosis (MTB). For TB presentation at various stages of HIV disease in a co-infected individual, combined treatment strategies were tested with different relative timings of treatment for each infection. The stages were early HIV disease, late HIV disease and AIDS. The main strategies were TB treatment followed by anti-retroviral therapy (ART) after delays of 15 days, 2 months and 6 months. ART followed by TB treatment was an additional strategy that was tested. Treatment was simulated with and without drug interaction. Simulation results were that TB treatment first followed by ART after a stage-dependent delay has the best outcome. During early HIV disease a 6 month delay is acceptable. During late HIV disease, a 2 month delay is best. During AIDS it is better to start ART after 15 days. However, drug interaction works against the benefits of early ART. These results agree with expert reviews and clinical trials.