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Remodelling core group theory: the role of sustaining populations in HIV transmission
  1. Charlotte Watts,
  2. Cathy Zimmerman,
  3. Anna M Foss,
  4. Mazeda Hossain,
  5. Andrew Cox,
  6. Peter Vickerman
  1. Department of Global Health and Development, Faculty of Public Health and Policy, London School of Hygiene & Tropical Medicine (LSHTM), London, UK
  1. Correspondence to Dr Charlotte Watts, Department of Global Health and Development, Faculty of Public Health and Policy, London School of Hygiene & Tropical Medicine (LSHTM), 15-17 Tavistock Place, London, UK; charlotte.watts{at}lshtm.ac.uk

Abstract

Background and objectives Core group theory describes the central role of groups with high rates of sexual partner change in HIV transmission. Research illustrates the heterogeneous and dynamic nature of commercial sex, and that some men involved in the organisation or policing of sex work regularly have sex with sex workers. These findings are used to explore gaps in core group theory.

Methods Evidence from developing countries on the duration that women sell and men buy sex was reviewed. Simple compartmental dynamic models were used to derive analytical expressions for the relative HIV equilibrium levels among sex workers and partners, incorporating partner change rates and duration in commercial sex settings. Simulations explored the degree to which HIV infection can be attributable to men with low partner change rates who remain in sex work settings for long periods, and their influence on the impact of HIV intervention.

Results Partner change rates and duration of time in a setting determine equilibrium HIV levels. Modelling projections suggest that men with low mobility can substantially contribute to HIV prevalence among sex workers, especially in settings with prevalences <50%. This effect may reduce the impact of sex-worker interventions on HIV incidence in certain scenarios by one-third. Reductions in impact diminish at higher sex-worker prevalences.

Conclusion In commercial sex settings, patterns of HIV risk and transmission are influenced by both partner change rates and duration in a setting. The latter is not reflected in classic core group theory. Men who control the sex industry and regular clients may form an important ‘sustaining population’ that increases infection and undermines the impact of intervention. Intervention activities should include these groups, and examine the social organisation of sex work that underpins many of these relationships.

  • Core group
  • epidemiological theory
  • HIV
  • STI
  • commercial sex
  • sustaining populations
  • mobility
  • prostitution
  • sexual behaviour

https://doi.org/10.1136/sti.2010.044602

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    Background

    Core group theory describes the central role of groups with high rates of sexual partner change in STI and HIV transmission.1 2 A number of classic analyses on the role of core groups have led to a prevention strategy focusing on sex workers and their clients. Social science studies have highlighted the heterogeneous, dynamic nature of sex-worker settings and shown that some men involved in the organisation or policing of sex work regularly have sex with sex workers.3–5 This complexity has not been incorporated into classic core group theory. This paper re-examines this theory and uses findings on the diverse social organisation of sex work to consider whether there may be important gaps in this widely accepted model and to explore the implications for HIV prevention.

    Classic concepts of the basic reproductive rate and the ‘core group’

    In epidemiology, the basic reproductive rate (R0) gives a measure of the rate at which an STI will spread within a susceptible population.2 Mathematically, this can be expressed as R0=(ßcD) where:

    • ß—average probability of infection transmission (assuming sex between an infected and susceptible individual)

    • c—rate of sexual partner change

    • D—average duration of STI infectivity.

    R0 provides a measure of the number of people that an infected person will infect in a totally susceptible population over the duration of their infection.2 6 In this mathematical expression, the term cD represents the total number of sexual partners an infected person will have over the duration of their infection, and ß the probability of transmission. If R0 is >1, the epidemic will spread to an endemic level, which is also dependent on R0. If R0 is <1, infection will die out.

    The core groups are traditionally conceptualised as the groups with high rates of sexual partner change, such as female and male sex workers, men who have sex with men and, at times, clients.1 2 6–8 Core groups also include injecting drug users who share needles with others.9

    Figure 1 provides a typical representation of sexual networks linked to commercial sex used in mathematical epidemiological modelling to project patterns of HIV transmission. The darker colours represent groups with the highest rate of sexual partner change (ie, highest risk). Policy makers often use this basic ‘picture’ to design sex work intervention programmes.

    Figure 1
    Figure 1

    Representation of commercial sex often used in epidemiological modelling of HIV transmission.

    Especially in concentrated HIV epidemics, most HIV infection is among core groups and will only become more generalised if HIV spreads to the wider population. For this reason, interventions focusing on these groups are central to an effective prevention response.10

    Insights from social science about the social organisation of sex work

    A growing body of social science research illustrates the heterogeneity of commercial sex, showing that there is substantial variation both within and between settings. Women (and men) may, for example, sell sex occasionally and informally to gain additional income or might trade sex regularly in brothels, clubs, bars or the street.9 11–14 Particularly during political, economic or personal crises, sex work is a survival strategy. Individuals selling sex often move to areas populated by men (eg, truck stops, mining or construction sites, military barracks).15 During times of conflict, women may trade sex for food, safe passage or other resources that are often controlled by men.16

    Studies have also shown that sex workers experience varying levels of freedom. Many can make independent decisions about the form and timing of their sex-work engagement, while women who are trafficked, sold or bonded into sex work have extremely limited, if any, choice.17

    The men who have sex with sex workers include clients, intimate partners, brothel managers, pimps and police. Like sex workers, their circumstances and practices are varied. Clients may be consistent users of sex workers or irregular or one-time users. A young man might buy sex for a few years before entering into a steady relationship or remain a long-term client.18 Men might buy sex solely when away from a partner or buy sex routinely while in a relationship.

    Qualitative work on the social organisation of sex work highlights that there are often men (and sometimes older women) who have a central role in the structure of the local sex industry.5 10 They may control how many clients women accept in a day, whether condoms are used or anal sex is provided and how long women will stay within a particular setting.19 Men in positions of power, such as controllers or police (hereafter labelled ‘pimps’ for brevity), may have sex regularly with several sex workers. In cases where women are trafficked or bonded, these men commonly wield near-complete control and may be responsible for ‘initiating’ women and girls into prostitution through rape or gang rape.17

    Sex workers frequently experience high levels of violence by clients, pimps or other men in positions of control in the sex industry.20 For example, in Bangladesh, between 52% and 60% of street-based sex workers reported being raped by men in uniform and between 41% and 51% reported being raped by local criminals in the previous 12 months. A survey in Cambodia found that over 50% of female street-based sex workers and just under 50% of male sex workers had been gang raped by, on average, five to six men.21 However, these pimp-sex worker relationships are often complex, because while these men may add to women's vulnerability to HIV, they may also provide women with protection from violence.

    Methods

    To bring together these different perspectives, we conducted three complementary analyses. First, we reviewed published and grey literature on the duration of women selling sex and men's engagement in the sex industry. Specialised datasets from high-risk populations, such as sex workers and police, Behavioural Surveillance Surveys (BSS) and Demographic Health Surveys (DHS) publically available online were searched. A PubMed search was conducted using key words (female sex worker, duration, clients, military and police). For female sex workers (FSWs), data were extracted on time spent in the current location and number of paying clients and steady partners. For client groups, such as police and military, information was extracted about their duration in location and/or the proportion of the sample buying sex. Data were compiled from 12 settings in Africa and Asia with data on sex workers and clients.

    Next, to explore how mobility affects HIV, simple compartmental dynamic models were developed to simulate HIV transmission between sex workers and male partners, incorporating partner change rates and duration in commercial sex settings (appendix 1 and figure 2). The first model considered sex workers and one group of male partners only (termed ‘clients’). This was deliberately kept simple to enable analytical expressions for the relative HIV equilibrium levels in each group to be calculated, incorporating partner change rates and commercial sex duration (appendix 1).

    Figure 2
    Figure 2

    Model structure for dynamic HIV modelling. The black arrows signify possible routes of HIV transmission, the light grey arrows show movements between groups due to becoming HIV infected. FSW, female sex worker.

    Model 2 extended the analysis to consider HIV transmission between sex workers and two groups of men (clients and ‘pimps’) (appendix 2 and figure 2). This model was solved numerically and used to consider whether HIV transmission may be increased by men with relatively low partner change rates, who remain in the setting for several years. We also explored how this might influence the impact of interventions targeted at commercial sex.

    Four ‘pimp’ scenarios were considered (S1, S2, S3 and S4). The first assumes that each ‘pimp’ regularly has sex with eight different sex workers twice a month, using condoms in 40% of sex acts, and this behaviour continues for 10 years. The second assumes that ‘pimps’ have two sex acts with four sex workers each month. In the third ‘pimps’ have one sex act with four sex workers each month. The last scenario represents a scenario where men have sex less frequently (ie, one sex act with one sex worker per month), but continue this behaviour for much longer (20 years).

    In all of these scenarios, model simulations were run for a range of sex worker client rates (6–90 clients per month), client sex worker rates (1.3–5 clients per month), sex-worker durations (from 6–167 months), client durations (24–147 months) and condom use in commercial sex (50–95%), with these uncertainty ranges developed using available data.

    Fixed estimates were used for the HIV biological and natural history parameters (full uncertainty in the biological parameters was not considered because projections are for illustration only) (table A1). For each ‘pimp scenario’, the model was run for 1000 different sex-work and client behavioural scenarios to produce a wide range of different HIV epidemics. For each epidemic, the model was run with and without the ‘pimp effect’ to estimate the degree to which the ‘pimp effect’ increases the HIV prevalence among sex workers. This output was estimated as the sex-worker HIV prevalence with ‘pimp effect’ minus the sex worker HIV prevalence without the ‘pimp effect’, with all outputs estimated at 400 months after the start of the HIV epidemic. After 400 months, the model was then run with and without a simple intervention effect that reduced by 25% the number of unprotected sex acts between clients and sex workers.

    Results

    Evidence on the duration that men and women engage in a commercial sex setting

    Table 1 presents data on 12 different sex-work settings. The average durations that women engage in sex work varied widely, with the shortest mean time of 3.4 months in Cambodia,22 23 suggesting a regular influx of new sex workers.

    View this table:
    Table 1

    Illustrative data on durations and heterogeneity in engagement in commercial sex

    The extent to which men have sex with sex workers varies widely between settings, with the proportion of men who reported having paid for sex ranging from 0.4% in the past 12 months in Ethiopia24 to a high of 49.8% among uniformed forces in Cambodia.23

    How do temporal factors influence equilibrium levels of HIV transmission?

    The equilibrium HIV prevalence among sex workers and ‘clients’ is dependent on both partner change rates and the duration that each group remains in a particular setting. Indeed, our findings indicate that the HIV equilibrium prevalence among clients could be higher than among sex workers if sex workers have fewer sexual partners than these men while in that setting.

    This suggests a very different ordering of vulnerability in some circumstances. For example, if sex workers have, on average, 15 new clients per month, a sex worker will have 900 (=15×12×5) sexual partners if she stays in that setting for 5 years. However, if she only remains for 1 year she would have 180 (=15×12) sexual partners. If we contrast these numbers with those for a client in the same setting, who has sex with four new sex workers each month, over 5 years, he will have sex with 240 different sex workers (=4×12×5).

    A comparison of the relative number of sexual partners of sex workers and clients shows that if sex workers are not mobile they are at greater risk of HIV than clients (although the risk to the client is not negligible), which makes sex workers a key target for prevention. However, with high sex-worker mobility the total numbers of sexual partners for sex workers and clients are relatively similar (180 and 240, respectively), despite the sex-workers' higher rate of partner change.

    The ‘pimp effect’ on FSW HIV transmission

    When we incorporate the effect of ‘pimps’ on patterns of transmission, for the first three scenarios, ‘pimps' could substantially contribute to the HIV prevalence among sex workers, especially at sex worker HIV prevalence levels <50% and >10% with no pimp effect (figure 3). This remains the case even if each sex worker only has sex with one pimp per month and the pimp has one sex act with four sex workers per month (figure 3c). In this scenario, and other scenarios where the ‘pimp effect’ is more substantial (figures 3b and 3c), the model projects that the ‘pimp effect’ could increase the sex-worker HIV prevalence by >10% in absolute terms (30% in relative terms) if the sex worker HIV prevalence with no pimp effect is <30% after 400 months (but >10%), and by >7% (15% in relative terms) if the sex worker HIV prevalence is >30% but <50% after 400 months.

    Figure 3
    Figure 3

    Absolute increase in sex-worker HIV prevalence at 400 months due to the ‘pimp’ effect for female sex worker populations with different HIV prevalence (when no pimp effect included). The increase in sex-worker HIV prevalence was estimated as the sex-worker HIV prevalence with ‘pimp effect’ included minus the sex-worker HIV prevalence without the ‘pimp effect’ included. All other parameters are shown in table A1. Sex work for average duration of 6–167 months. Clients have 1.3–5 sex workers/month for 24–147 months' duration. (A) Scenario1: Pimp duration 120 months, eight sex workers/month, two sex acts/month. (B) Scenario 2: Pimp duration 120 months, four sex workers/month, two sex acts/month. (C) Scenario 3: Pimp duration 120 months, four sex workers/month, one sex act/month. (D) Scenario 4: Pimp duration 240 months, one sex worker/month, one sex act/month.

    Importantly, the model projections in figure 3 also suggest that ‘pimps’ could sustain sex worker HIV epidemics in settings where no HIV epidemic would have occurred otherwise (R0<1 without pimp effect—see figure 3). However, the sex worker HIV prevalence is likely to be low in these scenarios (≤3% after 400 months) because the R0 for pimps and their sex workers is relatively modest (R0≤2.1 in all scenarios modelled) and the long duration of pimps (120 or 240 months in our projections) results in very slow epidemic spread. Despite this slow epidemic spread, extending the model simulations for a further 30 years does nevertheless suggest that HIV prevalences close to 15% could potentially occur.

    Lastly, if pimps have sex with one or fewer sex workers per month (figure 3d), the absolute increase in sex worker HIV prevalence is likely to be modest—<2.5% (<5% in relative terms) if the sex-worker HIV prevalence is >50%, and only >15% in relative terms (2.5% in absolute terms) if the sex worker HIV prevalence without the pimp effect is <20%.

    The ‘pimp effect’ on impact of generic FSW prevention intervention

    When we consider an intervention (starting 400 months after initiation of the HIV epidemic) that results in a 25% relative increase in the proportion of sex acts protected by condoms, we find that the pimp effect for scenarios 1–3 can result in a substantial reduction in the impact of the intervention on HIV incidence among FSWs (figure 4).

    Figure 4
    Figure 4

    Relative reduction (%) in intervention's impact on HIV incidence (immediately after intervention starts) due to ‘pimp effect’. All other parameters are shown in table A1. Sex workers have 6–90 clients/month in sex work for average duration of 6–167 months. Clients have 1.3–5 sex workers/month for 24–147 months' duration. (A) Scenario 1: Pimp duration 120 months, eight sex workers/month, two sex acts/month. (B) Scenario 2: Pimp duration 120 months, four sex workers/month, two sex acts/month. (C) Scenario 3: Pimp duration 120 months, four sex workers/month, one sex act/month. (D) Scenario 4: Pimp duration 240 months, one sex worker/month, one sex act/month.

    The largest effect is in scenario 1, where there is a possible 35% relative reduction in the impact on HIV incidence immediately after the intervention starts, if the sex-worker HIV prevalence with pimp effect is ≤40%. For scenarios 2 and 3, the reductions are more modest with a possible 20% and 10% relative reduction in impact on HIV incidence, respectively, if the sex worker HIV prevalence with pimp effect is ≤40%. The effect in scenario 4 is always small. In all scenarios the reduction in impact diminishes at higher sex-worker HIV prevalence.

    Discussion

    Mathematical modelling and its underlying conceptualisation allow us to consider who may be most vulnerable to HIV infection, and helps us pose more informed questions about where to target resources. However, in its simplicity, the broad theory may not capture adequately the role of different groups in a specific setting.

    Reconsidering the R0=(ßcD) equation

    In its simplest formulation R0 estimates the total number of susceptible individuals an infected person will infect over the duration of their infectivity. However, this expression does not consider where these infections might occur. If a person moves between settings, her or his contribution in any particular setting will be reduced. Therefore, if we want to use the R0 equation to consider a group's contribution within a particular setting, the ‘D’ component of the equation—which has traditionally represented the average duration of HIV infectivity—should be replaced by the ‘duration that an individual is in a single setting and infectious’. The term cD will then represent the number of sexual partners in this particular setting. This reconfiguration of R0 is especially important in commercial-sex situations, which may have both high levels of sexual activity and mobility, and for any STIs that have a long duration, such as HIV.

    When assessing vulnerability there has been a focus on partner change rates, but what may be of greater relevance to local HIV equilibrium levels is the relative number of partners an individual has over the period he or she is in the setting. Although behavioural surveys of sex workers often collect data on the duration of commercial sex, this is frequently not compiled or used. Moreover, there are generally limited data about other groups who may remain for long periods in sex-work settings, wield power over the conditions of sex work, and may have regular sex with sex workers (termed as ‘pimps’ in this analysis).

    Our analysis, which points to the disproportionally large influence of ‘pimps’ on HIV transmission, is supported by broader mathematical epidemiological theory, which shows that in a heterosexual population, the aggregate R0 is the square root of the product of the R0s among men and women.2 Thus, even if the R0 among women is high, if the R0 among men is small, the product of the two could be below 1, and so not sustain an HIV epidemic. In contrast, in several of the scenarios that we presented, although the R0 for clients and their sex workers is low or even below 1 (HIV prevalence without pimp effect is near zero in figure 3), the R0 for sex workers and their pimps brings the aggregate much higher and above 1 in some scenarios (increase in HIV prevalence due to pimp effect greater than zero in figure 3), and so has a dominant effect on the aggregate rates of population HIV transmission.2 This equation applies to HIV and also to other STIs, suggesting that this finding may apply more broadly to all STIs.

    Our analysis also parallels recent mathematical modelling of gonorrhoea, which considers the influence of infection being concentrated among distinct subgroups of a meta-population. Similarly, this model suggests that infection can largely be driven by subpopulations with higher than average concentrations of individuals with high sexual risk activity.38

    Could sustaining populations help maintain HIV infection in some sex-worker settings?

    While the modelling presented is illustrative it raises several important questions: in some circumstances, might men who regularly have sex with sex workers (such as some men involved in the organisation of sex work and resident clients) represent an important, but overlooked ‘sustaining population’ who help fuel and maintain infection—especially in situations where sex workers are moving relatively rapidly into and out of that setting, and where HIV infection levels among sex workers are <50%? Might infection build up in these men, so that they are a significant source of infection for new sex workers entering that setting—especially if men in the sustaining population have unprotected sex with young women at the time of their debut into commercial sex? Similar to the concept of a ‘reservoir of infection’ or ‘maintenance population’ discussed in literature on multi-host pathogens and disease control,39 might ‘sustaining populations’ represent an epidemiologically important group in certain sex-work settings? Moreover, might their epidemiological influence be further amplified by the power and control that many exert over sex work and sexual practices (figure 5)?

    Figure 5
    Figure 5

    Sustaining populations for HIV transmission.

    Conclusion

    Several questions arise: (1) who might comprise a sustaining population in different sex-work settings; (2) to what extent might these groups undermine prevention activities; (3) what interventions might be effective for these groups?

    More data are needed on the range of men who may be regular users of sex workers; the HIV infection levels among men in positions of power and the relative mobility and duration of different groups. Currently, empirical evidence on the patterns of sexual behaviour of men linked to the sex industry is scarce, although there is some empirical evidence which suggests that in some cases, sex workers are at greatest risk from men other their clients, including boyfriends and other partners.40 Moreover, data are needed on the role of injecting drug use in HIV transmission among men and women in commercial sex settings, a variable that was not considered in this modelling exercise. Future modelling of HIV and sex work should take into consideration these additional parameters.

    Interventions specifically targeting the sexual behaviour of men in positions of power are rare, with these men often viewed as gatekeepers rather than as central to transmission. The underlying power differentials that disadvantage sex workers are too often overlooked or considered hurdles rather than intervention targets.

    Key messages

    • Core group theory describes the central role of groups with high rates of sexual partner change in HIV transmission.

    • Commercial sex is heterogeneous and dynamic. In some settings, there may be a high turnover of sex workers. Some men may have sex with sex workers over extended periods.

    • Modelling highlights that HIV transmission is influenced both by partner change rates and duration in a setting. The latter is not reflected in classic core group theory.

    • Men who control the sex industry and regular clients may form an important ‘sustaining population’ that helps maintain infection and undermine the impact of intervention.

    Acknowledgments

    We thank Dr Mark Chen for his useful comments on our manuscript.

    Appendix

    Model 1: HIV transmission between sex workers and men, and the analytical derivation of the influence of rates of partner change and HIV equilibrium prevalence in a simple core group transmission model

    Most simply, the differential equations for a simple HIV sex-worker/client model with no STIs or high viraemic phases can be written as follows, where y0 and y1 are the prevalences of HIV in the clients and the FSWs respectively:dy0dt=λ0(1−y0)y1−ηy0−α0y0dy1dt=λ1(1−y1)y0−ηy1−α1y1Equation 1

    The parameters α0 and α1 are the rates of stopping being a client or sex worker, respectively, η is the HIV death rate and λ0 and λ1 are the forces of infection to clients and FSWs, respectively. The parameters λ0 and λ1 are calculated simply as follows:λ0=β0c0(1−ef)λ1=β1c1(1−ef)Equation 2

    where β0 and β1 are the transmission probabilities to clients from FSWs and to FSWs from clients, c0 and c1 are the rate of commercial partners for clients and FSWs, e is the efficacy of condoms and f is the consistency of use in commercial partnerships. Now the total number of clients that FSWs have has to equal the total number of FSWs that clients have and so:c0n0=c1n1Equation 3

    where n0 and n1 are the sizes of the client and FSW populations. This gives the following if we assume that β0 and β1 are equal:λ0=n1n0λ

    The system in equation 1 can be solved to obtain the equilibrium prevalence in the FSWs and clients by setting the differential equations to zero:y0=λ1λ0−(η+α1)(η+α0)λ1λ0+λ1(η+α0)y1=λ1λ0−(η+α1)(η+α0)λ1λ0+λ0(η+α1)Equation 4

    The ratio of the HIV prevalence of FSWs to clients can then be written:y1y0=λ1λ0+λ1(η+α0)λ1λ0+λ0(η+α1)Equation 5

    Substituting equation 2 and 3 in equation 5, the equilibrium HIV prevalence among sex workers (y1) is less than the equilibrium HIV prevalence among clients (y0) if:c1c0<(η+α1)(η+α0)Equation 6

    That is, the ratio of the rate of partner change among sex workers and clients is smaller than the ratio of the rate of turnover of sex workers and clients (due to both HIV and other forms of mobility).

    If T1 and T0 are the durations that men and sex workers are in the setting respectively (where T1 and T0 are less than D, the duration of HIV infectivity), Equation 6 can be rewritten as:c1T1(1+T1/D)<c0T0(1+T0/D)Equation 7

    Note that if T1 equals T0 equals D, then equation 7 reduces to c1 < c0, the standard condition that we are familiar with to assess the relative epidemiological importance of different groups.

    Similarly, if T1/D << 1 and T0/D << 1, to first order terms, equation 7 approximates as

    c1T1<c0T0

    In other words, for the HIV equilibrium prevalence among men to be higher than the equilibrium prevalence of sex workers, the total number of sexual partners of sex workers while they are in the setting must be smaller than the number of sexual partners of the men with whom they are having sex.

    Appendix

    Model 2: Analytical description of the pimp model and model parameterisation

    Model one can be extended, to enable projections of HIV transmission between three groups – men who remain in a sex worker setting for some time (y2), female sex workers (y1) and men who are in a sex worker setting for less time (y0) (equation 8). This model has been termed the ‘pimp’ model as the first group is parameterised considering a ‘pimp’-style scenario, where men in this group have regular sex with several FSWs over an extended period of time.

    For simplicity, the model does not include the early or late high viraemic phase of HIV and does not model the transmission of STIs. The proportion of FSWs, pimps or clients that are susceptible is assumed to be one minus the prevalence of HIV in each of these risk groups. The model incorporates mobility, with each risk group spending a specified duration time being a FSW, client or men in position of power in that setting. Individuals may also leave the group owing to severe HIV morbidity.

    dy0dt=β0c01(1−ef10)y1(1−y0)−y0(μ0+η)dy1dt=β1[c10(1−ef10)y0+c12(1−ef12)y2](1−y1)−y1(μ1+η)dy2dt=β0c21(1−ef12)y1(1−y2)−y2(μ2+η)Equation 8

    Model simulations undertaken

    Table A1 summarises the inputs used in the modelling, and their data sources.

    Model parameterModel parameterRange or value usedSource for data
    FSW behaviour
     Rate of clients per monthc106–9036 41
     Percentage of last sex acts with client protected by a condomf1050–95%
     Rate of pimp sex acts per monthc12S1: 2, S2: 2, S3: 1, S4: 14 Scenarios, last one based on Cambodia
     Percentage of last sex acts with pimp protected by a condomf1240%42– kept constant
     Duration of commercial sex work in monthsμ16–16736 and range of review findings
    Client behaviour
     Rate of FSWs per monthc011.3–5.042 43
     Duration of being client in monthsμ024–14742 43
    Pimp behaviour
     Rate of FSWs per monthc21S1: 8, S2: 4, S3: 4, S4: 14 Scenarios with last one based on Cambodia
     Duration of being pimp in monthsμ2S1–3: 120, S4: 240In range of review findings
    Hypothetical intervention effect
     Reduction in unprotected sex acts between clients and female sex workers25%Hypothetical scenario
     Time intervention starts after start of HIV epidemic in months400Assumes HIV epidemic continuing for 33 years
    HIV transmission and epidemiological parameters
     HIV transmission probability per sex actAssume β1=β00.00844
     Duration from HIV infection to severe morbidity in monthsH10045 46
     Effectiveness of condoms per sex acte85%47 48
    Table A1

    Model parameter values

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    Footnotes

    • Funding Support for this research was provided by the AIDS, Security & Conflict Initiative, convened by the Netherlands Institute of International Relations ‘Clingendael’ and the Social Science Research Council. Partial funding for this analysis also came from the Sigrid Rausing Trust.

    • Competing interests None.

    • Provenance and peer review Not commissioned; externally peer reviewed.