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Epidemiology and Social

Male circumcision for HIV prevention in sub-Saharan Africa: who, what and when?

White, Richard Ga; Glynn, Judith Ra; Orroth, Kate Ka; Freeman, Esther Ea; Bakker, Roelb; Weiss, Helen Aa; Kumaranayake, Lilania; Habbema, J Dik Fb; Buvé, Annec; Hayes, Richard Ja

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doi: 10.1097/QAD.0b013e32830e0137
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Male circumcision (circumcision) is likely to have been very important in explaining the heterogeneous spread of HIV in sub-Saharan Africa [1–4]. Three individual randomized controlled trials in Africa have shown circumcision to reduce HIV incidence in men by 50–60% [5–7]. Following the trial results, the United Nations Joint Programme on HIV/AIDS (UNAIDS)/WHO recommend that settings with high prevalence, generalized or hyper-endemic heterosexual HIV epidemics and low circumcision rates should consider increasing access to circumcision as an additional HIV prevention strategy [8], prioritizing access for young men (12–30 years).

There are insufficient data to know whether circumcision results in a direct reduction of HIV transmission from men to women [8]. There is some observational evidence of a protective effect [9,10] but preliminary data suggest that circumcised HIV-infected men who resume sex before wound-healing may have placed their partners at higher risk of HIV infection [11]. There are also concerns about the likely impact of risk compensation if circumcised men increase risk behaviours in response to the partial protection offered by circumcision [12,13].

Modelling studies [14,15] suggest that circumcision could prevent 5.7 million HIV infections over 20 years in Africa and will be cost-saving. In this article we estimate the likely population-level impact and cost-effectiveness of increasing the prevalence of circumcision in sub-Saharan Africa and explore how these vary by target age group, coverage, time-to-scale-up, level of risk compensation and circumcision of HIV-infected men.



The individual-based model STDSIM simulates the natural history and transmission of HIV and sexually transmitted infections (STIs) in a population consisting of individuals with characteristics that can change over time. The formation and dissolution of heterosexual relationships and transmission of STIs during contacts between sexual partners are modelled as stochastic events [16,17]. STDSIM allows for the simultaneous and interactive simulation of up to 16 different STIs (supporting-material: section-S1, available from the authors). STDSIM has previously been used to explore the impact of STI treatment for HIV-1 prevention and the heterogeneous spread of HIV-1 in Africa, and the diverging HIV-1 and HIV-2 prevalence trends in West Africa [1,18–24].

Baseline scenario

The simulated population used in this study was based on previously published work [1,23]. STDSIM was fitted to the demographic, behavioural and epidemiological characteristics of a typical high-HIV, low-circumcision prevalence population (Kisumu, Kenya) for the years 1997 and 2006 and to available data on trends over time (C. Cohen, personal communication, USCF and [1]), except that the mean survival time from HIV infection to death was increased from 10 to 11 years in line with the findings of a recent meta-analysis [25], and an additional increase in condom use rates was simulated in 2000 (to 40% of casual and sex worker contacts) in Kisumu to fit recent falls in HIV prevalence (C. Cohen, personal communication, USCF). No condom use was assumed in long duration partnerships [26]. HIV, herpes simplex virus type 2 (HSV-2), chancroid, syphilis, gonorrhoea and chlamydia were simulated. STIs were assumed to enhance HIV susceptibility and infectivity. The assumed per-contact cofactor effects [1] reflected their relative clinical severity [27]. Multiple cofactor effects in the same individual were assumed to sum and overall cofactor effect for each partner in HIV-discordant partnerships to multiply (supporting-material: section-S1). In line with data, we assumed that 25% of men were already circumcised [1].

Simulated effects of male circumcision

We assumed three direct and three indirect effects of male circumcision on HIV transmission. Lack-of-circumcision was assumed to directly increase the risk of HIV acquisition in men. The magnitude of the per-contact cofactor for HIV acquisition in men was fitted to empirical individual-level data from the Kenyan trial [6] (see below). We also assumed two direct effects due to sexual intercourse before circumcision wound-healing. Among HIV-infected men in the Ugandan trial, there was a nonsignificant increase in the proportion of wives infected within 6 months of circumcision in men who resumed sex before wound-healing (25%) compared with those who did not (11%) [11]. Using these data and assuming that the median time to wound-healing was 4 weeks in HIV-uninfected men (R. Gray, personal communication, Johns Hopkins), we used a Bernoulli model to calculate that the per-contact cofactor for HIV infectiousness in contacts between HIV-infected men who resume sex before wound-healing, and their HIV-uninfected partners, was 9.8 (supporting-material: section-S2). We assumed 15% of HIV-infected men resumed sex before wound-healing [28]. When fitting the model to the trial data we also assumed that 15% of HIV-uninfected men were subject to the same increased risk of HIV acquisition in the month following their circumcision in contacts with HIV-infected women, as postulated [29].

Much uncertainty remains in the effect of circumcision on the acquisition and transmission of cofactor STIs [5–7,30,31]. We assumed three indirect effects. We assumed that lack-of-circumcision doubled the per-contact risk of syphilis and chancroid acquisition (but had no effect on HSV-2 acquisition) [30] and HSV-2 ulcer point-prevalence was reduced by 50% in circumcised/HSV-2-infected men, in line with data suggesting that circumcision halves genital ulcer rates [6,7].

Fitting to individual-level impact data

We simulated three scenarios of the individual-level impact of male circumcision in previously uninfected men on HIV incidence corresponding to the central estimate (59%) and the upper (76%) and lower (30%) 95% confidence limits from the intervention trial in Kenya [6]. In each scenario the projected impact of the simulated intervention was fitted to the central, upper or lower estimate of impact from the trial by varying the magnitude of the lack-of-circumcision cofactor for HIV acquisition in men and refitting the observed HIV prevalence in 1997 and 2006. The simulated trial intervention circumcised 100% of 15–24-year-old HIV-uninfected men on 1 January 2004. Incidence rate ratios in this age group were calculated over 2 years, corresponding to the median follow-up period [6].

We used the fitted model to estimate the proportion of the observed trial impact that was due to direct and indirect effects of circumcision, by simulating scenarios in which the direct and indirect effects on HIV were removed in turn.

Simulated interventions

The three baseline scenarios, fitted to the central, upper and lower bounds of individual-level impact, were then used to estimate the population-level impact of various scenarios of the roll out of circumcision. All simulated interventions were simulated to start on 1 January 2007. Our ‘default’ intervention resulted in a linear increase in the proportion of circumcised HIV-uninfected men in the targeted age group, from 25% (preintervention prevalence) to 75% 5 years later with no risk compensation. In separate simulations the following age groups were targeted: 15–24, 25–29, 30–34, 35–49, 15–49, neonates and 15 year olds. HIV-uninfected men aging into the targeted age group were also circumcised at the appropriate prevalence for that year of the intervention. This maintained circumcision prevalence in the targeted age group over time and led to increases in circumcision prevalence in older age groups as circumcised males aged. Results were based on means over 500 simulation runs.

The (cost-)effectiveness of the intervention was calculated over 2, 5, 10, 20, 30, 40 and 50 years. We allowed for varying time horizons to reflect different time preferences by society.

Impact on HIV incidence was calculated as one minus the mean annual incidence rate ratio in 15–49 year olds over the period. Over the same periods we also calculated the number of HIV infections averted in adults 15–49 years old per 1000 circumcisions in men of all ages, and the cost per-HIV-infection-averted. Adult circumcision costs were based on the published data from the trials and adjusted for inflation to constant 2007US$, using the US consumer price index. Our central, lower and upper estimates of the cost of an adult circumcision were US$ 51, 33 and 69, based on 2007US$ and data from the South Africa intervention excluding publicity [32], the Kenyan intervention [33] and the Ugandan intervention [34], respectively. Costs were incremental to clinic facilities, and included the direct costs of a circumcision procedure including supplies and personnel. Costs also included capital equipment specific to circumcisions but not training. Neonatal circumcision costs in sub-Saharan Africa are poorly known but are likely to be lower than for adults. American studies suggest that neonatal circumcision costs could be as low as 10% of adult costs [35,36]. Conservatively, we adjusted the adult costs for likely lower supply costs and shorter procedure time. We assumed that the central estimate was 30% of the adult cost (US$ 15), with an upper and lower estimate of US$ 7 and 25. Future costs and effects were discounted at 3% per year and cost-effectiveness was shown in present value terms [32]. Our cost per-HIV-infection-averted estimates were compared to a recent estimate of the present value of lifetime treatment costs of an HIV infection in Africa (US$ 3469 in 2004US$) [37], recalculated using a 3% discount rate and adjusted for inflation to 2007US$ (US$ 4043).

Scenario and sensitivity analysis

We explored various alternative scenarios of coverage, scale-up period, risk compensation, circumcision of HIV-infected men and other uncertain parameter values. We varied the coverage of HIV negatives between 25 and 100% in line with acceptability data [38] and the scale-up period between 0 and 20 years. We modelled two scenarios in which newly circumcised men or all-circumcised men changed their condom use rate from 40 to 0–30% (risk compensation) and 50–80% (effective counselling). We simulated a scenario in which the same proportions of HIV-infected and HIV-uninfected men were circumcised while ensuring that the number of circumcisions over each period was equal to that in the default scenario in which only HIV-uninfected men were circumcised. We combined this with a scenario in which we assumed a strong direct effect of male circumcision on male-to-female HIV transmission. In this scenario, we assumed that the per-contact cofactor for HIV infectiousness for HIV-infected and circumcised men was 50% of that for HIV-infected uncircumcised men.

To assess the robustness of our results to different epidemiological scenarios and uncertainties in parameters known to affect (cost-)effectiveness, alternative scenarios were simulated and key parameter values were varied while refitting HIV-prevalence wherever appropriate, and the (cost-)effectiveness of the default intervention targeted at 15–49 year olds was recalculated. First, we removed the effects of circumcision on chancroid, syphilis and HSV-2. Second, we increased the proportion of men who resumed sex before wound-healing. Third, we explored the impact of the intervention in populations in which HIV-prevalence (a) remained around 25% after 1997, (b) fell more steeply after 1997 to 10% in 2020, and (c) was lower overall, peaking at 10% in 1997. These fits were obtained by varying condom use and risk behaviour rates (see supporting-material: section-S3, for full details). Fourth, we varied the baseline circumcision prevalence from 25 to 0 and 50%. Finally, we varied the unit circumcision cost for adults/neonates between US$ 33/7 and 69/25, respectively, and the discount rate between 0 and 6%.


Baseline scenario

The simulated characteristics of 15–49 year olds in the baseline (no intervention) scenario are shown in Fig. 1. The age/sex/regular-partnership distributions in the population were fitted well (Fig. 1a and b). The mean debut age of men was 17 years. The simulated prevalence of short duration bacterial STIs were much lower than HSV-2 (Fig. 1c). The simulated overall HIV prevalence in 15–49 years olds in 1997 and 2006 provided a good fit to the data (Fig. 1d), and the age-specific prevalence was fitted adequately (Fig. 1e and f).

Fig. 1
Fig. 1:
Baseline population characteristics. (a) Observed and simulated population structure by age and sex. Grey bars represent data and white bars are the model projections. (b) Observed and simulated prevalence of regular partnerships (marriage) by age and sex. (c) Observed (mean and 95% confidence interval) and simulated sexually transmitted infections prevalence in 1997 by sex, 15–49 years. (d) Observed and simulated male and female HIV prevalence trend (15–49 years). (e and f) Observed and simulated male and female HIV prevalence, by age. Data: general population surveys in 1997 [39] and 2006 (C. Cohen, personal communication, USCF) and antenatal clinic data for urban Kisumu 1990–2003 [40]. NG, Neisseria gonorrhoeae, CT, Chlamydia trachomatis, TP, Treponema pallidum, HD, Haemophilus ducreyi, HSV-2, Herpes-simplex virus, type 2.

The central estimate and the lower and upper 95% confidence interval (CI) bounds for impacts of circumcision in 15–24-year-old men in the Kenyan trial over 2004/5 (59, 30 and 67% respectively [6]) were fitted by assuming per-contact cofactor effects for HIV acquisition in uncircumcised men of 4.0, 1.7 and 9.0, respectively. Over the 2-year period of the simulated trial intervention, more than 95% of the projected impact was attributed to the direct effect of circumcision on HIV acquisition, less than 5% was attributed to its effect on HSV-2 ulcers and none to its effect on syphilis and chancroid acquisition.

Population-level impact: default intervention

Over the short-term, the impact of the default intervention targeted at different age groups on HIV incidence was projected to be larger in men than in women, but this difference reduced over time (Fig. 2a and b). The impact of the default intervention targeted at 15–49-year-old men over 2, 5, 10, 20, 30, 40 and 50 years on HIV incidence was 8.1% (95% CI = 4.0–10.7%), 15.4% (7.6–21.3%), 22.8% (11.4–31.7%), 31.8% (17.6–42.7%), 39.4% (23.1–51.2%), 45.5% (27.8–57.7%) and 50.6% (31.9–62.7%) in men and 1.3% (1.0–1.5%), 3.7% (2.4–4.7%), 9.9% (6–12.7%), 21.5% (13.1–27.8%), 30.4% (19.1–38.6%), 37.6% (24.2–46.9%) and 43.5% (28.6–53.3%) in women, respectively.

Fig. 2
Fig. 2:
Population-level impact. Impact of the default circumcision intervention targeted at different age groups on HIV incidence in (a) men and (b) in women aged 15–49 years old, over time. (c) Number of HIV infections averted in adults aged 15–49 years per 1000 circumcisions, over time. (d) Cost required to avert one HIV infection in adults aged 15–49 years, over time in 2007US$. The ‘default’ intervention assumes a linear increase in the proportion of HIV-uninfected men circumcised in the target age group from 25 to 75% over 5 years from 2007 without risk-compensation. For comparison, in panel (d) a recent estimate of the lifetime treatment costs of an HIV infection in sub-Saharan Africa, (US$ 4043) [37], is shown as a horizontal dashed line.

As expected, targeting 15–49 year olds had the largest impact on HIV incidence over all periods (Fig. 2a and b) because in this scenario the number of circumcisions was highest. Targeting men aged 15–24 or 25–29 years both had a similar impact on HIV incidence over the first 2 years in men and over the first 10 years in women. Over longer periods, targeting 15–24-year-old men had a larger impact on HIV incidence in both sexes. Targeting men 30+ years led to smaller reductions in HIV incidence over all periods. Our results suggest that circumcising neonates would begin to reduce HIV incidence in the general population after 20–30 years in men and 30–40 years in women, whereas circumcising most men before sexual debut (‘15 year olds’) would have a quicker impact.

Figure 2c and d shows the results accounting for the differing number and likely cost of circumcising men of different ages. The default intervention targeted at 15–49 year olds would avert 28.3 (14.4–38.6), 53.3 (26.4–75.1), 126.9 (65.1–177.5), 307.2 (169.6–414.7), 487.9 (282.9–633.5), 629.8 (377.3–793.6) and 745.1 (458.1–913.0) infections per 1000 circumcisions in adults over 2, 5, 10, 20, 30, 40 and 50 years, respectively (Fig. 2c). Up until 10 years after the start of the intervention, more infections were averted per 1000 circumcisions by targeting HIV-uninfected 25–29 or 30–34 year olds, than by targeting other age groups. Targeting HIV-uninfected 35–49 year olds initially averts a similar number of infections per 1000 circumcisions, but targeting this age group becomes relatively less effective over more than 5 years. Over 20+ years, strategies that targeted 15–49 or 15–24 year olds would have averted most infections per 1000 circumcisions. Strategies that included circumcising younger individuals (‘neonates’ or ‘15 year olds’) led to fewer infections averted per 1000 circumcisions.

The cost (2007US$) of averting one HIV infection in adults, by the default intervention targeted at 15–49 year olds, over 2, 5, 10, 20, 30, 40 and 50 years, was US$ 1806 (1327–3554), 974 (691–1964), 431 (308–842), 195 (143–356), 132 (100–232), 104 (81–179), and 89 (71–150), respectively (Fig. 2d). Over the first 10 years, cost-effectiveness was highest if 25–29 or 30–34-year-old men were targeted and targeting any adult age group was predicted to be cost-saving compared with HIV lifetime treatment costs. In the short-term, targeting neonates or men just before debut would not be cost-saving because circumcision occurs many years before men experience their highest HIV risks. However, these interventions became as cost-effective as targeting adults after 20 and 40 years, respectively. The age-specific HIV incidence impact of the intervention is shown in supporting-material: section-S4.

Coverage and rollout timing, and effect of behaviour change in circumcised men

Both coverage and scale-up duration were approximately linearly related to intervention impact (Fig. 3a and b). Increased risk behaviour in circumcised men reduced intervention impact, such that impact was negated if condom use reduced from 40% in casual and sex-worker contacts (vertical dashed line) to 15% if changes were restricted to newly circumcised men (Fig. 3c), or 20% if changes occurred in all-circumcised men (Fig. 3d). More optimistically, a larger number of HIV-infections would be averted if counselling increased condom use.

Fig. 3
Fig. 3:
Coverage and rollout timing and effect of behaviour change in circumcised men. (a) Effect of varying the coverage and (b) the time taken to scale-up of the default circumcision intervention targeted at 15–49-year-old men on HIV incidence in adults aged 15–49 years, over time. Effect of changes of risk behaviour after 2007 in newly circumcised men (c) and all-circumcised men (d). In (a) and (b) coverage varied between 25% (baseline prevalence of circumcision) and 100%. Time taken to scale up was varied between 0 years to 20 years. The assumed coverage and scale-up time in the ‘default’ intervention scenario are highlighted by vertical dashed lines. In (c) and (d) the proportion of sexual contacts in casual and sex-worker contacts that are protected by condoms (with 10% failure rate) is varied between 0 and 80% compared with 40% in the default scenario (highlighted by a vertical dashed line).

Effect of circumcising HIV-infected men

Circumcising the same proportion of HIV-infected as HIV-uninfected men had little effect on the population-level impact (Fig. 4; default vs. grey-lines). The projected impact on HIV-incidence in men was slightly lower than when circumcision was restricted to HIV-uninfected men, primarily because fewer HIV-uninfected men were circumcised, rather than because recently circumcised men were assumed briefly more infectious and susceptible to HIV. The lower projected impact among men did not translate into lower impact among women, because it was offset by lower cofactor-STI rates in STI/HIV coinfected men.

Fig. 4
Fig. 4:
Impact of circumcising HIV-infected men and assuming circumcision halves the per-contact male-to-female HIV transmission probability. All graphs show impact of intervention targeted at 15–49-year-old men on HIV incidence in men (left) and women (right) aged 15–49 years, over time. Note that the lines for ‘default except circumcise HIV−/+’ and ‘default except circumcise HIV−/+ and no effects due to sex before healing’ are coincident.

Figure 4 also shows the impact of assuming that circumcision halves the male-to-female HIV transmission probability (default vs. dashed lines). If only HIV-uninfected men were circumcised, the short-term impact on HIV-incidence was predicted to be small because the reduced transmission probability only applied to HIV-infected men who had become HIV infected after circumcision. Over the longer term, the intervention impact was predicted to be larger than in the default scenario. If HIV-infected men were also circumcised, then the short-term impact on HIV incidence in women was markedly increased (Fig. 4, women, Δ-markers).

Further sensitivity analysis

The impact of the circumcision intervention was robust to the assumed effects of circumcision on chancroid, syphilis and HSV-2 (supporting-material: section-S3). Removing all indirect effects reduced impact on HIV-incidence over 50 years from 51 to 45% in men and 44% to 36% in women. The population-level impact of circumcision on HIV incidence was robust to increasing the assumed proportion of men who resumed sex before wound-healing to at least 60%. Impact was largely unaffected when HIV prevalence was stable or was lower overall, but the projected longer term impact was slightly lower when HIV prevalence declined more steeply, because of falls in STI rates due to the higher simulated condom use rates. The intervention was less cost-effective when the HIV prevalence declined more steeply or was lower overall, and more cost-effective when HIV prevalence was stable. The impact of the circumcision intervention was also robust to the assumed baseline prevalence of circumcision, but the intervention became slightly more cost-effective at higher circumcision prevalence and vice versa. The intervention was more cost-effective when the cost per-procedure was lower and vice versa.


This is the first study to show in detail how the (cost-)effectiveness of male circumcision for HIV prevention may vary by age at circumcision. Our results suggest that initially prioritizing men older than the UNAIDS recommended age group may be the most cost-effective strategy. Targeting men just before sexual debut, as suggested as a highly efficient strategy [41], would be markedly less cost-effective over the first 20 years because circumcision occurs many years before men experience their highest HIV risks. However, targeting any adult age group was predicted to be cost-saving compared with HIV/AIDS lifetime treatment costs, a result that was robust to all sensitivity analyses. Circumcising neonates, although cheaper, would only become cost-saving after around 30 years.

From the perspective of reduction in new HIV infections, the greater the coverage of circumcisions among all men, the better. However, given limited resources our cost-effectiveness analysis suggests the groups to prioritize immediately. Wherever possible, circumcision should initially be promoted in both neonates and young adult men, up to around age 35, progressively promoting the procedure first to older men in the range and then to younger men as programme scale-up permits. As neonate and adult programmes are likely to be relatively noncompetitive for staff, facilities and training, an optimal strategy may be to scale-up both simultaneously.

Our results are sensitive to the choice of time-horizon adopted by the decision-maker, the discount rate and the assumed lifetime treatment costs. The longer the time-horizon and the lower the discount rate, the relative cost-effectiveness of neonatal circumcision improves. There is uncertainty in the lifetime-treatment cost and it will vary between countries and over time [37,42]. If treatment costs are higher than we assumed, then circumcision will be more cost-saving than we predicted and vice-versa.

In line with other authors, our results suggest that large increases in risk behaviour would have the potential to negate the intervention impact [34], particularly if already circumcised men increased their risk behaviour. One study found the impact of risk compensation to be small, but in that study only relatively small changes in risk behaviour were modelled [41]. Plausibly, risk compensation may occur in circumcised men even without a circumcision intervention, as they learn of the protective effect of circumcision. This prospect, which should be monitored, suggests that Information, Education and Communication activities should be strengthened in circumcised populations regardless of plans to increase circumcision services.

Our results suggest that inadvertently circumcising HIV-infected men would reduce the impact on male HIV-incidence if this were accompanied by a reduction in the number of circumcised HIV-uninfected men. Although much uncertainty remains in the magnitude of the circumcision cofactor for other STIs [5–7,30,43], in line with the findings from a previous study, our results suggest that the contribution of the indirect effects of circumcision on cofactor STIs to the overall impact on HIV may be relatively small [44], but was sufficient to offset the negative effect of circumcising HIV-infected men on population-level female HIV-incidence. However, a re-analysis of HSV-2 data from the Uganda trial using a higher assay threshold has shown that circumcision may also reduce HSV-2 acquisition in men [31] in line with the meta-analysis of observational data [30]. Re-analysis of data from the other trials is required to confirm this finding, but, if true, we may have slightly underestimated the contribution of indirect effects. When we refitted the model, including this effect of circumcision on HSV-2 acquisition, our model predicted that 8% of the impact measured on HIV in the trial was due to the indirect effect on HSV-2.

We may have underestimated the impact of circumcision because we did not assume a direct effect on male-to-female HIV transmission or indirect effects on other reproductive tract infections in women [31]. If there are effects, our sensitivity analysis showed that the impact of circumcision might be greater than we predicted. To increase the clarity of our study, apart from changes to condom use rates, we also did not explore the interaction with other HIV prevention activities. A previous modelling study [45] has suggested that circumcision and other behavioural interventions may act synergistically to reduce HIV incidence.

We have shown circumcision is a cost-saving intervention in a wide range of scenarios of HIV and baseline circumcision prevalence. Our results suggest that the UNAIDS recommended target age group should be widened to include older HIV-uninfected men and counselling activities should be targeted at both newly and already circumcised men. To maximize the number of infections averted, circumcision must be scaled-up quickly while maintaining quality, and operational research is needed to identify the most appropriate ways to expand safe adult circumcision services and to monitor levels of risk compensation over longer periods and outside research cohorts.


We thank Craig Cohen and Ron Gray for access to unpublished data and two anonymous referees whose comments led to significant improvements in the manuscript.

Author's contribution: R.G.W., J.R.G., H.A.W., A.B. and R.J.H. designed the study. R.G.W. performed the mathematical modelling. R.B. adapted the mathematical model and wrote the supporting model documentation. H.A.W. carried out additional data analysis. L.K. designed the costs calculations. R.G.W. wrote the manuscript with contributions from all authors. All authors approved the final version of the manuscript.

Funding: R.G.W. and R.J.H. thank the MRC (UK) and the Wellcome Trust for funding. This study was in part funded by the Wellcome Trust, Grant No. 069509/Z/02/Z. The funders had no involvement in the design, collection, analysis or interpretation of the data, in writing the report or in the decision to submit.


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    cost-effectiveness; epidemiology; male circumcision; mathematical model; primary prevention; sexually transmitted diseases; sub-Saharan Africa

    © 2008 Lippincott Williams & Wilkins, Inc.