Screening household members of newly detected tuberculosis cases is an efficient method for finding previously undiagnosed cases in high-burden settings. Despite the intuitive appeal of this approach, randomized trials examining the population-level effects of these interventions in settings with sustained community transmission have shown mixed results. One explanation for these inconclusive findings is that household transmission is responsible for a varying proportion of overall tuberculosis burden between locations, with the impact of household transmission being a function of both the overall incidence and the relative intensity of disease-transmitting contacts in the community and the household. In this manuscript, we use an individual-based network model to explore how local incidence levels and patterns of community contact impact the effectiveness of household-based approaches for interrupting tuberculosis transmission. Our analyses suggest that protective benefits of household-based interventions are maintained across a wide range of epidemiological settings. Our findings provide evidence for the robustness of household-based interventions and suggest that variable results from trials may be primarily due to implementation challenges rather than inherent limitations of these interventions.