Figure 5.

The relationship between ART coverage and virulence at equilibrium, for different parameter sets. (a) (b) (R₀s calculated in the absence of ART). Different coloured lines represent different proportions of S2 transmissions removed as a result of ART. So, with reference to figure 4c, B_H/A_H is kept constant (parameters T_H = 3, d_H = 0.57) while B_L/A_L is varied from low (red line; parameters T_L = 8, d_L = 0.57) to high (yellow line; parameters T_L = 5, d_L = 0.2). The ODE model parameters corresponding to these PDE model parameters were calculated as set out in the main text and then the equilibrium position of the ODE model was computed (electronic supplementary material, §1.4) to produce these plots. The black line corresponds to the parameter set in which ART has no effect at equilibrium (equality in (2.8)). Inequality (2.8) was obtained under the assumption that the switching rate, m, is negligible whereas these calculations of the equilibrium behaviour use m = 0.001, hence this black line deviates marginally from the horizontal. Total number of AIDS-related deaths per untreated infected person per year is calculated as in figure 3. The extreme values of this are a_H = 1/5 and a_L = 1/11 and these are approached when S1 and S2 (respectively) completely dominate at equilibrium. (a) In the absence of ART, S1 dominates at equilibrium. Hence, when B_L/A_L < B_H/A_H then ART is able to switch the ordering of the R₀s so that S2 dominates at equilibrium. The more severe the inequality between B_L/A_L and B_H/A_H, the lower the ART coverage needed to cause this switch. (b) In the absence of ART, S2 dominates at equilibrium, and so this situation is the reverse of (a).