Revisiting Styblo's law: could mathematical models aid in estimating incidence from prevalence data?

Estimation of the true incidence of tuberculosis (TB) is challenging. The approach proposed by Styblo in 1985 is known to be inaccurate in the modern era where there is widespread availability of treatment for TB. This study re-examines the relationship of incidence to prevalence and other disease indicators that can be derived from surveys. We adapt a simple, previously published model that describes the epidemiology of TB in the presence of treatment to investigate a revised ratio-based approach to estimating incidence. We show that, following changes to treatment programmes for TB, the ratio of incidence to prevalence reaches an equilibrium value rapidly; long before other model indicators have stabilized. We also show that this ratio relies on few parameters but is strongly dependent on, and requires knowledge of, the efficacy and timeliness of treatment.