Introduction.
Treating HIV-infected individuals has both a therapeutic and a preventive effect, because treatment reduces viral load. Reducing viral load increases survival, but also decreases the infectivity of the individual. Consequently by treating HIV-infected individuals, HIV infections are prevented and transmission decreases. It is being debated whether to use a universal ‘test and treat’ (T&T) approach as a prevention strategy to control HIV epidemics [1]–[9]. A universal T&T strategy is based on treating all HIV-infected individuals whether they need treatment or not. In resource-constrained countries individuals are not considered to need treatment until their CD4 count has fallen to 350 cells/µL, this generally occurs ~5–7 years after infection.

Unfortunately, universal access to treatment for those in need has yet to be achieved in many countries. Granich and colleagues at the World Health Organization (WHO) have claimed, based on mathematical modeling, that a universal T&T strategy would lead (within a decade) to HIV elimination in South Africa and cost less (over 40 years) than achieving universal access to treatment in that country [5], [10]. Here we refer to the HIV transmission model, used by Granich and colleagues, as the WHO model. We use a modified version of this model, which incorporates greater realism, to predict the impact on the HIV epidemic in South Africa of (i) a universal T&T strategy and (ii) achieving universal access to treatment. We predict the impact on transmission and drug resistance, we also estimate treatment costs. The universal T&T strategy is based on annual HIV testing for the entire population of South Africa (~30 million adults aged between 15 and 49 years) and providing immediate treatment for all HIV-infected adults regardless of their CD4 cell count (i.e., their need for treatment). We compare our predictions with the WHO's predictions [5], [10].

We began by predicting the impact of treatment on reducing transmission; we quantified the impact (as did the WHO [5], [10]) in terms of the Control Reproduction Number (RC). RC is defined as the average number of new infections one infected individual generates during their lifetime, assuming the entire population is susceptible and biomedical and/or behavioral interventions are in place. If interventions can reduce the value of RC to below one it can be concluded that (theoretically) it is possible to eliminate the disease. We calculated the effect of treatment on reducing the value of the RC under a range of assumptions for: (i) the CD4 cell count level at which treatment is initiated, (ii) the frequency at which the population is tested for HIV infection, and (iii) the degree to which treatment reduces infectivity. We used these results to determine whether universal T&T and/or achieving universal access to treatment could (theoretically) lead to HIV elimination in South Africa. As well as analyzing RC we also numerically simulated our transmission model (as did the WHO [5], [10]). We used our simulations to determine whether elimination, if it was possible, could occur within 40 years. We used the WHO definition of elimination: less than 1 new HIV infection occurring per thousand individuals per year [5], [11].

Our transmission model more realistically represents the natural history of HIV infection than the WHO model [5], [10]. Our model includes three stages: primary infection, chronic infection and AIDS. We model viral loads (hence infectivity) to be highest in primary infection, lower in chronic infection and to increase again in AIDS. We assume HIV-infected individuals spend ~2 months in primary infection, ~7.5 years in the chronically infected stage and ~3.5 years in the AIDS stage. The WHO model the natural infection of HIV as four stages [5], [10]. They assume HIV-infected individuals have the same viral load (hence infectivity), and also spend the same amount of time (~2.75 years), in each of the four stages. Our transmission model also more realistically represents the effect of treatment than the WHO model. We assume, as in the “real-world”, some HIV-infected individuals develop drug resistance on treatment [12], [13]; consequently we model the evolution of acquired resistance and the dynamics of transmitted resistance. Therefore our model can be used to predict the number of individuals who would need second-line regimens. However the WHO transmission model does not include acquired or transmitted resistance [5], [10]. Therefore their model cannot be used to predict the number of individuals who would need second-line regimens. In addition, our modeling differs from the WHO's modeling in terms of the assumption we make with regard to survival time on treatment; see Methods for details. We also investigate the effect of heterogeneity in response to treatment in terms of viral suppression, hence heterogeneity in treatment-induced reduction in infectivity.

Abstract
In South Africa (SA) universal access to treatment for HIV-infected individuals in need has yet to be achieved. Currently ~1 million receive treatment, but an additional 1.6 million are in need. It is being debated whether to use a universal ‘test and treat’ (T&T) strategy to try to eliminate HIV in SA; treatment reduces infectivity and hence transmission. Under a T&T strategy all HIV-infected individuals would receive treatment whether in need or not. This would require treating 5 million individuals almost immediately and providing treatment for several decades. We use a validated mathematical model to predict impact and costs of: (i) a universal T&T strategy and (ii) achieving universal access to treatment. Using modeling the WHO has predicted a universal T&T strategy in SA would eliminate HIV within a decade, and (after 40 years) cost ~$10 billion less than achieving universal access. In contrast, we predict a universal T&T strategy in SA could eliminate HIV, but take 40 years and cost ~$12 billion more than achieving universal access. We determine the difference in predictions is because the WHO has under-estimated survival time on treatment and ignored the risk of resistance. We predict, after 20 years, ~2 million individuals would need second-line regimens if a universal T&T strategy is implemented versus ~1.5 million if universal access is achieved. Costs need to be realistically estimated and multiple evaluation criteria used to compare ‘treatment as prevention’ with other prevention strategies. Before implementing a universal T&T strategy, which may not be sustainable, we recommend striving to achieve universal access to treatment as quickly as possible. We predict achieving universal access to treatment would be a very effective ‘treatment as prevention’ approach and bring the HIV epidemic in SA close to elimination, preventing ~4 million infections after 20 years and ~11 million after 40 years.