Increasing risk behaviour can outweigh the benefits of antiretroviral drug treatment on the HIV incidence among men-having-sex-with-men in Amsterdam
© Mei et al; licensee BioMed Central Ltd. 2011
Received: 29 May 2010
Accepted: 11 May 2011
Published: 11 May 2011
The transmission through contacts among MSM (men who have sex with men) is one of the dominating contributors to HIV prevalence in industrialized countries. In Amsterdam, the capital of the Netherlands, the MSM risk group has been traced for decades. This has motivated studies which provide detailed information about MSM's risk behavior statistically, psychologically and sociologically. Despite the era of potent antiretroviral therapy, the incidence of HIV among MSM increases. In the long term the contradictory effects of risk behavior and effective therapy are still poorly understood.
Using a previously presented Complex Agent Network model, we describe steady and casual partnerships to predict the HIV spreading among MSM. Behavior-related parameters and values, inferred from studies on Amsterdam MSM, are fed into the model; we validate the model using historical yearly incidence data. Subsequently, we study scenarios to assess the contradictory effects of risk behavior and effective therapy, by varying corresponding values of parameters. Finally, we conduct quantitative analysis based on the resulting incidence data.
The simulated incidence reproduces the ACS historical incidence well and helps to predict the HIV epidemic among MSM in Amsterdam. Our results show that in the long run the positive influence of effective therapy can be outweighed by an increase in risk behavior of at least 30% for MSM.
We recommend, based on the model predictions, that lowering risk behavior is the prominent control mechanism of HIV incidence even in the presence of effective therapy.
The HIV epidemic is a global challenge and has a destructive impact on human life and welfare. One of the major or even dominating contributors to HIV prevalence in industrialized countries is the transmission through contacts among men who have sex with men (MSM). Particularly, in the Netherlands, MSM still accounts for the highest incidence of Sexually Transmitted Infections (STIs) including HIV . In fact, the proportion of MSM in new HIV cases recorded at the HIV registry continued to increase from 44% in 2003 to 59% in 2006 [1, 2].
Amsterdam harbors the majority of the largest MSM risk group in the Netherlands that has been traced and recorded for decades, providing us with detailed information about Amsterdam MSM's behavior characteristics. The Amsterdam Cohort Study (ACS) is such a study which has been conducted since 1984 with thousands of MSM recruited.
In order to embody heterogeneous behavior such as personal infection progressions and steady/casual partnership linkages, we use agent-based modeling to simulate the HIV spreading among MSM in Amsterdam, based on a previously presented Complex Agent Network model . This model helps to describe partnerships in detail, with (steady or casual) partnerships, durations and frequencies of sexual actions, influencing the HIV spreading among MSM in a well-structured in silico population. This enables modeling realistically heterogeneous populations and incorporation of social behavior data in the model. Risk behavior is of vital significance to HIV transmission and has sparked many psychological surveys.
Questionnaires completed by 324 MSM aged 18-34 were conducted by Davidovich et al., to assess sexual behavior and related cognitions . The results reveal, amongst others, that unprotected anal intercourse (UAI) is regarded as a symbol of trust and believing that the partner desires UAI is associated with less condom use; additionally, perceiving UAI as more gratifying was associated with having riskier UAI. Unfortunately, beliefs of people living with HIV about their own responsibility for preventing HIV transmission (personal responsibility) and their sex partners' responsibility for protecting themselves (partner responsibility) are poorly understood .
Despite psychological and sociological reasons, the so-called "safer sex fatigue" and excessive confidence in low viral load further intensify the reluctance on reducing risky behavior. Crepaz et al., concluded  that people's beliefs about Highly Active Antiretroviral Therapies (HAART) and viral load may promote unprotected sex, although HIV-positive patients receiving HAART did not exhibit increased sexual risk behavior, even when therapy achieved an undetectable viral load. In Amsterdam, the worrying increase of STIs was investigated in studies carried out by the department of AIDS research of the municipal health service. The result indicated that the introduction of HAART may have had an influence on the increase of STIs and risky sexual behavior .
Increase in risk behavior and resurgent epidemics have been reported post-HAART, and resurgent epidemics is most likely caused by increasing sexual risk behavior . Furthermore, low diagnosis fraction of infections may intensify this threat, since HIV-positive men who are unaware of their serostatus have higher risk behavior than the aware group [9–11]. Regarding the ACS, only 40% MSM accepted HIV testing at their STI consultation, among the recently infected at the STI clinic .
In this study, the primary objective is to explain and reproduce historical data and then assess the potential influence of varying risk behavior and therapy factors, with the aim to understand and predict the HIV spreading among MSM in Amsterdam. For this we need to combine sexual contact networks with HIV infection dynamics and individual behavior. To the best of our knowledge this is the first report on this combined evidence-based computational epidemics model.
Modeling the HIV epidemic in Complex Agent Networks
Using a previously developed Complex Agent Network , we model the HIV epidemics among MSM in Amsterdam through a sexual contact network in which each node represents an individual and edges represent potentially infectious contacts. Please see Figure 2 in  as a schematic illustration of virus spreading in a network. The number of edges emanating from a node is the degree of the node and the degree distribution is the distribution of this quantity across the population . In this study, the degree of a node, drawn from a specific degree distribution, is assumed to be static while the neighboring nodes that this node links to may change over time. There are classes of network geometry such as small-world, Poisson and scale-free networks. Since scale-free networks have been shown to be the representative of a variety of human sexual contact networks [15–17], we perform stochastic simulations of the spreading of HIV in undirected scale-free networks. The scale-free networks are characterized by a highly skewed distribution of contacts so that most of the nodes are weakly connected and a small number of nodes have very high connectivity. In particular, the degree distribution of this class of networks follows a power law distribution, i.e., pk = Ak -γ where is a normalization factor. After each node is assigned with a degree drawn from a given power law, these nodes are connected at random according to the so-called configuration model [18, 19] with the guarantee that the sum of all degrees is an even number and that there are no loops (nodes connected to themselves) and multiple edges (between two nodes).
The disease status of infected individuals is heterogenous with respects to infection stages, disease durations and infectiousness, etc., so that we can model individuals as agents and individuals' status transitions as internal changes of agents. The HIV infection progression occurs in roughly three stages: primary infection (PI), asymptomatic period (AP) and AIDS. Regarding status transition, for instance, infection reaches from PI to AP with a delay of about 3 months. We assume an irreversible "negative ⇀ PI ⇀ AP ⇀ AIDS" transition order for each infection, excluding the case that an individual with AIDS can with the right treatment go back to the asymptomatic phase, because in general patients are most likely diagnosed and treated before reaching the AIDS stage. During the HIV epidemic, each individual's infection status is related to temporally varying infectiousness due to the corresponding different plasma HIV RNA levels. The transmission probability across each edge depends on the status of the two connected individuals. Therefore, the probability with which a susceptible individual becomes infected is determined by the connectivity (degree) of the individual and the infection status of his partners (neighboring nodes) in the network. For simplicity, we assume no HIV mutations during the course of HIV epidemic. Additionally, individuals who die of AIDS will be replaced by healthy individuals, keeping the total of MSM under study static throughout simulations.
Our model distinguishes between steady and casual relationships as two types of sexual relationships, which brings different transmission probabilities that occur across likewise steady or casual edges. Results from previous models show that the transmission dynamics of HIV differ significantly depending on relationship type, i.e., long steady relationships or short casual partnerships . Moreover, there are strong indications that a substantial proportion of new HIV infections occur within steady partnerships [20, 21]. Multiple sexual actions can take place along a steady edge (within a steady relationship) yearly, while only one sexual action take place along a casual edge (within a casual partnership) yearly. Each individual can have at most one steady partner with whom he stays for some time. Casual partnerships can be formed between any two individuals, but men with a steady partner have fewer partners than single men. Even steady partners may be involved in casual partnerships during or between steady relationships, though they may negotiate safety agreements to be monogamous or to have no UAI outside the relationship. Considering two partners with one infected and the other susceptible, the number of sexual acts that they have within a specified time duration, together with the infected one's infectiousness and therapy effect, the susceptible one's susceptibility, and risk behavior involving the two, determines the transmission probability from the infected one to the susceptible one across their partnership edge (see Section 3.3 in  for details).
The values or distributions of parameters (partly) for modeling the HIV epidemic.
Duration of steady relationships
The duration of steady partnerships among Amsterdam MSM is reported to have an expected value of 1.5 years.
Duration of the asymptomatic stage for the untreated
This stage lasts 13 years for people with a failed treatment or without any therapy.
Duration of the asymptomatic stage for the successfully treated
This stage lasts a mean value of 22.5 years for people with a successful treatment. And the duration is likely increased to a mean value of 26 years, thanks to the wide use of HAART and the improvement in the therapy regimens.
Frequency of sexual actions per year between steady partners (with infected at stage AP)
The frequency of either URAI or UIAI between steady partners is 15 per year.
Frequency of sexual actions between steady partners in the first 3 months and the last 9 months, respectively (with infected at stage PI)
(8) & (22)
The PI stage lasts for about 3 months which is shorter than the 1-year time step, so that we divide individuals' first year of infection into two periods. Thus, the frequencies in these two periods adds up to 30.
Transmission probability per URAI/UIAI4 act (with infected at stage PI)
Transmission probability per URAI/UIAI act (with infected at stage AP)
The infected in the last 9 months of PI contribute the same to transmission possibility per act as they do at stage AP.
Reduction in risky behavior along casual partnerships for men who have a steady partner
Men may make an agreement with his steady partner to be monogamous or to have no UAI outside the relationship, leading to less risky behavior.
see Sec. 2 in 
Moderate (default) treatment-induced infectivity reduction factor5
ART can moderately reduce transmission probability by 50-90%.
Optimistic treatment-induced infectivity reduction factor
ART can optimistically reduce transmission probability by 90-100%.
Initial population size
People involved in all substudies add up to 2299.
The power-law degree distribution's exponent γ in this study
MSM population follows a power-law degree distribution with a value of γ in the interval between 1.5 and 2.
The power-law degree distribution's maximum degree k max
We assume so.
The fraction of vertices with a degree of 0
We assume that a small portion in a population not having any contact.
Designing scenarios for predicting the HIV epidemic
Scenarios for simulating the HIV epidemic among MSM in Amsterdam (factors changed since 2006).
Risk behavior factor
Treatment-induced infectivity reduction factor
Prediction 1 (P1)
Prediction 2 (P2)
Prediction 3 (P3)
Prediction 4 (P4)
Prediction 5 (P5)
Compared to 1.66 in 2006, the RS incidence does not change noticeably at the time steps following 2006. For example, the incidence increases to 1.69 in 2015 and 1.74 in 2020, and then declining to 1.63 in 2030 and 1.60 in 2040.
Resulting incidence from simulations of scenarios.
The P1 incidence is higher in each specified year than the RS incidence though a moderate treatment-induced infectivity reduction factor is adopted in both simulations. We observe an increases of 10.95% in 2030 and of 2.87% in 2040, respectively.
Once the optimistic therapy is adopted in the following P2-P4 simulations, the resulting incidence shows an obvious overall downtrend compared to the RS incidence, since down arrows are predominantly present in the P2, P3 and P4 columns of Table 3. Among incidence resulting from these 3 simulations, the P2 incidence declines to the largest extent, e.g., by 11.24% in 2030 and 28.7% in 2040.
Surprisingly, for the P5 simulation an overall uptrend occurs compared to the RS incidence, since up arrows are predominantly present in the P5 column of Table 3. Although the optimistic treatment-induced infectivity reduction factor is used for all P2-P5 simulations, the P5 incidence shows a totally different upgoing trend compared to the largely downgoing incidence resulting from the P2, P3 and P4 simulations in the long run. For example, in 2035 there is a 5.5%↑ for P5 incidence, while there are 26.3%↓, 10.7%↓ and 9.63%↓ for P2, P3 and P4 incidence, respectively. Additionally, from 2030 onward the P5 incidence approximately remains more or less at the same level as the RS incidence, for instance, 1.64 versus 1.63 in 2030 and 1.58 versus 1.60 in 2040, respectively.
In addition, the yearly fraction of the diagnosed (the number of the diagnosed divided by the number of the infected), inferred from our simulated results, is fluctuating within the range of 0.35-0.56 and finally approaching 0.41 (data not shown).
We construct an agent-based probabilistic Complex Agent Network model to gain increased insight into the spread of HIV among men who have sex with men in Amsterdam. In our approach, the in silico population is mimicked as sexual contact networks and the transmission dynamics of HIV is embedded in those networks describing complex interactions among MSM. Sexual contacts, steady or casual, between each pair of partners that have individual disease status, contribute to virus transmission from the infected to the susceptible. The simulated incidence in 1985-2006 is able to reproduce the ACS historical incidence well (Figure 1 and Figure 2), based on the null-hypothesis T-test performed. We examine how two factors of vital significance-the treatment-induced infectivity reduction factor and risk behavior factor-influence the HIV spreading by performing a set of scenario simulations. The resulting analyses (Table 3) reveal that in the long term the effects of the optimistic therapy can be counterbalanced by an increase in risk behavior of at least 30% for MSM. This is in line with the conclusion drawn by Wilson et al., that the risk of HIV transmission in male homosexual partnerships is high over repeated exposures even in the presence of effective treatment .
Our research takes advantage of the statistical details of MSM's behavior obtained from the ACS, showing a promising way of simulating HIV spreading among a specific group of people. In contrast, many other modeling studies were not able to incorporate this kind of detailed data. This study provides an alternative and reliable approach to model virus spreading in a highly connected population with individual details. The yearly fraction of the diagnosed is relatively low, restricting the positive influence of highly effective therapy. This low value is consistent with what has been observed in reality. For example, Xiridou et al., stated that 42% of the infected people at the asymptomatic stage know they are HIV positive (diagnosed) ; Gras et al., concluded that observed annual proportions of diagnoses for homosexual men were decreasing from about 57% in 1996 to 42% in 2004 taking into account all data in 1996-2004, or approximately remaining at 44% taking into account data in 2000-2004 . Accordingly, many infected people are unaware of their infection due to low fraction of diagnosis and thereby will not benefit from highly effective therapy. Extreme preventive measures have been proposed such as universal testing followed by immediate treatment . But this approach is not practical, as annual universal testing is a logistical challenge and immediate treatment regardless of CD4 count is not in line with current treatment guidelines. Policy makers therefore consider much more subtle and realistic countermeasures.
The simulations demonstrates that the incidence varies in different time points (Figure 2 and Figure 3). We believe that this sort of rapid fluctuations in incidence is inherent and is likely the result of network structures in combination with the stochastic nature of the models.
More precise data is needed to estimate the infectiousness of people who are receiving therapy, taking into consideration their adherence, behavior changes since receiving therapy and rates of resistance emergence. Also, a better model of estimating risk behavior is expected to further improve our understanding of the underlying determinants of risk behavior. For example, the fraction of MSM that use condoms without any exception or only during the last insertive anal intercourse can be introduced.
The transmission model has several challenges. Firstly, the model is validated by comparing the simulated yearly incidence to the ACS historical incidence, ignoring prevalence and other indicators. This is mainly due to the availability of the ACS incidence data, and also the the dimensionless feature of the incidence since the number of recruited MSM in the ACS varies each year while the network size remains constant throughout. To avoid a possible bias resulting from this incidence-biased process, we can supplement comparisons according to indicators other than incidence.
Secondly, for practicability, we assume that HAART can to an optimistic extent reduce patients' infectiousness by up to 99% instead of 100%. There exists a serious controversy on the effectiveness of HAART. Although HAART could reduce viral load to an undetectable level, Edwin J Bernard stated that being undetectable does not necessarily mean being entirely uninfectious . Additionally, quantifying the proportion of people who will reach undetectable viral load due to therapy still relies on further clinical surveillance and statistics.
The advantages of using the Complex Agent Network model have not been fully exploited in this study; for example we use neither an individually dynamic risk behavior factor nor consider individual histories of risky contact (due to the lack of data). Incorporating more data-driven details may result in dramatic increases in computational cost to which modeling a population in hierarchical networks can be a promising solution .
Our results suggest that the positive influence of effective therapy can be outweighed by an increase in risk behavior of at least 30% for MSM. This implies that if universal voluntary HIV testing is currently impossible or impractical, lowering risk behavior is the prominent control mechanism of HIV incidence even in the presence of effective treatment. This is an essential result since recent studies indicate that even in the presence of potent antiretroviral therapy, the incidence of HIV among MSM still increases.
The authors would like to acknowledge the financial support of China National Scientific Fund (No. 91024015, 91024030, 60974074, 60974073 & 61074107), the severe infectious diseases spreading research based on social networks (Chinese grant 2008ZX10004-013) and the European DynaNets http://www.dynanets.org grant (EU Grant Agreement Number 233847). The Research was also partly sponsored by a grant from the Leading Scientist Program' of the Government of the Russian Federation, under contract 11.G34.31.0019. In particular, we thank Dr. Viktor Müller for his helpful suggestions.
- Veen Mv, Koedijk F, Broek Ivd, Coul EOd, Boer Id, Sighem Av, Sande Mvd: Sexually transmitted infections in the Netherlands in 2006. 2006Google Scholar
- Laar Mvd, Boer Id, Koedijk F, Coul EOd: HIV and Sexually Transmitted Infections in the Netherlands in 2004. 2004Google Scholar
- Mei S, Sloot P, Quax R, Zhu Y, Wang W: Complex Agent Networks explaining the HIV epidemic among homosexual men in Amsterdam. Mathematics and Computers in Simulation. 2010, 80 (5): 1018-1030. 10.1016/j.matcom.2009.12.008.View ArticleGoogle Scholar
- Davidovich U, De Wit JBF, Stroebe W: Behavioral and cognitive barriers to safer sex between men in steady relationships: Implications for prevention strategies. AIDS Education and Prevention. 2004, 16 (4): 304-314. 10.1521/aeap.16.4.304.40398.View ArticlePubMedGoogle Scholar
- Wolitski RJ, Flores SA, O'Leary A, Bimbi DS, Gómez CA: Beliefs about personal and partner responsibility among HIV-seropositive men who have sex with men: Measurement and association with transmission risk behavior. AIDS and Behavior. 2007, 11 (5): 676-686. 10.1007/s10461-006-9183-6.View ArticlePubMedGoogle Scholar
- Crepaz N, Hart TA, Marks G: Highly active antiretroviral therapy and sexual risk behavior: A meta-analytic review. Journal of the American Medical Association. 2004, 292 (2): 224-236. 10.1001/jama.292.2.224.View ArticlePubMedGoogle Scholar
- Stolte G, Dukers NH, de Wit JB, Fennema H, Coutinho RA: A summary report from Amsterdam: increase in sexually transmitted diseases and risky sexual behaviour among homosexual men in relation to the introduction of new anti-HIV drugs. Euro surveillance: bulletin europeen sur les maladies transmissibles = European communicable disease bulletin. 2002, 7 (2): 19-22.Google Scholar
- Bezemer D, De Wolf F, Boerlijst MC, Van Sighem A, Hollingsworth TD, Prins M, Geskus RB, Gras L, Coutinho RA, Fraser C: A resurgent HIV-1 epidemic among men who have sex with men in the era of potent antiretroviral therapy. AIDS. 2008, 22 (9): 1071-1077. 10.1097/QAD.0b013e3282fd167c.View ArticlePubMedGoogle Scholar
- 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. Journal of Acquired Immune De ciency Syndromes. 2005, 39 (4): 446-453. 10.1097/01.qai.0000151079.33935.79.View ArticleGoogle Scholar
- 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 (10): 1447-1450. 10.1097/01.aids.0000233579.79714.8d.View ArticlePubMedGoogle Scholar
- Williamson LM, Dodds JP, Mercey DE, Hart GJ, Johnson AM: Sexual risk behaviour and knowledge of HIV status among community samples of gay men in the UK. AIDS. 2008, 22 (9): 1063-1070. 10.1097/QAD.0b013e3282f8af9b.View ArticlePubMedGoogle Scholar
- Dukers NHTM, Fennema HS, Van Der Snoek EM, Krol A, Geskus RB, Pospiech M, Jurriaans S, Van Der Meijden WI, Coutinho RA, Prins M: HIV incidence and HIV testing behavior in men who have sex with men: Using three incidence sources, the Netherlands, 1984-2005. AIDS. 2007, 21 (4): 491-499. 10.1097/QAD.0b013e328011dade.View ArticlePubMedGoogle Scholar
- Mei S, Vijver Dvd, Xuan L, Zhu Y, Sloot P: Quantitatively Evaluating Interventions in the Influenza A (H1N1) Epidemic on China Campus Grounded on Individual-based Simulations. the International Conference on Computational Science 2010 (ICCS 2010). 2010, Amsterdam, the Netherlands: Springer-Verlag, 1669-1676.Google Scholar
- Albert R, Barabasi A: Statistical mechanics of complex networks. Rev Mod Phys. 2002, 74: 47-97. 10.1103/RevModPhys.74.47.View ArticleGoogle Scholar
- Liljeros F, Edling CR, Amaral LAN: Sexual networks: Implication for the transmission of sexually transmitted infection. Microbes and Infections.
- Liljeros F, Edling CR, Amaral LAN, Stanley HE, Aberg Y: The web of human sexual contacts. Nature. 2001, 411: 907-908. 10.1038/35082140.View ArticlePubMedGoogle Scholar
- Schneeberger A, Nat R, Mercer CH, Gregson SAJ, Ferguson NM, Nyamukapa CA, Anderson RM, Johnson AM, Garnett GP: Scale-free networks and sexually transmitted diseases: A description of observed patterns of sexual contacts in Britain and Zimbabwe. Sexually Transmitted Diseases. 2004, 31 (6): 380-387. 10.1097/00007435-200406000-00012.View ArticlePubMedGoogle Scholar
- Bender E, Canfield E: The asymptotic number of labelled graphs with given degree sequences. J Combin Theory Set A. 1978, 24: 296-307. 10.1016/0097-3165(78)90059-6.View ArticleGoogle Scholar
- Britton T, Deijfen M, Martin-Löf A: Generating simple random graphs with prescribed degree distribution. Journal of Statistical Physics. 2006, 124 (6): 1377-1397. 10.1007/s10955-006-9168-x.View ArticleGoogle Scholar
- 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 (7): 1029-1038. 10.1097/00002030-200305020-00012.View ArticlePubMedGoogle Scholar
- Davidovich U, De Wit JBF, Albrecht N, Geskus R, Stroebe W, Coutinho R: Increase in the share of steady partners as a source of HIV infection: a 17-year study of seroconversion among gay men. AIDS. 2001, 15: 1303-1308. 10.1097/00002030-200107060-00013.View ArticlePubMedGoogle Scholar
- The Amsterdam Cohort Studies on HIV infection Annual Report 2006. 2006, [http://www.amsterdamcohortstudies.org/menu/reports/ACSannualreport2006.pdf]
- Overview of the Amsterdam Cohort Studies among homosexual men and drug users. 2006, [http://www.amsterdamcohortstudies.org/menu/reports/ACSoverview2006.pdf]
- Hendriks JCM, Craib KJP, Veugelers PJ, van Druten HAM, Coutinho RA, Schechter MT, van Griensven GJP: Secular trends in the survival of HIV-infected homosexual men in Amsterdam and Vancouver estimated from a death-included CD4-staged Markov model. Int J Epidemiol. 2000, 29 (3): 565-572. 10.1093/ije/29.3.565.View ArticlePubMedGoogle Scholar
- Ronald BG: Methods for estimating the AIDS incubation time distribution when date of seroconversion is censored. Statistics in Medicine. 2001, 20 (5): 795-812. 10.1002/sim.700.View ArticleGoogle Scholar
- Detels R, Munoz A, McFarlane G, Kingsley LA, Margolick JB, Giorgi J, Schrager LK, Phair JP: Effectiveness of Potent Antiretroviral Therapy on Time to AIDS and Death in Men With Known HIV Infection Duration. JAMA: Journal of the American Medical Association. 1998, 280 (17): 1497-10.1001/jama.280.17.1497.View ArticlePubMedGoogle Scholar
- Dorrucci M, Balducci M: Temporal Changes in the Rate of Progression to Death Among Italians With Known Date of HIV. JAIDS: Journal of Acquired Immune Deficiency Syndromes. 1999, 22: 65-10.1097/00042560-199909010-00008.PubMedGoogle Scholar
- Tarwater PM, Mellors J, Gore ME, Margolick JB, Phair J, Detels R, Munoz A: Methods to Assess Population Effectiveness of Therapies in Human Immunodeficiency Virus Incident and Prevalent Cohorts. American Journal of Epidemiology. 2001, 154 (7): 675-681. 10.1093/aje/154.7.675.View ArticlePubMedGoogle Scholar
- Leynaert B, Downs AM, De Vincenzi I: Heterosexual transmission of human immunodeficiency virus: Variability of infectivity throughout the course of infection. American Journal of Epidemiology. 1998, 148: 88-96.View ArticlePubMedGoogle Scholar
- Vittinghoff E, Douglas J, Judson F, McKirnan D, Macqueen K, Buchbinder SR: Per-contact risk of human immunodeficiency virus transmission between male sexual partners. American Journal of Epidemiology. 1999, 150 (3): 306-311.View ArticlePubMedGoogle Scholar
- DeGruttola V, Seage Iii GR, Mayer KH, Horsburgh Jr CR: Infectiousness of HIV between male homosexual partners. Journal of Clinical Epidemiology. 1989, 42 (9): 849-856. 10.1016/0895-4356(89)90098-X.View ArticlePubMedGoogle Scholar
- Boily MC, Bastos FI, Desai K, Masse B: Changes in the Transmission Dynamics of the HIV Epidemic after the Wide-Scale Use of Antiretroviral Therapy Could Explain Increases in Sexually Transmitted Infections: Results from Mathematical Models. Sexually Transmitted Diseases. 2004, 31 (2): 100-112. 10.1097/01.OLQ.0000112721.21285.A2.View ArticlePubMedGoogle Scholar
- Wilson DP, Law MG, Grulich AE, Cooper DA, Kaldor JM: Relation between HIV viral load and infectiousness: a model-based analysis. Lancet. 2008, 372 (9635): 314-320. 10.1016/S0140-6736(08)61115-0.View ArticlePubMedGoogle Scholar
- Gras L, Sighem Av, Valkengoed Iv, Zaheri S, Wolf Fd: Monitoring of human immunodeficiency virus (HIV) infection in the netherlands. 2004, [http://www.hiv-monitoring.nl/index.jsp?ACTION=GOGEN&GEN1=20]Google Scholar
- Granich RM, Gilks CF, Dye C, De Cock KM, Williams BG: Universal voluntary HIV testing with immediate antiretroviral therapy as a strategy for elimination of HIV transmission: a mathematical model. The Lancet. 2008Google Scholar
- Bernard EJ: 'Undetectable' But Infectious?. 2004Google Scholar
- Quax R, Bader DA, Sloot PMA: Simulating Individual-Based Models of Epidemics in Hierarchical Networks. Proceedings of the 9th International Conference on Computational Science: Part I. 2009, Baton Rouge, LA, USA: Springer-Verlag, 5544: 725-734.Google Scholar
- The pre-publication history for this paper can be accessed here:http://www.biomedcentral.com/1471-2334/11/118/prepub