Without including transmission, there is no way of assessing the indirect benefits interventions may have through onward cases averted. For an infectious disease like TB, making quantitative predictions about the population-level impact of interventions requires models that explicitly account for the transmission process. The use of mathematical modelling as a tool in public health for understanding the behaviour of complex systems, and of assessing the impact and cost-effectiveness of interventions has grown. However, the fairly constant HIV prevalence and still-elevated risks of developing TB even among PLHIV on ART means that HIV will continue to affect TB epidemiology for decades to come and remain a crucial aspect of modelling in high-HIV burden settings. A higher, but more uncertain, proportion of TB deaths are HIV-associated, but vital registration cause-of-death coding rules and frequent comorbidities make such estimates more difficult. Today, around 10% of TB is thought to be HIV-associated globally (74% of this in sub-Saharan Africa). As the epidemic declined in some countries, including Zimbabwe and Ethiopia, and ART was rolled out very aggressively, as in Botswana and South Africa, the TB notification rates declined but not to the pre-HIV levels. With the wider roll-out of antiretroviral therapy for HIV (ART) beginning around 2004, initially provided to those meeting certain CD4 count thresholds and now recommended for all PLHIV, these population-level associations between HIV and TB incidence began to weaken. We conclude with a summary of the uses and achievements of TB/HIV modelling and some suggested future directions.

We first review studies whose focus was on purely epidemiological modelling, and then studies whose focus was on modelling the impact of interventions. We then go on to consider population-level effects, reviewing the TB/HIV modelling literature. We then review the ways HIV influences the natural history of TB, the interventions that have been considered in models, and the way these individual-level effects are represented in models. We review the natural history of TB and illustrate how its features are simplified and incorporated in mathematical models. In this chapter, we focus on mathematical models of tuberculosis epidemiology (TB) that include interactions with HIV and an explicit representation of transmission.

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