Understanding the Impact of Male Circumcision Interventions on the Spread of HIV in Southern Africa

Background Three randomised controlled trials have clearly shown that circumcision of adult men reduces the chance that they acquire HIV infection. However, the potential impact of circumcision programmes – either alone or in combination with other established approaches – is not known and no further field trials are planned. We have used a mathematical model, parameterised using existing trial findings, to understand and predict the impact of circumcision programmes at the population level. Findings Our results indicate that circumcision will lead to reductions in incidence for women and uncircumcised men, as well as those circumcised, but that even the most effective intervention is unlikely to completely stem the spread of the virus. Without additional interventions, HIV incidence could eventually be reduced by 25–35%, depending on the level of coverage achieved and whether onward transmission from circumcised men is also reduced. However, circumcision interventions can act synergistically with other types of prevention programmes, and if efforts to change behaviour are increased in parallel with the scale-up of circumcision services, then dramatic reductions in HIV incidence could be achieved. In the long-term, this could lead to reduced AIDS deaths and less need for anti-retroviral therapy. Any increases in risk behaviours following circumcision , i.e. ‘risk compensation’, could offset some of the potential benefit of the intervention, especially for women, but only very large increases would lead to more infections overall. Conclusions Circumcision will not be the silver bullet to prevent HIV transmission, but interventions could help to substantially protect men and women from infection, especially in combination with other approaches.


Text S1: Circumcision Model Technical Specification
The model is described in the following four sections: (i) Differential equations; (ii) Simulating the intervention; (iii) Calculating the force of infection; (iv) Parameterisation; and, (v) Model outputs.

(i) Differential equations
The model is defined by a set of ordinary differential equations which are solved numerically using Euler's method with a time-step of 1/12 years. The state variables are given by s l k X , : s is the infection-status (1= susceptible; 2= acute infection; 3= latent infection; 4= pre-AIDS; 5= AIDS; 6= on ART; 7= failed ART), k is gender/circumcision status (1= female; 2= uncircumcised male; 3= circumcised male wound healing; 4= circumcised male wound healed) and l is the sexual activity risk group (1= (highest risk), 2 and 3= (lowest risk)).
The ordinary differential equations describing changes in the state variable over time are: In the absence of AIDS, the population grows exponentially at a rateα . The fraction of men and women starting sexual activity in each risk group is l k , Here, l s r , is the rate at which uncircumcised men of that sero-status in that risk group are circumcised in the intervention and w is the mean duration of wound healing.
The fraction of individuals progressing to AIDS that start treatment is given by a(t). This value changes over time according to: a is the maximum level of coverage achieved, start a is the time in the simulation when ART coverage starts to increase and rate a is the rate in increase in coverage.
The rate of deaths due to AIDS include those dying of AIDS and those dying after ART has failed: Over the course of epidemics, some risk-groups may suffer greater AIDS-related mortality than others, leading to progressive changes in distribution of risk in the population. In the model, this can be allowed and it is assumed that individuals cannot change risk-group during their lifetime and the proportion of individuals entering each risk group is constant over time (this assumption is labelled R=0). Alternatively, the model can counteract that change and allow individuals to move between risk-groups in such a way that the fraction of adult men and women in each risk-group remains constant over time (this assumption is labelled R=1) -this is the default assumptions used in the simulations presented. This is simulated in the following way: The overall rate at which men are circumcised is ) (t v ,which increases from zero linearly over a period τ to its maximum value max v . The fraction of men starting sex that are already circumcised ( ) (t h ) follows the same pattern (with maximum fraction max g ). Holding the overall rate at which men are circumcised constant, the rate at which in particular groups are circumcised is varied in the following way.
The first term in this equation limits the total fraction of the male population that are circumcised to less than p max. The fraction circumcised at time t is: T are the relative chance that uncircumcised men that are infected with HIV or in the higher two risk groups (l=1 or 2) get circumcised in the intervention, relative to uninfected and low risk men, respectively.

(iii) Calculating the force of infection
The force of infection is calculated on the basis of the partner change rate of individuals, HIV prevalence among their sexual partners, the number of sex acts in each partnerships and the use of condoms.
Individuals in each gender and risk-group form partnerships at a set rate: l k c , , which is parameterised using a mean rate of partner change for that gender ( k c ) and two parameters that give the relative partner change rate for those in the highest ( 1 , k ϖ ) and next-highest ( 2 , k ϖ ) risk groups relative to those in the lowest risk group (for convenience, we also define To ensure that the total number of partnerships formed by men (circumcision status a, riskgroup b) and women (risk-group d) are consistent, the following correction is made: In this way, θ determines the extent to which the pattern of partnership formation is determined by the parameters estimated from men's reported sexual behaviour.
In a partnership between individuals in the in risk groups l and l', the number of sex acts and the level of condom use is determined by whether the partnership is classified as 'regular' or 'casual'. If the sum of risk groups of the partners is less than 4, the partnership is classified as 'casual', otherwise it classified as 'regular'. The scheme used to decide this is tabulated below: Partner's risk group (l') 1 (highest risk) 2 3 (lowest risk) Own risk group (l)  The force of infection is calculated as: Default values for all parameters are given in Table 1. Sexual behaviour parameters are based on published observations in rural Eastern Zimbabwe [1], where possible. HIV transmission probabilities are informed from cohort studies of discordant couples in Uganda [2]. Figure 1 shows the simulated course of the HIV epidemic using the default parameters, which is good agreement with other models and measurements of prevalence in national surveillance systems [3]. Population growth rate pre-AIDS and in the AIDS-era are in good agreement with empirical observations in rural Zimbabwe [4].

Parameter Symbol
Meaning Value  The incidence rate ratio (IRR) is calculated by running the simulation with and without the intervention, and comparing the derived incidence time-series: The IRR disaggregated by gender and circumcision status is adjusted to prevent confounding through, for example, circumcised men being disproportionately high-risk or infected, or different patterns of infection leading to differential depletion of the risk-groups over in the baseline and intervention scenarios. The risk-distribution adjusted-IRR for the k th gender is denoted ) (t aIRR k :