Introduction Ambitious targets have been set for the control of the HIV pandemic [ 1– 3]. While access to life-saving anti-retroviral therapy (ART) for those infected with HIV is increasing rapidly throughout the world, effective programmes to reduce HIV transmission are still needed [ 4], especially in Africa. Many factors influence the risk of acquiring and transmitting HIV [ 5], but where measures intended to reduce transmission have been rigorously tested at a population level, the results have been mixed [ 6, 7]. Furthermore, an effective vaccine will probably not be available for a decade or more [ 8]. There is now clear evidence that male circumcision (MC) significantly reduces female-to-male transmission of HIV. In the first randomized controlled trial (RCT) to report on MC, Auvert and colleagues [ 9] have shown that MC reduces transmission from women to men by 60% (32%−76%; unless otherwise stated ranges are 95% CI). An earlier meta-analysis of observational studies found an adjusted relative risk for HIV in circumcised men of 0.42 (0.34−0.54) [ 10], although a Cochrane review gave a more cautious interpretation [ 11]. In sub-Saharan Africa, estimates of HIV prevalence [ 12] ( Figure 1) are significantly associated with the estimated prevalence of MC (correlation coefficient, ρ = −0.61; p < 0.0001). In countries where fewer than 30% of men are circumcised, the median prevalence of HIV is 17% (IQR: 6% to 27%, n = 9 countries); where more than 90% of men are circumcised it is 2.9% (IQR: 1.5% to 5.5%, n = 13 countries). In a multi-centre study in Africa, Herpes simplex 2 and not being circumcised were independent risk factors for HIV [ 13]; the prevalence of HIV was negatively correlated with the proportion of men who were circumcised (correlation co-efficient, ρ = −0.85; p < 0.001) [ 14]. RCTs in Kenya [ 15] and Uganda [ 16] will provide further information on the impact of MC on HIV and in particular on the possible impact of MC on male-to-female transmission of HIV. The impact of increasing MC coverage on HIV depends on the prevalence of HIV and of MC and we assess this impact using both static and dynamic models. For purposes of illustration, country estimates are aggregated to four regions, but we also present results for South Africa where MC could have the greatest impact and where the estimates of MC and HIV prevalence are reliable. Estimates are made of the reduction in incidence, prevalence, and deaths in each region. Assuming that the prevalence of MC is increased from present levels to full coverage (as defined in Protocol S1 and illustrated in Figure S1) in either 2010 or 2015, we determine the relative impact that MC will have on HIV incidence, prevalence, and related mortality among circumcised and uncircumcised men and on women over the next thirty years. We consider MC independently of the changes that might arise from the implementation of other effective prevention programmes in order to focus on the impact of increasing MC coverage. Methods To estimate the potential impact of MC on HIV prevalence, we first use a static model to estimate Δ J, the reduction in the incidence of infection J. Using the result derived below ( Equations 8–10), the reduction in incidence, if all men were circumcised, would be where π is the reduction in HIV transmission from women to men, χ is the proportion of men who are already circumcised, and the incidence is taken to be one-tenth of the current prevalence, corresponding to a mean life expectancy of ten years in the endemic state. The reduction in incidence, calculated using Equation 1, gives an estimate of the impact of MC on the incidence of HIV but does not account for changes in the long-term dynamics of the epidemic. An immediate reduction in the rate of new infections will only be reflected in the prevalence of HIV and HIV-related deaths some years later, because prevalence depends on cumulative incidence and the mean time from infection to death is about ten years. For this reason, we also develop dynamic models to explore the impact of MC on incidence, prevalence, and deaths over several decades. Although the models are general, we focus the discussion of the model development on parameter values pertaining to South Africa, which has the best national data on HIV and where MC is likely to have the biggest impact. We extrapolate to other countries by adjusting the relevant parameters to fit the data on national trends in HIV prevalence and the local prevalence of MC. Parameter Estimates for South Africa Early in the epidemic, the prevalence of HIV in South Africa increased exponentially at a rate r = 0.55 ± 0.16/year, giving an intrinsic doubling time d = 1.26 ± 0.37 years [ 17]. The life expectancy after infection with HIV and without ART, standardized to a mean age at infection of 27 years, is τ = 9.8 ± 0.5 years [ 18, 19]. The average mortality rate δ = 1/τ is then 0.102 ± 0.005/year and the case reproduction number R 0 = ( r + δ)/ δ is 6.4 ± 1.6 [ 20], where we have used Monte Carlo sampling from normal distributions to estimate the standard deviations [ 21]. Asymmetry in Sexual Transmission An infected man is about twice as likely, per contact, to infect a susceptible female partner, as an infected woman is to infect a susceptible male partner. In two European studies, the transmission ratio was 2.3 (1.1−4.8) [ 22] and 1.9 (1.1−3.3) [ 23], respectively, although the ratio was significantly lower for sex during menses and higher for anal sex and for sex involving older women [ 22]. The results of the RCT [ 9] suggest that MC will increase the transmission ratio by a further factor of 2.5 (1.5−4.2). Relative Prevalence of HIV in Men and in Women To determine the relative prevalence of HIV in men and women as a function of the transmission parameters, we use a two-sex, susceptible–infected model. We let i f and i m be the prevalence of HIV in women and men. We assume that HIV-related mortality, δ, is independent of time since infection to facilitate the development of analytical expressions that can be used to parameterize the different effects on men and women in terms of an overall effect averaged over men and women. In the detailed analysis below ( Equations 12–15), we represent HIV-related mortality using a Weibull survival curve [ 24]. Although viral load is high during primary infection and near the end of life, we assume here that infectiousness is independent of time since infection. Then assuming an effective contact rate c, and probabilities of infection per contact of φ m for female-to-male transmission and φ f for male-to-female transmission, the model is Early in the epidemic, i f and i m are both much less than 1, the initial growth rate is the ratio of the prevalence in women to that in men in the early stages of the epidemic is while the case reproduction number is In the endemic state, the ratio of the prevalence in women to that in men is For the South African epidemic, if no men were circumcised, we estimate that R 0 = 7.2 ± 1.8 so that with δ = 0.102 ± 0.005/y and φ f /φ m = 2.0 ± 0.5 Equation 6 gives cφ m = 0.52 ± 0.16/year and cφ f = 1.04 ± 0.29/y. From Equation 7 the proportion of infected adults who are women is 52% ± 1%. (A more detailed examination of the proportion of infected adults who are women is given in Protocol S1 and Figure S2.) Collapsing the Two-Sex Model to a One-Group Model To determine rates of infection, averaged over men and women, we replace Equations 2 and 3 by where i is the population prevalence averaged over men and women, and so that R 0 for Equation 8 is the same as in Equation 6. It follows that reducing φ m by a factor of 1 − π is equivalent to reducing both φ m and φ f by a factor of . To allow for the fact that not all men are circumcised, we let χ be the proportion of men who are circumcised and π be the reduction in female-to-male infectiousness when men are circumcised. Then assuming random mixing the average female-to-male infectiousness is reduced to If the proportion of men who are already circumcised is χ, the effect of circumcising all men will be to reduce φ m to In Protocol S1 and Figures S4 and S5, we analyse a three-group model (distinguishing women, circumcised men, and uncircumcised men), and show that under certain assumptions it can be reduced to a one-group model with errors of less than 2.5% in the endemic prevalence for parameter values of interest. The Effect of Heterogeneity in Sexual Activity Levels of sexual activity are highly skewed [ 25, 26]. If men and women have contact rate distributions with means and, and variances and , and mixing is random, then Equation 6 still holds [ 27] but with so that heterogeneity in sexual activity increases R 0. However, MC only affects the transmission probabilities φ m and φ f and not the contact rates c m and c f, so that Equations 6–10 still hold. With R 0 ≈ 6, the predicted steady state prevalence, ( R 0 − 1)/ R 0 ≈ 83%, is much higher than is generally observed. In some models this is allowed for by assuming that people have either zero risk or a fixed risk, and then varying the risk-free fraction to fit the steady-state prevalence [ 28]. If we assume, more realistically, that there is a continuous distribution of risk, those at greater risk will tend to be infected earlier, and the risk of infection for uninfected people will fall as prevalence rises. Here we assume (and corroborate with South African data) that the average contact rate for those who are uninfected declines exponentially with prevalence (see Protocol S1 and Figure S6). The Aggregate Model Based on the above arguments, we constructed an aggregate model in which we considered the HIV prevalence, incidence, and related deaths averaged over circumcised and uncircumcised men. The model was fitted to the available time series of HIV prevalence for each country and used to make projections. We let S( t) and I( t) be the number of susceptible and infected adults over the age of 15 years at time t, with N( t) = S( t) + I( t) , and i( t) = I( t)/ N( t). Adults enter the population at risk at a rate b times the population 15 years earlier so that the total population growth rate matches the reported values for each country [ 29]. To allow for heterogeneity in sexual behaviour and to fit the observed asymptotic prevalence of infection, the transmission parameter takes the value λ 0 at the start of the epidemic and declines exponentially at rate α times the prevalence of infection. The background death rate is μ. We use a Weibull survivorship, W( t) , with a median of 9.8 years and a shape parameter of 2.25 to capture the dependence of HIV-related mortality on time since infection [ 24]. The model is then where o× indicates convolution (see Protocol S1) and D is number of HIV-related deaths per unit time. For those few countries, such as Uganda, where there is evidence that the prevalence of HIV is falling, we allow the transmission parameter to decline with mortality, D/N, to account for behavioural changes in response to the epidemic. To do this, we multiply λ 0 in Equations 12–14 by e −ɛD/N and vary ɛ to fit the data. The dynamic model was fitted to the UNAIDS estimates of national HIV prevalence in adults by least-squares. Epidemics were projected 30 years into the future assuming that the coverage of MC increases logistically (see Protocol S1 and Figure S1) from present levels to full coverage over ten years. Changing MC coverage is allowed for by scaling λ 0 as in Equations 9 and 10. Three scenarios were considered for the impact of MC on female-to-male transmission of HIV corresponding to the best estimate and to the lower and upper 95% confidence limits from the RCT [ 9]. Data The data on circumcision ( Table 1) are taken from a study by Murdock in 1967 [ 30] updated by Bongaarts et al. in 1989 [ 31] and adjusted for ethnic groups by Wendell and Werker in 2004 [ 32]. We updated these estimates further using data from Demographic and Health Surveys (DHS) carried out by Macro International (Calverton, Maryland, United States) in Kenya, Tanzania, Mozambique, Uganda, Burkina Faso, Cameroon, and Ghana [ 33], and on national population–based surveys carried out in Botswana [ 34] and South Africa [ 35]. A study in Tanzania [ 36] where 41% of men were circumcised, found that self-reported MC had a sensitivity of 94% and a specificity of 72%, so self-reported rates may overestimate true rates. The most important change to the earlier data arises from the assumption that men in a particular ethnic group, bordering Ghana and Côte d'Ivoire, are not circumcised. The DHS survey for Ghana suggests that 95% of men are circumcised in contrast to the earlier estimate of 42% [ 32]. A study carried out in Abidjan [ 37] suggests that in Côte d'Ivoire the true rate of circumcision is 93%. We used these values here. The estimates of HIV prevalence are from UNAIDS [ 12], the estimates of population size and growth rates are from the United Nations Development Programme [ 29]. Data for the time trend in the prevalence of HIV in South Africa were obtained from the series of 14 annual antenatal clinic surveys [ 38]. Results In West Africa MC is common and the prevalence of HIV is low ( Figure 1 and Figure 2A and 2B), while in southern Africa the reverse is true. Using these values in our static model ( Equation 1), circumcising all uncircumcised men in Africa would reduce the incidence of HIV as shown in Figures 2C and 2D. When incidence is measured as an absolute reduction in the number of incident infections expressed as proportion of the adult population, the potential reduction in HIV transmission is greatest in southern Africa ( Figure 2); when measured as a reduction in the total number of incident cases, the region of greatest impact extends to parts of East and Central Africa, as well as Ethiopia and Nigeria, which have large populations ( Figure 2). In South Africa alone, increasing MC coverage has the potential to avert up to 174,000 new infections each year ( Table 1). While useful and immediate, the results in Figure 2 do not provide estimates of the differential impact of MC on the risk of infection in circumcised and uncircumcised men and in women, and do not capture the temporal dynamics of the impact on incidence, prevalence, and deaths. Using a two-sex model ( Equation 7), we first determine the ratio of the prevalence of HIV in women to men at the steady state. In South Africa, if no men were circumcised, we predict that 52% ± 4% of HIV-positive adults would be women, whereas if all men were circumcised this proportion would increase to 58% ± 4%. Using a three-group model ( Protocol S1), the expected prevalence of HIV in circumcised men is close to 80% of that in uncircumcised men regardless of the overall proportion of men who are circumcised (see Figure S3). We note that these results assume random mixing and use a simplified description of heterogeneity in risk behaviour; where this assumption is not true the relative prevalence in the two groups of men may be different. Whereas MC provides greater long-term benefits to circumcised than to uncircumcised men, and to men than to women, the differences in the steady-state prevalence among the three groups are not large and suggest that the use of a simplified one-group model will be acceptable. In developing a one-group model to fit country-level data and to project changes in HIV incidence, prevalence, and deaths, we note ( Equation 6) that reducing female-to-male transmission by a proportion π, without changing male-to-female transmission, is equivalent to reducing transmission in the one-group model by factor of . In particular, if MC reduces female-to-male transmission by 60%, then this is equivalent to reducing transmission in the one-group model by 37%, so that MC would have a population-level impact equivalent to an intervention that reduces transmission in both directions by 37%. We fitted this model to UNAIDS estimates of HIV prevalence over time for each country in sub-Saharan Africa to determine the model parameters, as illustrated for South Africa in Figure 3. The centre panel ( Figure 3B) shows the prevalence of HIV in South Africa obtained from national antenatal clinic data [ 38], adjusted to match UNAIDS estimates for the adult population [ 12]. We fit the model to the prevalence data, from which incidence ( Figure 3A) and deaths ( Figure 3C) follow directly. We then allow MC coverage to increase from 35% in 2005 to full coverage in 2015 and in 2010 (see Protocol S1) as illustrated in the top three panels and bottom three panels of Figure 3, respectively. We first examine the impact on HIV if full coverage of MC is reached in 2015. The incidence of HIV infection responds immediately to the intervention ( Figure 3A) and by 2015 is close to its new asymptotic value. Prevalence responds more slowly and only approaches its new asymptotic value in 2025, while the reduction in mortality is slower still. In South Africa ( Figure 3 and Table 2), MC could avert 0.5 (0.3−1.0) million infections but only 0.1 (0.0−0.1) million deaths in the first decade of the program, 0.9 (0.5−1.8) million new infections and 0.7 (0.4−1.3) million deaths in the following decade, and 1.0 (0.5−2.0) million new infections and 1.2 (0.6−2.3) million deaths in the decade after that. The percentage reductions from the baseline scenario (with no increase in MC) as shown in Table 2 are much less in West Africa than in the other regions, but, because of the large population, the number of cases or deaths averted in West Africa is almost as great as in Central Africa, although still much less than in East and southern Africa. Over the 20 years from 2005 to 2025, in the whole of sub-Saharan Africa, MC could avert 5.7 million new cases and 3.0 million deaths, while reducing the number of people infected with HIV in 2025 by 4.1 million ( Table 2). We note that in South Africa the prevalence of HIV is high and the prevalence of MC is low, but the population is large, and approximately one-quarter of all infections prevented and deaths averted could be in South Africa. Figure 3D– 3F repeats Figure 3A– 3C, but with the intervention being introduced twice as quickly and reaching full coverage in 2010. While the incidence declines much more rapidly ( Figure 3D and 3A, respectively), there is little change in the rate at which prevalence and deaths respond ( Figure 3E and 3B; Figure 3F and 3C; respectively), reflecting the low incidence and slow progression to death for people infected with HIV. Discussion Our analysis uses a simple, parsimonious model to evaluate the potential impact of MC, and further empirical research is needed to support more detailed models. However, this analysis shows that MC could avert nearly six million new infections and save three million lives in sub-Saharan Africa over the next twenty years. Especially in southern Africa this could go some way to meeting the 2001 United Nations General Assembly Special Session on AIDS targets, the Millennium Development Goals, and the objectives set by bilateral donors, such as the US President's Emergency Plan for AIDS Relief. Many questions remain to be answered. Better data are needed on the national prevalence of HIV in Africa, as well as on the associated uncertainties. UNAIDS gives plausibility bounds for estimates of national HIV prevalence that are typically about ±30% [ 12], so the absolute values of the estimates presented here are also uncertain to this extent, although the trends should be more reliable. Better data are also needed on the prevalence of MC in Africa and on the age at circumcision, preferably at the subnational level. Most of the currently available data on the prevalence of MC are several decades old, while several of the recent studies were carried out as adjuncts to demographic and health surveys and were not designed to determine the prevalence of MC [ 33]. Without such data it is difficult to make reliable estimates of the overall uncertainty in the potential impact of MC on HIV in Africa. Data are also needed on current circumcision practices, especially with regard to safety, on the acceptability of MC, on the cost of MC, and on the feasibility of making it available in places where it is not routinely done. A detailed study is needed of the cost effectiveness of MC as a way of managing the HIV epidemic in Africa using a dynamic model of transmission, accounting for the cost of MC and allowing for the savings that follow reductions in AIDS-related morbidity and the need for ART. In addition, this analysis is based on the result of just one RCT; it will be necessary for the results of that trial to be confirmed before it is clear how accurate these estimates of future infections are. While the models presented here are a first step towards predicting the impact of MC on HIV in Africa, more detailed models are needed to explore the effect of MC on the age-specific incidence and prevalence of HIV among men and women and on the relative benefits of initially targeting men in certain age groups or in high risk occupations, such as truck drivers or mine workers. Synergies with other potential interventions, including HIV vaccines, should also be explored, as well as possible synergies acting through the impact of MC on other sexually transmitted infections. Since R 0 for HIV is on the order of 5–10, the 37% reduction in overall transmission associated with MC could make a significant contribution towards reaching the target of reducing R 0 to 1 in the areas where few men are currently circumcised. Combined with other interventions to reduce transmission, this raises the possibility of reducing the prevalence of HIV to such low levels that it is no longer a major public health problem. The impact of MC in South Africa may also be mediated by its impact on other sexually transmitted infections; the results of the other two RCTs of MC, currently being conducted in Kenya [ 15] and Uganda [ 16] where the prevalence of other sexually transmitted infections may be different, should throw light on this. The impact of MC on HIV should also be considered in the context of the increasing availability of ART. To the extent that ART reduces transmission, it will also reduce R 0 and act synergistically with MC. Many studies have shown that ART leads to substantial declines in plasma viral load [ 39] and may reduce the risk of transmission for those on ART [ 40]. However, if people in Africa start ART late in the course of their HIV infection, the provision of ART is unlikely to reduce overall transmission significantly [ 41, 42]. As a cautionary note, increases in risk-taking behaviour among circumcised men could reduce the benefit of MC. The RCT [ 9] on which these models are based followed men for an average of 18 months, so that the effects of short-term behaviour changes have been accounted for. Community or population level studies of MC are now needed to determine the likelihood of behavioural disinhibition and to assess its impact on transmission in the long term. While MC confers greater direct benefits on men than on women, women benefit indirectly through the reduction in the prevalence of HIV among their male sexual partners. Nevertheless, it is already the case that in Africa more women than men are infected with HIV [ 12], and additional methods that help to protect women, such as the development of effective vaginal microbicides, are still needed. A trial under way in Uganda [ 16] has been designed to measure the impact of MC on male-to-female transmission of HIV. The earlier observational studies and the recent RCT all suggest that MC will have a long-term, population-level impact on HIV transmission. However, this assumption needs to be tested at the population level, and a large-scale, community-based programme to implement MC as widely as possible should be implemented and carefully monitored to determine the population level impact of MC directly. This analysis makes it clear that MC could have an immediate impact on HIV transmission, but the full impact on prevalence and deaths will only be apparent about ten to fifteen years later. The reason is that circumcision averts infections some years into the future among people who would have died ten years later, on average. The same argument applies, of course, to other prevention methods because reductions in illness and death will only be manifested a decade or more after their introduction. The need to keep HIV-positive people alive through the provision of ART remains the most immediate priority while ways are found to reduce transmission using MC and other interventions. Supporting Information Figure S1 The Increase of MC in South Africa Starting from a Coverage of 35% and Reaching Full Coverage in 2015 (Red Line) and 2010 (Blue Line) (365 KB JPG) Click here for additional data file. Figure S2 The Percentage of All HIV Cases That Occur in Women, as a Function of Circumcision Parameters (A) Circumcision is assumed to have no protective benefit for women ( π f = 0). (B) Circumcision coverage is 100% ( χ = 1). Other parameters were chosen with reference to the South African HIV epidemic as discussed in the main text: δ = 0.102 yr −1, cφ m = 0.52 y −1, cφ f = 1.04 y −1. (2.7 MB JPG) Click here for additional data file. Figure S3 Ratio of the Prevalence of HIV in Circumcised to Uncircumcised Men at the Steady State Assuming an Average Infectious Period of 9.8 Years The relationship is almost completely independent of the circumcision coverage, χ, and the possible protective effect for women, π f . Other parameters: χ = 1, π f = 0, cφ m = 0.52/y, and cφ f = 1.04/y. (490 KB JPG) Click here for additional data file. Figure S4 Comparison of Three-Group (Blue Line) and the Equivalent One-Group (Red Line) Models Parameter values: χ = 0.35, π m = 0.60, π f = 0, cφ m = 0.52/y, and cφ f = 1.04/y, δ = 0.102/y, and p = 0.29. (7.8 MB TIF) Click here for additional data file. Figure S5 Absolute Difference between the Percent Prevalence as Predicted by the One-Group (Collapsed) Model and the Three-Group Model for Different Levels of MC Coverage The lines give different levels of protective efficacy π m : green, 0.76; red, 0.60; black, 0.32. Other parameters are the same as in Figure S4. (431 KB JPG) Click here for additional data file. Figure S6 Force of Infection, Scaled to One at Zero Prevalence, as a Function of Prevalence The red line is estimated from survey data for Carletonville, South Africa. The green line assumes that the risk declines exponentially with prevalence, the blue line that the risk has the same value for all those who are at risk as assumed in the EPP model. The curves are scaled to pass through the point where the curve based on the Carletonville data passes through the prevalence among men in the survey (21%). (587 KB JPG) Click here for additional data file. Protocol S1 MC and HIV in Africa (5.1 MB DOC) Click here for additional data file.