Now nearing the end of its third decade, the HIV/AIDS pandemic resists easy characterization. The major risk factors have been known for some time, but our understanding of how these risk factors mesh with human and viral dynamics continues to evolve. Although still referred to as epidemic, HIV/AIDS is now perceived as an endemic, chronic disease  whose critical features are markedly heterogeneous . In any given setting, the complex combination of risk epidemiology, viral characteristics, host immunology, social networks, demographic phenomena, and social determinants influences transmission, incidence, prevalence, mortality, and the efficacy of interventions. HIV transmission networks provide an organizing principle for viewing these multifaceted issues, and networks have received substantial attention in this setting. One of the important concepts in the field has been that active transmission takes place in groups that have a disproportionate number of persons with many contacts (often referred to as ‘scale-free’ networks, although this name is probably a statistical misnomer  in most instances). Recent work, predominantly focused on heterosexual networks that are dominated by persons with relatively few contacts (‘low degree’) but a high level of simultaneity (‘high concurrency’), suggests that some alternative network substrates may also underlie transmission.
Men continue to predominate in the notification of HIV/AIDS cases in the USA. From 2004–2007, the number of reported cases of HIV/AIDS in men who have sex with men (MSM) increased from 17 898 to 22 472, and the number of male injecting drug users (IDU) was relatively constant at about 3000 . Nonetheless, the overall HIV/AIDS ‘endemic’ is frequently described as having a disproportionate effect on women – in particular, those who are members of minority groups [4,5]. For both men and women, the number of reported cases of HIV/AIDS attributable to high-risk heterosexual contact (defined as sexual contact with an infected person of the opposite sex, or sex with an IDU of the opposite sex, or, for a woman, with a MSM) has remained constant or declined during the current decade. The proportion of such cases has risen, however, more dramatically for women than for men (Fig. 1). These trends suggest that women now have an increasing share of a declining disease occurrence. A recent upward adjustment of the estimate of overall HIV/AIDS incidence , based on the emerging technology to detect recent infection, may change the perception of this disproportion.
Men who have sex with men and injecting drug user transmission networks
Investigations of male-to-male and IDU transmission during the past several years have focused on social network characteristics as risk factors [7–13]. For example, in a study of men in Baltimore, MSM were more likely to be HIV positive than were heterosexual men, the networks of MSM were less dense, and those MSM who reported IDU also reported greater needle sharing than their heterosexual counterparts . Similarly, among IDU in Winnipeg, relationship to a risk network member, difficulty of access to syringes, and dyads who pooled resources were all at greater risk for syringe sharing . Although these investigations are important contributions to the epidemiology of risk, their primary concern was not with transmission dynamics.
Heterosexual transmission networks
In contrast, studies of heterosexual transmission have investigated both risk factors and dynamics. As noted, heterosexual transmission has increasing prominence in the epidemiology of HIV/AIDS in the USA, and has been of special importance in many other areas of the world for some time. Although their settings differ from that of the United States, several other countries – notably Russia , Brazil , and France  – have furnished data that supports the increasing prominence of heterosexual transmission. Current epidemiologic investigation continues to focus on risk factors for transmission in the heterosexual setting, including unsafe sex and history of sexually transmitted infections (STIs) (Thailand) , illicit drug use and migration (Caribbean) , childhood sexual and physical abuse (south-eastern USA) , and inadequate condom use (south-western USA) [19•]. A meta-analytic review of 68 epidemiologic studies [20••] confirmed that the number of sex partners, history of paid sex, and infection with herpes simplex virus type 2 or other STIs were significantly associated with HIV infection. The authors also found that these associations were present after stratification for high- and low-prevalence areas, suggesting that risk factors persist even as epidemics mature. This association of sexual risk factors with HIV is at odds with the findings of several large studies [21–24] conducted in Africa during the 1990s and the findings from a subsequent review . Some of the discrepancy may lie in the study approach. The earlier reports and review examined ecologic correlations between the level of sexual risk factors in multiple sites and the prevalence of HIV (although note was made as well of inconsistencies in the association of personal risk factors and HIV). The current meta-analytic review [20••] is a comprehensive assessment of the association between an individual's risk factors and HIV. The underlying assumption of both the ecologic and cross-sectional approach is that current sexual activity reflects risk at the time that HIV was acquired, and is supported to some extent by the review's finding that the associations were similar in high and low-prevalence areas. None of the studies under consideration, however, was in a position to know the relationship of current HIV infection to sexual activity at the time of acquisition. The studies are markedly heterogeneous with regard to the level of risk variables , and two critical factors – frequency of sexual contact and time since acquisition (a surrogate for the transmission probability) – are missing, rendering interpretation of both ecologic and risk factor associations difficult. The emerging technology for identifying acute infection may clarify future inquiry, but is unlikely to resolve past inconsistencies.
Some important recent work has gone beyond risk factor assessment, and explored the role of network phenomenon in heterosexual propagation of HIV. At least two major factors – concurrency and bridging – have been studied extensively without the use of formal network designs.
Concurrency, originally proposed as an important factor in transmission in the early 1990s , is a prominent feature of heterosexual groups at risk. In Houston, Texas, among a group of 553 women from high-risk, high-poverty, high-HIV prevalence areas, 49% reported concurrent partnerships (and only 26% reported condom use at their last sexual contact) [19•]. In the rural southern USA, 25% of women and 42% of men had multiple partnerships in the preceding year; 26% of such partnerships were concurrent, and 38% of partnerships in the preceding 5 years were concurrent . This sexual substrate, coupled with undereducation and food insecurity, makes poverty a major factor in person's taking on sexual risk , and economics in general a driving force in sexual reciprocity .
The latter studies are representative of the growing importance of qualitative contributions to the understanding of disease transmission. An ethnographic exploration of cohabitation suggests that marriage, or at least exclusivity, may be protective against transmission of HIV . Hattori and Dodoo [31••] addressed this issue in detail using a sample of women drawn from the slums of Nairobi, Kenya. They stress the complexity of relationships, noting the different forms of formal (officially recognized) and informal pairing, and their varying social implications. They note that the 2003 Demographic Health Survey in Kenya reported a low prevalence of women with multiple partnerships in the preceding year (1.7%), but that the frequency of such reports varied with cohabiting status. In their sample from the Nairobi slums, more than twice the proportion of women reported two or more partners in the past year (4.6%), and there was important variation in this group as well. One percentage of married, coresiding women (71% of the sample; representativeness is not discussed specifically, and the authors note that their study group is a selected subset) reported two or more partners, but 11.5% of coresiding women, 11.1% of widowed women, and 20.5% of divorced women reported two or more partners. Nonexclusivity was also a feature of older age, less education, and Catholic religion. Of special interest was the observation that women living with co-wives were more likely to have other male partners. Thus, the data suggest that in this impoverished group the overall population prevalence of 1-year nonmonogamy was not high, but was strongly influenced by social, cultural, and demographic factors. These findings confirm those of a subsequent review and commentary  that found widespread reporting of concurrent relationships embedded in complex social and sexual arrangements, and suggested that attention to such factors may be critical in the elucidation of transmission dynamics in Africa. Such thinking was underscored in a commentary by Dworkin and Ehrhardt , who pointed out the simple ABC approach (abstinence, be faithful, use condoms) needs to amplified by a focus on GEM (gender relations, economics, migration).
A formal network approach
Using a network design that incorporated both qualitative and quantitative elements, Helleringer and Kohler [34••] reported on 923 persons from Likoma Island, Malawi. They identified a network configuration characterized by long-term relationships of low degree [3-year mean number of partners was 2.6 for men and 2.2 for women; interquartile range (IQR) 1–3 for both] and high concurrency. The concurrent relationships generated a giant connected component containing about half of the participants, with a large bicomponent (in which every member is connected to at least two others), containing approximately 25% of survey respondents. That such a component structure can emerge from a low-degree high-concurrency sexual configuration was predicted theoretically and by simulation [35•]. This structure may be capable of supporting rapid transmission of HIV, particularly with new introduction of the virus, and a preponderance of acute infections [36,37]. In the Likoma group, HIV prevalence was 10.6% among women and 4.7% among men, with a greater concentration of HIV-positive persons in the periphery of the network (as opposed to the highly interactive bicomponent). In a letter, Brewer et al.  assert that this finding undermines the likelihood that the described network configuration underlies HIV transmission, because prior network descriptions had placed a preponderance of HIV-positive persons centrally in a network of high prevalence, and peripherally in a network of low prevalence. Likoma, a setting substantially different from either of the two networks cited, lies between them on the prevalence spectrum, and appears to be past any period of rapid transmission that may have taken place, so that prior observations cited by Brewer et al.  may not be predictive of Likoma's HIV configuration.
In the USA, most of the recent work on bridging has focused on African American men who identify as heterosexual but also have sex with men without making their female partners aware of this activity (the so-called ‘down low’) as well as on the general population of men who have sex with both men and women (MSMW). For the former, several have written that the term is socially constructed and in many ways inappropriate [39–41], as it ‘exoticizes’ the activity and makes it qualitatively distinct from identical behavior in men who are not of African American ethnicity. In addition, Satcher et al.  refer to United States national data to point out that the proportion of women who report having possibly contracted HIV because of sex with a bisexual man has remained constant in recent years, and was highest for African American women. Malebranche reviews the issue in detail, and supports the view that African American MSMW may be a ‘bisexual bridge’ to African American women, and may account in part for their higher prevalence . Other recently described bridging populations include bisexual men in China , and transmission from IDU groups to non-IDU groups through heterosexual contact [14,45]. Several authors have stressed the nuances of sexual activity in assessing bridging. Although official reporting systems are silent on the matter, heterosexual anal sex is common , and may be increasing . Bisexual men in China are reported to have anal intercourse with their female partners more often if they also have anal sex with their male partners . The variability of sexual behaviors among those with a high risk of transmitting HIV , however, reinforces the idea that the simple presence of possible sexual connections, in the absence of behavioral, biological, and network information, makes assessment of bridging difficult. Finally, investigations of bisexual bridging have focused on the origination, rather than the destination, of the bridge. Requisite studies that compare women of differing ethnicities with regard to the sexual activity of their partners appear to be lacking.
Modeling heterosexual transmission
Mathematical consideration of the trajectory of HIV has for many years been dominated by sexual transmission between men, or by IDU. Recently, considerable attention has been devoted, directly or indirectly, to models of heterosexual transmission [49–63]. Although the models are sophisticated, complex, and detailed, the major results for most of them are simply stated, and in some instances contradictory. Abbas and colleagues  assert that antiretrovirals would not have a major impact on transmission, with only an 11.2% greater decline with their widespread use in 10 years compared with the decline in their absence. In contrast, Granich et al.  present a model that finds that universal testing coupled with widespread use of antiretrovirals would successfully eliminate HIV.
Several models have explored the complexity of simultaneous effects. A decline in prevalence attributed to a behavioral intervention may actually result from changes in immigration patterns and declines in mortality through treatment rather than from the intervention itself . In a similar vein, a decrease in cross-generational sex and limiting partner change may decrease individual risk but would have little effects on the overall epidemic trajectory . Hertog  stressed that models must take into simultaneous consideration mixing patterns, pattern change, and infectiousness, since these factors interact and do not occur in isolation. Finally, Gouws et al.  have stressed the importance of geographic area in assessing the proportion of HIV attributable to different routes of transmission.
Models have been used recently to explore several contested areas of HIV/AIDS epidemiology. Dunkle et al.  presented a construct to show that between 60 and 94% of heterosexual transmissions occur between (cohabiting) serodiscordant couples. (In an exhaustive review of the available empirical data, Guthrie et al.  reach a similar, although nonquantified, conclusion about the importance of discordance. The default assumption in this work is that serodiscordant couples are monogamous, and missing from this discussion is a consideration of the potential interaction of serodiscordance and concurrency.) Deuchert and Brody  report a model-based statistical analysis that questions whether parameters used in many models are in keeping with the extant empirical estimates for transmission probabilities or partner change. This conclusion might be reconsidered in light of changing concepts about the probability of transmission. Similar points were raised in an exchange in which Rapatski and colleagues [61,66] assert that the bulk of transmission occurs during late-stage HIV disease, rather than during acute or early infection.
Modeling continues to be a fundamental tool for evaluating disease transmission. Recent theoretical advances in network modeling, based on a family of exponential random graph models, have led to operational approaches and the development of practical tools for performing such analyses [67,68]. Such approaches offer considerable promise for amalgamating theoretical considerations and simulations with empirical observations, such as those made on Likoma Island.
Several themes motivate current investigation in HIV transmission networks. The simplistic sense of an epidemic as the sum of homogeneous events is giving way to the view of transmission as a complex and heterogeneous phenomenon, embedded in networks that may facilitate rapid propagation. Investigators are paying increasing attention to contextual issues, and qualitative tools are now being brought to bear more seriously on this complex system. These studies create some discordance between the frequent qualitative description of concurrent sexual arrangements and the survey reporting of infrequent multiple partnerships. An expanding view of HIV transmission heterogeneity will hopefully resolve some of the inconsistencies, create a more coherent picture of the interrelationship of elements, and ultimately lead to a setting-specific mix of appropriate interventions.
This review was supported in part by R01 DA019393 from the National Institute on Drug Abuse, National Institutes of Health.
References and recommended reading
Papers of particular interest, published within the annual period of review, have been highlighted as:
• of special interest
•• of outstanding interest
Additional references related to this topic can also be found in the Current World Literature section in this issue (p. 336).
1 Chin J, Bennett A. Heterosexual HIV transmission dynamics: implications for prevention and control. Int J STD AIDS 2007; 18:509–513.
2 Beyrer C. HIV epidemiology update and transmission factors: risks and risk contexts–16th International AIDS Conference Epidemiology Plenary. Clin Infect Dis 2007; 44:981–987.
3 Hamilton DT, Handcock M, Morris M. Degree distributions in sexual networks: a framework for evaluating evidence. Sex Transm Dis 2008; 35:30–40.
5 Pence BW, Reif S, Whetten K, et al
. Minorities, the poor, and survivors of abuse: HIV-infected patients in the US deep South. South Med J 2007; 100:1114–1122.
6 Hall HI, Song R, Rhodes P, et al
. Estimation of HIV Incidence in the United States. J Am Med Assoc 2008; 300:520–529.
7 Aitken CK, Higgs P, Bowden S. Differences in the social networks of ethnic Vietnamese and non-Vietnamese injecting drug users and their implications for blood-borne virus transmission. Epidemiol Infect 2008; 136:410–416.
8 Choi KH, Ning Z, Gregorich SE, Pan QC. The influence of social and sexual networks in the spread of HIV and syphilis among men who have sex with men in Shanghai, China. J Acquir Immune Defic Syndr 2007; 45:77–84.
9 Gyarmathy VA, Li N, Tobin KE, et al.
Injecting equipment sharing in Russian drug injecting dyads. AIDS Behav 2009. Epub ahead of print. DOI 10.1007/s10461-008-9518-6.
10 Peterson JL, Rothenberg R, Kraft JM, et al
. Perceived condom norms and HIV risks among social and sexual networks of young African American men who have sex with men. Health Educ Res 2009; 24:119–127.
11 Schneider JA, Saluja GS, Oruganti G, et al
. HIV infection dynamics in rural Andhra Pradesh south India: a sexual-network analysis exploratory study. AIDS Care 2007; 19:1171–1176.
12 Shaw SY, Shah L, Jolly AM, Wylie JL. Determinants of injection drug user (IDU) syringe sharing: the relationship between availability of syringes and risk network member characteristics in Winnipeg, Canada. Addiction 2007; 102:1626–1635.
13 Tobin KE, Latkin CA. An examination of social network characteristics of men who have sex with men who use drugs. Sex Transm Infect 2008; 84:420–424.
14 Burchell AN, Calzavara LM, Orekhovsky V, Ladnaya NN. Characterization of an emerging heterosexual HIV epidemic in Russia. Sex Transm Dis 2008; 35:807–813.
15 Fonseca MG, Bastos FI. Twenty-five years of the AIDS epidemic in Brazil: principal epidemiological findings, 1980–2005. Cad Saude Publica 2007; 23(Suppl 3):S333–S344.
16 Semaille C, Barin F, Cazein F, et al
. Monitoring the dynamics of the HIV epidemic using assays for recent infection and serotyping among new HIV diagnoses: experience after 2 years in France. J Infect Dis 2007; 196:377–383.
17 Tunthanathip P, Lolekha R, Liesbeth BJ, et al
. Indicators for sexual HIV transmission risk among Thais attending HIV care: the importance of positive prevention. Sex Transm Infect 2009; 85:36–41.
18 Surratt H. Sex work in the Caribbean Basin: patterns of substance use HIV risk among migrant sex workers in the US Virgin Islands. AIDS Care 2007; 19:1274–1282.
19• Richards JE, Risser JM, Padgett PM, et al
. Condom use among high-risk heterosexual women with concurrent sexual partnerships, Houston, Texas, USA. Int J STD AIDS 2008; 19:768–771.
20•• Chen L, Jha P, Stirling B, et al
. Sexual risk factors for HIV infection in early and advanced HIV epidemics in sub-Saharan Africa: systematic overview of 68 epidemiological studies. PLoS ONE 2007; 2:e1001. An exhaustive review of the association of sexual risk factors for HIV, comparing low- and high-prevalence areas as surrogates for early and mature epidemics. The data support the association of risk factors with current HIV, placing a different perspective on earlier studies of a lack of connection between risks and infection. The real extent of prior associations is hampered by the absence of several critical factors: frequency of sexual contact and time since HIV infection. These factors have taken on new importance in light of the emerging information about early infection, viral load, and infectivity.
21 Buve A, Lagarde E, Carael M, et al
. Interpreting sexual behaviour data: validity issues in the multicentre study on factors determining the differential spread of HIV in four African cities. AIDS 2001; 15(Suppl 4):S117–S126.
22 Carael M, Cleland J, Deheneffe JC, et al
. Sexual behaviour in developing countries: implications for HIV control. AIDS 1995; 9:1171–1175.
23 Lagarde E, Auvert B, Carael M, et al
. Concurrent sexual partnerships and HIV prevalence in five urban communities of sub-Saharan Africa. AIDS 2001; 15:877–884.
24 Auvert B, Buve A, Ferry B, et al
. Ecological and individual level analysis of risk factors for HIV infection in four urban populations in sub-Saharan Africa with different levels of HIV infection. AIDS 2001; 15(Suppl 4):S15–S30.
25 Brewer DD, Brody S, Drucker E, et al
. Mounting anomalies in the epidemiology of HIV in Africa: cry the beloved paradigm. Int J STD AIDS 2003; 14:144–147.
26 Hudson CP. Concurrent partnerships could cause AIDS epidemics. Int J STD AIDS 1993; 4:249–253.
27 Adimora AA, Schoenbach VJ, Doherty IA. HIV and African Americans in the southern United States: sexual networks and social context. Sex Transm Dis 2006; 33(7 Suppl):S39–S45.
28 Adimora AA, Schoenbach VJ, Martinson FE, et al
. Heterosexually transmitted HIV infection among African Americans in North Carolina. J Acquir Immune Defic Syndr 2006; 41:616–623.
29 Stratford D, Ellerbrock TV, Chamblee S. Social organization of sexual-economic networks and the persistence of HIV in a rural area in the USA. Cult Health Sex 2007; 9:121–135.
30 Reniers G. Marital strategies for regulating exposure to HIV. Demography 2008; 45:417–438.
31•• Hattori MK, Dodoo FN. Cohabitation, marriage, and 'sexual monogamy' in Nairobi's slums. Soc Sci Med 2007; 64:1067–1078.
32 Mah TL, Halperin DT. Concurrent sexual partnerships and the HIV epidemics in Africa: evidence to move forward. AIDS Behav 2008. Epub ahead of print. DOI 10.1007/s10461-008-9433-x.
33 Dworkin SL, Ehrhardt AA. Going beyond ‘ABC’ to include ‘GEM’: critical reflections on progress in the HIV/AIDS epidemic. Am J Public Health 2007; 97:13–18.
34•• Helleringer S, Kohler HP. Sexual network structure and the spread of HIV in Africa: evidence from Likoma Island, Malawi. AIDS 2007; 21:2323–2332.
35• Morris M, Goodreau S, Moody J. Sexual networks, concurrency, and STD/HIV. In: Holmes KK, Sparling P, Stamm W, Piot P, Wasserheit J, Corey L, et al.
, editors. Sexually transmitted diseases. 4th ed. McGraw-Hill; 2008. pp. 109–126. An excellent chapter that explores the network epidemiology of HIV and STDs. The authors demonstrate that complex networks that arise from low-degree, high-concurrency relationships.
36 Hollingsworth TD, Anderson RM, Fraser C. HIV-1 transmission, by stage of infection. J Infect Dis 2008; 198:687–693.
37 Powers KA, Poole C, Pettifor AE, Cohen MS. Rethinking the heterosexual infectivity of HIV-1: a systematic review and meta-analysis. Lancet Infect Dis 2008; 8:553–563.
38 Brewer DD, Potterat JJ, Muth SQ, et al
. Disconnects in presumed heterosexual HIV transmission in Malawi. AIDS 2008; 22:1377–1379.
39 Ford CL, Whetten KD, Hall SA, et al
. Black sexuality, social construction, and research targeting ‘The Down Low’ (‘The DL’). Ann Epidemiol 2007; 17:209–216.
40 Saleh LD, Operario D. Moving beyond ‘the Down Low’: a critical analysis of terminology guiding HIV prevention efforts for African American men who have secretive sex with men. Soc Sci Med 2008; 68:390–395.
41 O'Leary A, Jones KT. Bisexual men and heterosexual women: how big is the bridge? How can we know? Sex Transm Dis 2006; 33:594–595.
42 Satcher AJ, Durant T, Hu X, Dean HD. AIDS cases among women who reported sex with a bisexual man, 2000–2004: United States. Women Health 2007; 46:23–40.
43 Malebranche DJ. Bisexually active Black men in the United States and HIV: acknowledging more than the ‘Down Low’. Arch Sex Behav 2008; 37:810–816.
44 Lau JT, Wang M, Wong HN, et al
. Prevalence of bisexual behaviors among men who have sex with men (MSM) in China and associations between condom use in MSM and heterosexual behaviors. Sex Transm Dis 2008; 35:406–413.
45 Abdala N, Krasnoselskikh TV, Durante AJ, et al
. Sexually transmitted infections, sexual risk behaviors and the risk of heterosexual spread of HIV among and beyond IDUs in St. Petersburg, Russia. Eur Addict Res 2008; 14:19–25.
46 Stadler JJ, Delany S, Mntambo M. Sexual coercion and sexual desire: ambivalent meanings of heterosexual anal sex in Soweto, South Africa. AIDS Care 2007; 19:1189–1193.
47 Leichliter JS. Heterosexual anal sex: part of an expanding sexual repertoire? Sex Transm Dis 2008; 35:910–911.
48 Aidala AA, Lee G, Howard JM, et al
. HIV-positive men sexually active with women: sexual behaviors and sexual risks. J Urban Health 2006; 83:637–655.
49 Abbas UL, Anderson RM, Mellors JW. Potential impact of antiretroviral chemoprophylaxis on HIV-1 transmission in resource-limited settings. PLoS ONE 2007; 2:e875.
50 Deuchert E, Brody S. The role of healthcare in the spread of HIV/AIDS in Africa: evidence from Kenya. Int J STD AIDS 2006; 17:749–752.
51 Dunkle KL, Stephenson R, Karita E, et al
. New heterosexually transmitted HIV infections in married or cohabiting couples in urban Zambia and Rwanda: an analysis of survey and clinical data. Lancet 2008; 371:2183–2191.
52 Gomez-Gardenes J, Latora V, Moreno Y, Profumo E. Spreading of sexually transmitted diseases in heterosexual populations. Proc Natl Acad Sci U S A 2008; 105:1399–1404.
53 Gouws E, White PJ, Stover J, Brown T. Short term estimates of adult HIV incidence by mode of transmission: Kenya and Thailand as examples. Sex Transm Infect 2006; 82(Suppl 3):iii51–iii55.
54 Granich RM, Gilks CF, Dye C, et al
. Universal voluntary HIV testing with immediate antiretroviral therapy as a strategy for elimination of HIV transmission: a mathematical model. Lancet 2009; 373:48–57.
55 Hallett TB, Gregson S, Lewis JJ, et al
. Behaviour change in generalised HIV epidemics: impact of reducing cross-generational sex and delaying age at sexual debut. Sex Transm Infect 2007; 83(Suppl 1):i50–i54.
56 Hertog S. Heterosexual behavior patterns and the spread of HIV/AIDS: the interacting effects of rate of partner change and sexual mixing. Sex Transm Dis 2007; 34:820–828.
57 Merli MG, Hertog S, Wang B, Li J. Modelling the spread of HIV/AIDS in China: the role of sexual transmission. Popul Stud (Camb) 2006; 60:1–22.
58 Modjarrad K, Chamot E, Vermund SH. Impact of small reductions in plasma HIV RNA levels on the risk of heterosexual transmission and disease progression. AIDS 2008; 22:2179–2185.
59 Mukandavire Z, Garira W. Effects of public health educational campaigns and the role of sex workers on the spread of HIV/AIDS among heterosexuals. Theor Popul Biol 2007; 72:346–365.
60 Mukandavire Z, Garira W. Sex-structured HIV/AIDS model to analyse the effects of condom use with application to Zimbabwe. J Math Biol 2007; 54:669–699.
61 Rapatski BL, Suppe F, Yorke JA. Reconciling different infectivity estimates for HIV-1. J Acquir Immune Defic Syndr 2006; 43:253–256.
62 Sani A, Kroese DP, Pollett PK. Stochastic models for the spread of HIV in a mobile heterosexual population. Math Biosci 2007; 208:98–124.
63 Walker PT, Hallett TB, White PJ, Garnett GP. Interpreting declines in HIV prevalence: impact of spatial aggregation and migration on expected declines in prevalence. Sex Transm Infect 2008; 84(Suppl 2):ii42–ii48.
64 Guthrie BL, de BG, Farquhar C. HIV-1-discordant couples in sub-Saharan Africa: explanations and implications for high rates of discordancy. Curr HIV Res 2007; 5:416–429.
65 Deuchert E, Brody S. Plausible and implausible parameters for mathematical modeling of nominal heterosexual HIV transmission. Ann Epidemiol 2007; 17:237–244.
66 Koopman JS, Simon CP. Response to Rapatski BL, Suppe F, Yorke JA. HIV epidemics driven by late disease stage transmission. J Acquir Immune Defic Syndr 2006; 41:677.
67 Handcock MS, Hunter DR, Butts CT, et al
. Statnet: software tools for the representation, visualization, analysis and simulation of network data. J Stat Softw 2008; 24:1548–7660.
68 Morris M, Handcock MS, Hunter DR. Specification of exponential-family random graph models: terms and computational aspects. J Stat Softw 2008; 24:1548–7660.