Model structure and assumptions. A. Schematic of modelled progression from HIV infection to death.
People living with HIV are modelled using a continuous time-since-infection. Their time-of-death without ART, is drawn from a Weibull distribution, which determines their rate of CD4 cell count decline (see Figure 1B). When CD4 cell count reaches some threshold value CD4A individuals may start ART with probability determined by the coverage at this calendar-time, in which case their time-of-death is postponed to a time dependent on their age and CD4 count and their CD4 count dynamics altered (see Figure 1B). B. Model of CD4 positive lymphocyte count by time since HIV infection. CD4 counts (cells per microliter) are assumed to begin at CD40 = 1000, drop by 25% upon infection, and decline linearly to zero at death in the absence of treatment. ART begins at a threshold CD4A and is modelled as instantaneously increasing CD4 cell count to the level achieved after immune reconstitution has plateaued, CD42. To explore the uncertainty in the durability of this recovery due to treatment failure and loss to follow-up, the mean cohort CD4 cell count is assumed to linearly decline resulting in the loss of a fraction f of CD42 on death. The optimistic (blue line, f = 0) corresponds to fully maintained CD4 recovery. The pessimistic (red line, f = 1) corresponds to the eventual complete loss of CD4 cells. C. The model of the TB incidence rate ratio (IRR) by time since HIV infection. The IRR for TB (relative those not infected by HIV) is taken to increase exponentially with loss of CD4 count, from an initial value of around 2.5 caused by the initial CD4 drop. The increase in CD4 count associated with starting ART reduces the IRR by a factor a, from R (just before ART) to a value of 4.4, in line with . The red and blue lines correspond to the pessimistic and optimistic CD4 trajectories shown in the same colors in Figure 1B. The area with forward-slanting hatching is the lifetime risk of TB on ART; the area with backward-slanting hatching is the lifetime risk of TB for an individual who does not start ART.