Secondary Logo

Journal Logo

Modelling the HIV epidemic among MSM in the United Kingdom

quantifying the contributions to HIV transmission to better inform prevention initiatives

Punyacharoensin, Narata; Edmunds, William Johna; De Angelis, Danielab; Delpech, Valeriec; Hart, Grahamd; Elford, Jonathane; Brown, Alisonc; Gill, Noelc; White, Richard G.a

doi: 10.1097/QAD.0000000000000525
EPIDEMIOLOGY AND SOCIAL
Free
SDC

Objectives: HIV is a major public health problem among MSM in the United Kingdom with around 2400 new infections annually. We quantified the contribution of biological and behavioural factors.

Design: Modelling study.

Methods: A partnership-based model of HIV transmission among UK MSM aged 15–64 years was developed and calibrated to time series HIV prevalence. The calibration was validated using multiple surveillance datasets. Population-attributable fractions were used to estimate the contribution of behavioural and biological factors to HIV transmission over the period 2001–2002, 2014–2015, and 2019–2020.

Results: The contribution of most biological and behavioural factors was relatively constant over time, with the key group sustaining HIV transmission being higher-sexual activity MSM aged below 35 years living with undiagnosed HIV. The effect of primary HIV infection was relatively small with 2014–2015 population-attributable fraction of 10% (3–28%) in comparison with other subsequent asymptomatic stages. Diagnosed men who were not on antiretroviral therapy (ART) currently contributed 26% (14–39%) of net infections, whereas ART-treated MSM accounted for 17% (10–24%). A considerable number of new infections are also likely to occur within long-term relationships.

Conclusion: The majority of the new HIV infections among MSM in the United Kingdom during 2001–2020 is expected to be accounted for by a small group of younger and highly sexually active individuals, living with undiagnosed HIV in the asymptomatic stage. Bringing this group into HIV/AIDS care by improving testing uptake is a vital step for preventing onward transmission and will determine the success of using ART as prevention.

aCentre for the Mathematical Modelling of Infectious Diseases and Department of Infectious Diseases Epidemiology, London School of Hygiene and Tropical Medicine, London

bMedical Research Council Biostatistics Unit, Cambridge

cHIV and STI Department, Public Health England, Colindale

dCentre for Sexual Health & HIV Research, Department of Infection & Population Health, Mortimer Market Centre, University College London

eSchool of Health Sciences, City University London, London, UK.

Correspondence to Narat Punyacharoensin, MSc, Department of Infectious Diseases Epidemiology, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, UK. Tel: +44 20 7636 8636; fax: +44 20 7436 5389; e-mail: narat.punyacharoensin@lshtm.ac.uk, narat.punyacharoensin@yahoo.com

Received 11 February, 2014

Revised 9 October, 2014

Accepted 22 October, 2014

Supplemental digital content is available for this article. Direct URL citations appear in the printed text and are provided in the HTML and PDF versions of this article on the journal's Website (http://www.AIDSonline.com).

Back to Top | Article Outline

Introduction

In the United Kingdom, more than 120 000 people have been diagnosed with HIV and the virus has accounted for more than 20 000 deaths since the start of the epidemic in the early 1980s [1]. During the past 5 years, the number of new HIV diagnoses has continued to decline in all population subgroups, except MSM, which currently represent the largest group of people diagnosed with HIV in the United Kingdom [2]. Despite the extremely high coverage of antiretroviral therapy (ART), which has been demonstrated to prevent HIV transmission, HIV incidence is continuing in this vulnerable group with no sign of a decline [2,3]. An estimated 41 000 MSM were living with HIV in 2012 (4.7% prevalence rate) [2], with approximately 2000–3000 MSM newly infected each year during 2001–2010 [4].

In this study, we sought to gain a better understanding of the factors that drive ongoing HIV transmission among MSM populations in the United Kingdom by developing a mathematical model of HIV transmission that simulates the underlying drivers of the epidemic. The comprehensive, well documented HIV epidemic among UK MSM allowed our model to be tailored-made to match the actual situation. The model was parameterized using multiple sources of survey and surveillance data, and fitted to the time-series estimates of HIV prevalence and followed with model validation and sensitivity analyses to confirm the resulting estimates. The key objective was to quantify the unknown contribution of various behavioural and biological factors to HIV transmission among MSM in the United Kingdom, including the stage of primary HIV infection (PHI), undiagnosed and untreated groups, type of partnerships, age groups, and sexual activity levels to better target prevention strategies. The future course of the epidemic was also projected in the absence of additional interventions.

Back to Top | Article Outline

Methods

We developed a mathematical model to simulate the HIV epidemic in MSM aged 15–64 years in the United Kingdom from the beginning of 2000 to the end of 2020. All the analyses started from year 2001, allowing a 1-year period to help stabilize the model estimates before being analysed. The Appendix (http://links.lww.com/QAD/A612) describes the model structure and analysis methods in detail. Here, we summarize them briefly.

Back to Top | Article Outline

Mathematical model

We formulated a deterministic partnership-based mathematical model in a system of ordinary differential equations (further details are provided in Appendix, section 1, http://links.lww.com/QAD/A612). The modelled populations were divided simultaneously into two age groups: 15–34 (age group 1) and 35–64 years (age group 2), and two sexual activity levels: low and high activity, defined, respectively, as MSM who have, on average, 1 or less and more than 1 new male sexual partner per year. Together, we had a total of four ‘classes’ of MSM, that is, age group 1 – low activity, age group 1 – high activity, age group 2 – low activity, and age group 2 – high activity. The HIV-negative individuals remain in the ‘susceptible’ compartment until either becoming infected with HIV and subsequently progressing through 11 HIV-positive stages defined by CD4+ cell counts, HIV diagnosis status, and ART status (Fig. 1), or being removed from the model due to mortality or exceeding the age of 64 years. The five disease progression stages (PHI, CD4+ ≥500, 350–499, 200–349, and <200 cells/μl) were associated with different HIV transmission probabilities derived on a basis of the average viral load in each stage [5]. Transmission probability and plasma viral load were related according to the function proposed by Smith and Blower [6]. We sampled from a beta distribution to create 10 000 sets of per-act transmission probability by viral load for each CD4+ stage and derived the lower, central, and upper estimates of the final per-act transmission probabilities using 2.5th, 50.0th, and 97.5th percentiles, respectively. The infectiousness of PHI stage was estimated by applying a relative risk of 9.17, as suggested by Boily et al.[7], to the baseline transmission probabilities suggested by Baggaley et al.[8]. A very low, but non-zero, calendar year-dependent transmission probability calculated using the 2005–2009 viral load and CD4+ data was applied to the treatment stage. A change over time in infectiousness of ART-treated men was incorporated to reflect the improved drug efficacy and adherence [9–11]. No linkage to and retention in HIV care were explicitly modelled in this study. All derived estimates of HIV transmission probability are summarized in Table 1.

Fig. 1

Fig. 1

Table 1

Table 1

MSM were also divided into ‘current’ and ‘past’ MSM in which the former still acquire new male sexual partners, whereas the latter no longer have sexual relationship with men. We defined two types of sexual partnerships: a one-off sexual partnership and a repeat sexual partnership. The one-off partnership has only a single sex act, whereas the repeat sexual partnership consists of multiple sex acts with the same partner. Our partnership-based model [12,13] allowed a repeat sexual partnership to last for a finite period of time, during which HIV transmission can occur. MSM in a repeat sexual partnership could also acquire a one-off sexual partner and HIV transmission could occur from both types of partners. The repeat and one-off sexual partner change rates were stratified by four MSM classes with the lowest rate assigned to the low-activity MSM aged 35 years or more and the highest to high-activity MSM aged below 35 years (Table 2). Non-random mixing between partners according to age group, sexual activity level, and perceived HIV serostatus was implemented using the method based on odds ratios (ORs) [17]. Sex between men was the only route for transmitting HIV which included protected and unprotected receptive anal intercourse (URAI), protected and unprotected insertive anal intercourse (UIAI), and unprotected receptive oral intercourse (UROI). Condom use with repeat sexual partners was modelled using the class-specific proportions of susceptible individuals who have unprotected anal intercourse (UAI) with perceived HIV-negative and with diagnosed HIV-positive repeat sexual partners (Appendix, section 3.2.5, http://links.lww.com/QAD/A612). The perceived HIV-negative men included all susceptible (compartment 1 in Fig. 1) and undiagnosed HIV-positive MSM (compartments 2, 4, 6, 8, and 10). The diagnosed HIV-positive men included all diagnosed HIV-positive MSM (compartments 3, 5, 7, 9, and 11) and MSM on treatment (compartment 12). For one-off partnerships, susceptible individuals were categorized into three groups, that is, MSM who had no UAI one-off partner, MSM who had UAI only with a perceived HIV-negative one-off partner, and MSM who had UAI with a diagnosed HIV-positive one-off partner (Appendix, section 3.2.5, http://links.lww.com/QAD/A612). These proportions of MSM for modelling unsafe sex and condom use were assumed to remain constant over time and are presented in Table S8 (http://links.lww.com/QAD/A612) in the Appendix (http://links.lww.com/QAD/A612).

Table 2

Table 2

Back to Top | Article Outline

Data and parameter estimation

The National Survey of Sexual Attitudes and Lifestyles (NATSAL) for the year 2000 [18], the Gay Men's Sexual Health Survey (GMSHS) in London [19] for years 2000–2006 and 2008, and the London Gym Survey (GYM) [20] for years 2000–2008 were the primary sources for estimating demographic and behavioural parameters. We adjusted the data from the community-based convenience-sample GMSHS and GYM surveys to match four important variables from the national-based probability-sample NATSAL survey (Appendix, section 2.3, http://links.lww.com/QAD/A612). Table 2 summarizes the derived parameters for sexual behaviour.

The model's biological parameters were mainly derived from the systematic reviews and meta-analyses available in the literature. The data from the national HIV surveillance databases including HIV/AIDS diagnoses and CD4+ surveillance [1,5] were used extensively throughout the parameterization. Other unknown parameters were estimated through model fitting to match the HIV epidemic in MSM in the United Kingdom during 2001–2009 using Monte-Carlo filtering method [21]. Model validation was achieved by comparing the model outputs to the estimates of annual new HIV infections, the number of new HIV diagnoses, and the number of ART-treated MSM during 2001–2009 (Appendix, section 5, http://links.lww.com/QAD/A612).

Back to Top | Article Outline

Analysis of factor contribution to HIV infections

The method suggested by Orroth et al.[22] was used to estimate the proportion of HIV infections contributed by the following factors: PHI and non-PHI stages stratified by CD4+ cell counts, undiagnosed and diagnosed MSM, ART-treated and untreated MSM, repeat sexual and one-off partners, MSM aged 15–34 and 35–64 years, and low and high-activity MSM. We simulated counterfactual scenarios by setting HIV infectiousness corresponding to each factor to zero during 2001–2002, 2014–2015, and 2019–2020, independently. The period of 2001–2002 allowed the above factors to show their effects as early as possible in the modelling time frame, whereas the period of 2014–2015 represented an immediate intervention at the current transmission, and 2019–2020 represented the end of the decade and the modelling timeline.

To quantify the magnitude of contributions, population-attributable fractions (PAFs) associated with each factor were calculated from

, where IRs is the annual HIV incidence rate in the counterfactual scenarios and IRb is the annual HIV incidence rate in the baseline scenario, where the default HIV infectivity was used throughout the simulation period. Within each scenario, we derived annual HIV incidence rates and calculated the PAF for each filtered parameter set. The median estimates, as well as the 2.5th and 97.5th percentiles of these PAFs, were obtained for 2001–2002, 2014–2015, and 2019–2020. The population sizes at the end of these years in relation to the sources of infections were derived from the model outputs. We also assessed differences in the PAFs across age groups and sexual activity levels in all scenarios. Note that PAFs do not need to sum to 100% [23].

The sets of parameters resulting from the estimation were used to obtain projections of the epidemic of HIV in MSM in the United Kingdom up to the end of 2020 based on the assumption that all model parameters remained constant at the values of the end of 2009 and no additional interventions implemented during the projection period. The sensitivity of model projections was assessed using the regression trees technique [24] (Appendix, section 6.3, http://links.lww.com/QAD/A612).

Back to Top | Article Outline

Results

We present the findings from the analysis of factor contribution to HIV infections with median estimates and 2.5th and 97.5th percentiles. The proportions of HIV incidence attributable to various factors are shown in Table 3, with the average HIV-positive population sizes of the sources of infections at the end of analysis years. The projections of HIV epidemic among UK MSM are shown in Fig. 2. Additional results from model fitting and validation, as well as sensitivity analysis, are shown in the Appendix, sections 4, 5, and 6 (http://links.lww.com/QAD/A612).

Table 3

Table 3

Table 3

Table 3

Fig. 2

Fig. 2

Back to Top | Article Outline

Population-attributable fractions

Primary HIV infection

The transmission of HIV from individuals in the PHI stage accounted for the smallest proportion of infections with the current PAF (year 2014–2015) of 10% (3–28%), whereas around 98% (90–99%) are attributable to transmission after PHI. MSM in non-PHI stages (excluding treated) with CD4+ at least 350 cells/μl, are estimated to contribute considerably more to new infections than those with lower CD4+ cell counts (current PAF of 29–32 vs. 11–13%). However, dividing the average PAF of PHI by the average number of men in PHI stage shows that, on an individual basis, each MSM living with PHI contributes most among all disease stages (PAF ratio of 0.0185) to net transmission (Table 3). The later disease stages also contribute more to new infections which followed the pattern of the assumed transmission probability (Table 3).

Back to Top | Article Outline

Undiagnosed HIV

Undiagnosed HIV-positive men are currently estimated to contribute as much as 63% (49–80%) of onward transmissions, but only 19% (11–30%) are from those with CD4+ below 350 cells/μl, whereas 47% (36–59%) are from MSM with higher CD4+ cell counts. The current PAF of diagnosed men, including those on ART, is, on the contrary, considerably less, with around 44% (24–60%), although its contribution becomes more apparent as the epidemic progresses [from a PAF of 28% (17–41%) in 2001–2002 to 46% (26–61%) in 2019–2020]. Moreover, the average number of men living with undiagnosed HIV (7853) at any point in time is approximately four times smaller than that of diagnosed HIV (31 369), which clearly highlighted the importance of undiagnosed men in driving further HIV transmission in UK MSM.

Back to Top | Article Outline

Untreated HIV

The HIV epidemic in UK MSM is driven mainly by untreated men with 2014–2015 PAF of 85% (78–92%). However, an increased proportion of treated men due to widespread use of ART leads to a decline over time in the PAF of untreated men, whereas the PAF of treated men continues to increase, from 11% (5–18%) in 2001–2002 to 20% (11–28%) in 2019–2020. The PAF ratio of the untreated is more than 11-fold greater than that of ART-treated men (Table 3), which is influenced by a relatively small number of untreated men (12 884) in comparison to those on treatment (26 585).

Back to Top | Article Outline

Sexual behaviour

HIV transmission within repeat sexual partnerships accounts for almost all infections among MSM in the United Kingdom, with a current PAF of 90% (87–93%). The one-off partnership, on the contrary, is estimated to contribute substantially less with a PAF of 17% (12–24%), but this is accounted for by a small group of individuals engaging in one-off partnerships (885) in comparison with a large number of men having repeat sexual partners (15 350). The 2014–2015 PAF of repeat sexual partnerships dropped to 69% (63–74%) and to 23% (19–29%) if we consider only repeat sexual partners of high-activity and low-activity MSM, respectively.

Back to Top | Article Outline

Age and sexual activity groups

HIV-positive MSM aged 15–34 years contribute considerably more to HIV transmission than those aged 35–64 years with 2014–2015 PAFs of 62% (47–74%) and 44% (32–59%), respectively, although most HIV-positive MSM were in the older group (14 781 vs. 24 622). For sexual activity levels, the majority of new infections [current PAF of 80% (70–87%)] are associated with the high-activity MSM, who account for only 40% of all MSM in the model. This can be explained by their high-risk behaviours and the fact that HIV is highly prevalent within this group (22 231) compared to low-activity men (17 272). The PAFs of high-activity men as well as MSM aged 15–34 years remain consistent over the three analysis periods, suggesting their key role in consistently driving HIV transmission in the population of MSM in the United Kingdom.

Back to Top | Article Outline

Discussion

The study is among the first to show the contribution of various HIV-positive subpopulations to the epidemic of HIV among MSM in the United Kingdom. The epidemic has continued to expand during the past decade with the key group sustaining HIV transmission being high-sexual activity MSM aged below 35 years living with undiagnosed HIV and in the asymptomatic stage.

Our analyses of factor contributions to HIV infections showed that the effects of the PHI stage are smaller than the following stages regardless of population subgroup. Our sensitivity analysis (Appendix, section 6, http://links.lww.com/QAD/A612) also confirmed that non-PHI infectiousness was one of the most important drivers of the epidemic, while PHI-related parameters were not among them. This is probably because of a relatively short duration of high infectiousness in the stage of PHI compared to all other subsequent stages. A recent systematic review by Blaser et al.[25] suggested that HIV transmission rate during PHI should be around 10 and 30 times higher than that of asymptomatic stage if PHI lasted, respectively, for 6 and 2 months. In comparison to our study in which the duration of PHI was assumed to be 1.24–6 months, we calculated transmission rate from the lower and upper bounds of the per-act transmission probability of PHI and compared to that of CD4+ at least 500 (Table 1) and found that the PHI transmission rate ratio for URAI and UIAI could range from 0.4 up to 250, which is markedly wider than the review suggested [25]. However, even with the wide range of assumed PHI infectiousness, our findings still suggest that it is unlikely that PHI contributes more than 29% to all infections in UK MSM during 2001–2020, as illustrated by the upper limits of the PAF uncertainty ranges. There were also a number of recent studies that arrived at similar findings [26–29]. By contrast, Phillips et al.[30] showed in the simulation study that around half of the new infections in UK MSM were from men in PHI, which can probably be explained by assumptions about transmission risk and partnership formation that are different from our model.

The model suggested that around two in three new infections were attributable to men living with undiagnosed HIV, especially with high CD4+ cell counts (≥350 cells/μl). Similarly, a recent back-calculation study estimated large and stable numbers of undiagnosed MSM in England and Wales during 2001–2010, which suggests undiagnosed infections may continue to be a major driver of HIV transmission in the United Kingdom [4]. Outside the United Kingdom, an HIV transmission model predicted that around 82% of new cases among MSM in Switzerland were acquired HIV from undiagnosed men [31], whereas in the United States, the majority of new infections could be attributable to persons living with undiagnosed HIV [32,33]. This may be explained by the prevalence of risky behaviours, that is, UAI among MSM, which is much higher in HIV-positive persons unaware of their serostatus compared to diagnosed men [14]. Our finding clearly emphasizes a major role of undiagnosed and untreated men at asymptomatic stages in transmitting HIV and consequently requires more effort to be invested in further improvement of the coverage and frequency of HIV testing to detect the virus as early as possible. This is also supported by a recent national survey in the United Kingdom that showed that almost half of MSM had not tested for HIV in the past 5 years [34]. While limited resources should be allocated primarily to promote testing in high-activity MSM under the age of 35, as they are the key group sustaining the epidemic, there is also a case for encouraging all MSM to test regularly for HIV regardless of their age. Including HIV testing in routine health checks or when MSM present with other health problems in the United Kingdom may increase HIV testing uptake and provide necessary counselling for HIV-positive MSM.

The study showed that the majority of new infections of MSM in the United Kingdom occurred within a repeat sexual partnership and the epidemic cannot be controlled by preventing HIV transmission within one-off sexual partnership alone. Our definition of repeat sexual partnership can be matched to any real-life relationships that involve more than one sex act, including both steady relationships and casual encounters. Unfortunately, we were unable to explicitly differentiate between these two types of relationships in our model (i.e. steady vs. casual) due to insufficient behavioural data. On the basis of our belief, however, that low-activity men are more likely to establish a long-term, steady relationship rather than have a one-off casual encounter, an estimated contribution of steady relationships to HIV transmission may be derived from the 23% PAFs of repeat sexual partnerships of low-activity MSM. If a cautious assumption was then made that a quarter of HIV infections attributable to repeat sexual partnerships of high-activity men actually occurred with their long-term, steady partner, the contribution of all steady relationships to HIV transmission could be as high as 40–50%. With such a level of impact, it may be sensible for policy makers to consider interventions that aim specifically at reducing transmission within long-term, steady relationships such as encouraging steady partners to test together at the beginning of their relationship or to test immediately after breaking up.

The key limitation of our study is the uncertainty around all model parameters even after rigorous filtering and validation. Several issues with the available data, including absence, completeness, and representativeness, are among the main sources of uncertainty. For instance, NATSAL2000 was a national-based probability-sampling survey of sexual behaviours and attitudes that were representative of the UK population. However, the survey included only a small number of MSM, so that further stratifications, for example, by age and sexual activity, were sometimes not practical. The age range of the surveyed populations of 16–44 years was also not compatible with the 15–64 age range in this study. In contrast, GMSHS and GYM studies were community-based convenience-sampling surveys in London which, without a prior adjustment, would not be suitable for representing MSM populations at the national level. The sample size and age range were, on the contrary, sufficiently large for in-depth analyses. We handled parameter uncertainty by sampling from wide ranges of plausible parameter values informed by various sources, and fit and validate the model outcomes to the multiple estimates and empirical datasets simultaneously. The derived uncertainty ranges of PAFs demonstrate that our conclusions are robust to variations in the key parameters of the model.

The majority of new HIV infections among MSM in the United Kingdom during 2001–2020 is expected to be accounted for by a small group of highly sexually active individuals under the age of 35 years, living with undiagnosed HIV in the asymptomatic stage. An intensification of the current interventions to increase HIV test uptake and bring this group into the HIV/AIDS care system is a vital step for the prevention of transmission and will determine the success of prevention measure using immediate ART. Intervention programs that are tailor-made for MSM in a long-term relationship could prevent more new infections than previously thought [20]. Taken together, reducing the incidence of HIV among UK MSM may be possible even without the introduction and implementation of any new prevention technologies: we have the means to reduce transmission now.

Back to Top | Article Outline

Acknowledgements

The authors thank the staff of the HIV/AIDS division of the Public Health England for providing access to the national HIV surveillance data, and Anne Presanis and Paul Birrell for providing important estimates.

Author contributions: All authors contributed to the research questions, design of the mathematical model, and analysis methods. R.G.W., W.J.E., and D.D.A. conceived the study and helped design the model, fitting algorithms and sensitivity analyses. N.P. developed the programming codes, acquired and analysed the data, and drafted the manuscript with contributions from all authors. All authors read and approved the final version of this article.

This research received no specific grant from any funding agency.

N.P. is supported by a studentship from the Public Health England. R.G.W. is supported by a Medical Research Council (United Kingdom) (MR/J005088/1) Methodology Research Fellowship (G0802414), the Consortium to Respond Effectively to the AIDS/TB Epidemic (19790.01), the Bill and Melinda Gates Foundation (21675; OPP1084276), and USAID/IUTLD/The Union North America (GHN-A-OO-08-00004-00). D.D.A. is supported by the Medical Research Council (U105260566) and Public Health England. The funders had no role in study design, in the collection, analysis, and interpretation of data, in the writing of the report, and in the decision to submit the paper for publication. All researchers involved in the work were independent of the funder.

Back to Top | Article Outline

Conflicts of interest

The authors have declared that no competing interests exist.

Back to Top | Article Outline

References

1. Health Protection AgencyUnited Kingdom: new HIV diagnoses data to end December 2011. Tables No.2: 2011. London: Health Protection Agency; 2011.
2. Public Health EnglandHIV in the United Kingdom: 2013 report. London: Public Health England; 2013.
3. Presanis AM, De Angelis D, Goubar A, Gill ON, Ades AE. Bayesian evidence synthesis for a transmission dynamic model for HIV among men who have sex with men. Biostatistics 2011; 12:666–681.
4. Birrell PJ, Gill ON, Delpech VC, Brown AE, Desai S, Chadborn TR, et al. HIV incidence in men who have sex with men in England and Wales 2001–10: a nationwide population study. Lancet Infect Dis 2013; 13:313–318.
5. The UK Collaborative Group for HIV and STI SurveillanceA complex picture. HIV and other sexually transmitted infections. London: Health Protection Agency, Centre for Infections; 2006.
6. Smith RJ, Blower SM. Could disease-modifying HIV vaccines cause population-level perversity?. Lancet Infect Dis 2004; 4:636–639.
7. Boily MC, Baggaley RF, Wang L, Masse B, White RG, Hayes RJ, et al. Heterosexual risk of HIV-1 infection per sexual act: systematic review and meta-analysis of observational studies. Lancet Infect Dis 2009; 9:118–129.
8. Baggaley RF, White RG, Boily M-C. HIV transmission risk through anal intercourse: systematic review, meta-analysis and implications for HIV prevention. Int J Epidemiol 2010; 39:1048–1063.
9. Cambiano V, Lampe FC, Rodger AJ, Smith CJ, Geretti AM, Lodwick RK, et al. Long-term trends in adherence to antiretroviral therapy from start of HAART. AIDS 2010; 24:1153–1162.
10. Lampe FC, Gatell JM, Staszewski S, Johnson MA, Pradier C, Gill MJ, et al. Changes over time in risk of initial virological failure of combination antiretroviral therapy: a multicohort analysis, 1996 to 2002. Arch Intern Med 2006; 166:521–528.
11. Bannister WP, Kirk O, Gatell JM, Knysz B, Viard JP, Mens H, et al. Regional changes over time in initial virologic response rates to combination antiretroviral therapy across Europe. J Acquir Immune Defic Syndr 2006; 42:229–237.
12. Xiridou M, Geskus R, De Wit J, Coutinho R, Kretzschmar M. The contribution of steady and casual partnerships to the incidence of HIV infection among homosexual men in Amsterdam. AIDS 2003; 17:1029–1038.
13. Dietz K. On the transmission dynamics of HIV. Math Biosci 1988; 90:397–414.
14. Marks G, Crepaz N, Senterfitt JW, Janssen RS. Meta-analysis of high-risk sexual behavior in persons aware and unaware they are infected with HIV in the United States: implications for HIV prevention programs. J Acquir Immune Defic Syndr 2005; 39:446–453.
15. Fox J, White PJ, Macdonald N, Weber J, McClure M, Fidler S, et al. Reductions in HIV transmission risk behaviour following diagnosis of primary HIV infection: a cohort of high-risk men who have sex with men. HIV Med 2009; 10:432–438.
16. Macdonald N, Elam G, Hickson F, Imrie J, McGarrigle CA, Fenton KA, et al. Factors associated with HIV seroconversion in gay men in England at the start of the 21st century. Sex Transm Infect 2008; 84:8–13.
17. Goodreau SM, Golden MR. Biological and demographic causes of high HIV and sexually transmitted disease prevalence in men who have sex with men. Sex Transm Infect 2007; 83:458–462.
18. Johnson AM, Mercer CH, Erens B, Copas AJ, McManus S, Wellings K, et al. Sexual behaviour in Britain: partnerships, practices, and HIV risk behaviours. Lancet 2001; 358:1835–1842.
19. Dodds JP, Mercey DE, Parry JV, Johnson AM. Increasing risk behaviour and high levels of undiagnosed HIV infection in a community sample of homosexual men. Sex Transm Infect 2004; 80:236–240.
20. Elford J, Bolding G, Davis M, Sherr L, Hart G. Trends in sexual behaviour among London homosexual men 1998-2003: implications for HIV prevention and sexual health promotion. Sex Transm Infect 2004; 80:451–454.
21. Rose KA, Smith EP, Gardner RH, Brenkert AL, Bartell SM. Parameter sensitivities, Monte Carlo filtering, and model forecasting under uncertainty. J Forecast 1991; 10:117–133.
22. Orroth KK, White RG, Korenromp EL, Bakker R, Changalucha J, Habbema JD, et al. Empirical observations underestimate the proportion of human immunodeficiency virus infections attributable to sexually transmitted diseases in the Mwanza and Rakai sexually transmitted disease treatment trials: simulation results. Sex Transm Dis 2006; 33:536–544.
23. Rowe AK, Powell KE, Flanders WD. Why population attributable fractions can sum to more than one. Am J Prev Med 2004; 26:243–249.
24. Hastie T, Tibshirani R, Friedman J. The elements of statistical learning: data mining, inference, and prediction. 2nd edNew York: Springer Sceince+Business Media; 2009.
25. Blaser N, Wettstein C, Estill J, Vizcaya LS, Wandeler G, Egger M, et al. Impact of viral load and the duration of primary infection on HIV transmission: systematic review and meta-analysis. AIDS 2014; 28:1021–1029.
26. Punyacharoensin N, Edmunds WJ, De Angelis D, White RG. Mathematical models for the study of HIV spread and control amongst men who have sex with men. Eur J Epidemiol 2011; 26:695–709.
27. Xiridou M, Geskus R, de Wit J, Coutinho R, Kretzschmar M. Primary HIV infection as source of HIV transmission within steady and casual partnerships among homosexual men. AIDS 2004; 18:1311–1320.
28. Hollingsworth TD, Anderson RM, Fraser C. HIV-1 transmission, by stage of infection. J Infect Dis 2008; 198:687–693.
29. Cohen MS, Dye C, Fraser C, Miller WC, Powers KA, Williams BG. HIV treatment as prevention: debate and commentary: will early infection compromise treatment-as-prevention strategies?. PLoS Med 2012; 9:e1001232.
30. Phillips AN, Cambiano V, Nakagawa F, Brown AE, Lampe F, Rodger A, et al. Increased HIV incidence in men who have sex with men despite high levels of ART-induced viral suppression: analysis of an extensively documented epidemic. PLoS One 2013; 8:e55312.
31. van Sighem A, Vidondo B, Glass TR, Bucher HC, Vernazza P, Gebhardt M, et al. Resurgence of HIV infection among men who have sex with men in Switzerland: mathematical modelling study. PLoS One 2012; 7:e44819.
32. Marks G, Crepaz N, Janssen RS. Estimating sexual transmission of HIV from persons aware and unaware that they are infected with the virus in the USA. AIDS 2006; 20:1447–1450.
33. Hall HI, Holtgrave DR, Maulsby C. HIV transmission rates from persons living with HIV who are aware and unaware of their infection. AIDS 2012; 26:893–896.
34. Sonnenberg P, Clifton S, Beddows S, Field N, Soldan K, Tanton C, et al. Prevalence, risk factors, and uptake of interventions for sexually transmitted infections in Britain: findings from the National Surveys of Sexual Attitudes and Lifestyles (Natsal). Lancet 2013; 382:1795–1806.
Keywords:

compartmental model; epidemic model; HIV/AIDS; homosexual; mathematical model; MSM

Supplemental Digital Content

Back to Top | Article Outline
© 2015 Lippincott Williams & Wilkins, Inc.