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The authors have declared that no competing interests exist.

Conceived and designed the experiments: BGW SB. Performed the experiments: BGW. Analyzed the data: BGW SB. Wrote the paper: BGW SB. Supervised the project: SB.

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

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

We began by predicting the impact of treatment on reducing transmission; we quantified the impact (as did the WHO _{C}). R_{C} 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 R_{C} 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 R_{C} 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 R_{C} we also numerically simulated our transmission model (as did the WHO

Our transmission model more realistically represents the natural history of HIV infection than the WHO model

Our model, like the WHO model

Following the WHO, we made two assumptions regarding the effect of treatment on increasing survival time of HIV-infected individuals. Our first assumption is the same as the WHO's. Specifically, we assume the survival time of an individual who initiates treatment immediately after infection is ∼6 years longer than the survival time of an individual who initiates treatment when their CD4 count has fallen to 350 cells/µL (i.e., at the current treatment threshold)

We used our transmission model to derive a mathematical expression for the Control Reproduction Number (R_{C}); see Section 2 in the SM. We calculated the value of R_{C} for a range of population-level testing frequencies (6 months to 4 years) and for a range of treatment initiation thresholds defined in terms of the CD4 cell count (100 cells/µL to 800 cells/µL). We also varied the average treatment-induced reduction in infectivity in a population. We used a maximum value of 96% based on the results of the HPTN 052 clinical trial _{C} we calculated the threshold at which R_{C} equals one and hence determined whether universal T&T and/or achieving universal access to treatment could (theoretically) lead to HIV elimination in South Africa.

We used demographic and epidemiologic data from South Africa to parameterize our model; all model parameter values are given in

We used our validated transmission model to predict the impact on the HIV epidemic in South Africa of (i) a universal T&T strategy (based on annual testing) and (ii) achieving universal access to treatment. We did not model any other prevention strategies in addition to treatment to avoid potential confounding effects. Following the WHO, we ran simulations for 40 years. We predicted the: (i) reduction in incidence rates, (ii) cumulative number of infections prevented, (iii) number of individuals in need of first-line regimens, (iv) number of individuals in need of second-line regimens and (v) annual and cumulative treatment costs for both first-line and second-line regimens. We assumed acquired resistance would emerge at a rate of 3% per year in the treated population. We note this is a very low rate, but since this led to very high levels of drug resistance over a 40 year time period we did not examine the impact of higher rates. We assumed resistant strains would be 50% less fit than wild-type HIV strains in terms of transmissibility. We conducted two numerical analyses. We first simulated our model without including the development and transmission of resistance. We then simulated our model including the development of acquired resistance and the dynamics of transmitted resistance. In both numerical analyses we investigated the effect of heterogeneity in viral suppression due to treatment; hence, heterogeneity in treatment-induced reduction in infectivity. We express the heterogeneity by assuming the average heterogeneity in treatment-induced reduction in infectivity is 90% or 85%.

We calculated treatment costs in United States (US) dollars. Following the WHO

_{C} analysis are shown in the color-coded plots in _{C} at that particular pair of parameter values; dark blue is the lowest and dark red is the highest. In each plot the Y-axis shows the frequency (in years) of population-level HIV testing and the X-axis shows the treatment initiation threshold in terms of the CD4 cell count in cells/µL. The dotted black curve in each plot delimits the threshold at which R_{c} equals one; below the curve elimination is (theoretically) possible, and above the curve elimination is not possible.

The dotted black line represents the threshold R_{c} = 1; below this threshold (i.e., R_{c}<1) elimination is (theoretically) possible. Panels represent the average treatment-induced reduction in infectivity at the population level: (

If the treatment initiation threshold is high (CD4 count ∼600 cells/µL) and the reduction in infectivity is very high (96%), elimination could occur as long as the population is tested for HIV at least once every 4 years (

The dynamics of acquired and transmitted drug resistance are not included in these simulations. Solid lines denote the case where the treatment-induced reduction in infectivity is 96% and dashed lines denote the case where the reduction is 85%. Panels show (

Implementing the universal T&T strategy versus achieving universal access to treatment would result in very different treatment patterns (

Discounted annual (

Costs are discounted by 3.5% annually, following Granich

Dynamics of acquired and transmitted drug resistance are included in these simulations. To generate this figure we assumed a treatment-induced reduction in infectivity of 85%, acquired drug resistance develops in treated individuals at a rate of 3% per year

If resistance evolves, there would be a great need for second-line regimens. After 20 years, ∼2 million individuals would need second-line regimens if the universal T&T strategy is implemented (red curve,

Costs are discounted by 3.5% annually, following Granich

Our analysis of R_{c} shows if the treatment-induced reduction in infectivity is ≥85%, the HIV epidemic in South Africa could (theoretically) be eliminated by using a universal ‘test and treat’ strategy. These results are in agreement with those of the WHO _{c} shows if the treatment-induced reduction in infectivity is 96% the HIV epidemic in South Africa could (theoretically) be brought close to elimination by achieving universal access to treatment. Using R_{C} to identify the conditions under which HIV elimination could occur can be informative. However, using R_{C} can also be extremely misleading for four reasons. First, analyzing R_{C} does not provide any indication of how long it would take to achieve elimination; in the case of HIV epidemics it has been shown it could take 50 to 100 years _{C} does not account for the emergence and transmission of drug-resistant strains. When resistance emerges, multiple R_{c}'s need to be evaluated in order to determine if elimination is (theoretically) possible _{C} to below one (e.g., the degree of viral suppression that reduces infectivity to 96%) would need to be continuously maintained until all of the treated individuals have died. Incidence would increase if the necessary conditions were not continuously maintained. We recommend any analysis of R_{C} that shows HIV elimination is possible should be viewed with great caution.

The numerical simulations generated by our transmission model show a universal T&T strategy with a 96% treatment-induced reduction in infectivity could eliminate HIV in South Africa. This result is in agreement with the WHO

Our results have significant implications for evaluating prevention strategies and choosing the optimal combination of these strategies. Several different prevention modalities are now available. As well as ‘treatment as prevention’ clinical studies have also shown pre-exposure prophylaxis, vaginal microbicides and circumcision could be very effective in reducing transmission

Implementing a universal T&T strategy in South Africa would necessitate, almost immediately, treating ∼5 million individuals. This would require substantial financial resources and investment in healthcare infrastructure. Currently, these financial resources are not available. The WHO has argued that implementing a universal T&T strategy in South Africa is worthwhile because it would substantially reduce transmission, and (after 40 years) would cost ∼$10 billion

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We would like to thank Brian Coburn, David Gerberry, Myong-Hyun Go, James S. Kahn and Justin Okano for their helpful insights.