Fig. 5
From: Introducing risk inequality metrics in tuberculosis policy development
Model trajectories with heterogeneity in contact rates and gradual declines in disease progression (ϕ) and reactivation (ω). TB incidence from 2002 to 2015 (black dots) and model solutions under heterogeneous contact rates (a, c, e); homogeneous approximation (b, d, f). Initial parameters values calculated by adjusting the mean effective contact rates (β) to fit 2002 incidence rates: β = 3.23 yr−1 (a) or β = 10.7 yr−1 (b) in Vietnam; β = 2.94 yr−1 (c) or β = 17.3 yr−1 (d) in Brazil; β = 4.66 yr−1 (e) or β = 17.1 yr−1 (f) in Portugal. Incidence declines towards 2015 attributed to reducing disease progression and reactivation: \(\phi \left( t \right) = 0.05e^{r_\phi (t - 2002)}\) and \(\omega \left( t \right) = \omega _0e^{r_\omega (t - 2002)}\) (where ω0 = 0.0039 in Vietnam and ω0 = 0.0013 in Brazil and Portugal), with constant rates rϕ and rω estimated using MCMC (Supplementary Table 3). From 2020 onwards, the trajectories split to represent four scenarios: rates of parameter change are maintained (dashed black); scale rϕ and rω by a factor κ (represented as “×κ”) to meet WHO incidence targets for 2035 (solid black); apply the same scale up efforts to rϕ only (blue) or rω only (red). The bottom plots in each panel represent the cumulative reductions in disease progression and reactivation required to meet the targets calculated as \(\hat \phi (t) = 1 - \phi (t)/\phi (2002)\) and \(\hat \omega (t) = 1 - \omega (t)/\omega (2002)\), respectively. Clearance of infection upon successful treatment: θ = 1. Other parameters as in Table 1. Model described by Eqs. (1)–(5), and R0 given by (6)
