The distribution of asymptomatic disease duration in transmission models for tuberculosis: implications for epidemic projections and the impact of active case finding
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Tuberculosis (TB) transmission is sustained in part by asymptomatic disease(aTB). This limits the effectiveness of passive case finding interventions that rely on symptom-based diagnosis. Compartmental transmission models commonly represent the time spent with aTB as 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. We found the gamma-distributed model to fit the data at least as well the exponential model, indicating that the alternative model structures can also capture changes of aTB dynamics. Comparing the fitted gamma-distributed model and the exponential model, we quantify how assumptions about aTB dynamics 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 for asymptomatic disease, indicating the importance of better evidence on the natural history of asymptomatic disease for projecting of intervention effects.
Significance Statement
Compartmental tuberculosis (TB) models often assume constant transition rates between natural history states, leading to exponentially distributed waiting times. However, this assumption may not be realistic for all state transitions, and may have consequences for disease dynamics and projected responses of the system to interventions. Here, we use cohort data to evaluate alternative assumptions about the distribution of time spent with asymptomatic TB and incorporate these assumptions into a transmission model. We show that when the mean of waiting-time is fixed, its shape of the distribution can substantially influence the projected impact of active case-finding interventions, even when alternative distributions produce similar baseline incidence trajectories. These findings highlight the importance of carefully evaluating waiting-time assumptions and their associated structural uncertainty when using transmission models to estimate intervention effects.
