Review Article

Mathematical Modelling and Tuberculosis: Advances in Diagnostics and Novel Therapies

Figure 4

Proliferation of drug resistance following the launch of new first-line drug regimen. (a) The effective reproductive ratio of DR-TB () is the expected number of secondary cases of active, resistant TB resulting from a single case of DR-TB (shown as the grey shaded area). An increase in the relative transmission fitness of DR-TB (e.g., due to compensatory mutations; shown by the blue arrow) increases (shown by the blue hatched area). Shortening the average duration of DR-TB infections (e.g., by deployment of DST, and effective second-line treatment; shown by the red arrow) decreases (shown by the red hatched area). However, the rate of acquisition of drug resistance (e.g., due to de novo mutations against drugs in the treatment regimen) does not factor in the calculation of (b, c, and d). The trajectories of the prevalence of DR-TB just following the launch of a hypothetical new drug regimen are affected by both the acquisition rates and the of DR-TB, but their effects will be more pronounced at different time periods. Acquisition-driven drug resistance is expected to be more frequent in the first 5 years (pink area), while transmission-driven TB relatively later (blue area). (b) For two hypothetical DR-TB strains with similar , but different acquisition rates, we may observe difference in their prevalence in the short term, but over time they are expected to result in similar levels of resistance. (c) In contrast, for strains with similar acquisition rates, but different , we may not observe significant difference in their prevalence in the short term, but the levels of drug resistance can diverge significantly. Factors that affect will affect the trajectories of DR-TB prevalence—for example, deployment of DST that achieve reduction in average duration of infection (red arrow) can reduce prevalence of DR-TB over longer term. (d) DR-TB strain with larger acquisition rate and smaller is expected to be more prevalent over the short term compared to a strain with lower acquisition rate and higher , but the prevalence of DR-TB is flipped between two hypothetical strains over longer term. Hence, short term prevalence of DR-TB alone may not be a reliable predictor of the prevalence over longer term. Figures are only illustrative and not drawn to scale.