Mathematical modelling of the progression of active tuberculosis: Insights from fluorography data

Abstract

Little is known about the dynamics of the early stages of untreated active pulmonary tuberculosis: unknown are both the rates of progression and the model “scheme”. The “parallel” scheme assumes that infectiousness of tuberculosis cases is effectively predefined at the onset of the disease, and the “serial” scheme considers all cases to be non-infectious at the onset, with some of them later becoming infectious.Our aim was to estimate the progression of the early stages of pulmonary tuberculosis using data from a present-day population. We used the routine notification data from Moscow, Russia, 2013–2018 that contained the results and time of the last fluorographic screening preceding the detection of tuberculosis cases. This provided time limits on the duration of untreated tuberculosis.Parameters of TB progression under both models were estimated. By the goodness of fit to the data, we could prefer neither the “parallel”, nor the “serial” model, although the latter had a bit worse fit. On the other hand, the observed rise in the fraction of infectious tuberculosis cases with the time since the last screening was explained by the “serial” model in a more plausible way – as gradual progression of some cases to infectiousness. The “parallel” model explained it through less realistic quick removal of non-infectious cases and accumulation of the infectious ones.The results demonstrate the potential of using such detection data enriched with reassessments of the previous screenings.

Keywords

• Natural history of tuberculosis (TB)
• Mathematical modeling
• Minimal tuberculosis
• Model structure
• Fluorographic screening data