The distribution of asymptomatic disease duration in transmission models for tuberculosis: implications for epidemic projections and the impact of active case finding

Tuberculosis (TB) transmission is sustained in part by asymptomatic disease states that limit the effectiveness of passive case finding interventions that rely on symptom-based diagnosis. Transmission models commonly represent the time spent with aTB using a single disease state, thereby imposing an exponentially distributed waiting time and a constant hazard of leaving that state. We evaluated how differences in the shape of the aTB waiting-time distribution affect the fit to observed disease progression data and subsequent projections of TB incidence and active case finding (ACF) impact. We fitted exponential and chained-state gamma formulations to cohort data on aTB progression and incorporated them into transmission models. The gamma-distributed model fits the data at least as well the exponential model indicating that the alternative model structures can also capture the changes of aTB cases. Comparing the fitted gamma-distributed model and the exponential model, we quantify how assumptions about the distribution of the duration of asymptomatic TB affect future disease trajectories and the expected impact of ACF interventions. Using India as a case study, we found that the gamma-distributed model projects a slower decline in TB incidence under the status quo, but a substantially larger reduction in the projected incidence of TB when ACF is employed, compared with the exponential model. These results suggest that estimates of ACF impact, and consequently assessments of its cost-effectiveness, may be sensitive to assumptions regarding the shape of waiting-time distribution of asymptomatic disease, indicating the importance of a better understanding of the natural history of asymptomatic disease for projecting of intervention effects.