The distribution of clean syringes to injecting drug users (IDUs) is an effective intervention for reducing syringe sharing and HIV transmission.1-7 Maximizing syringe distribution is a universal principle of effective harm reduction among IDUs.8 International agencies have encouraged the "scaling up" of syringe distribution interventions as a cornerstone of HIV prevention in developing and transitional nations with large IDU populations.8,9 The critical question is what coverage is required to prevent or reverse HIV epidemics among IDUs? If coverage is defined as the number of syringes distributed per injector per injection,10 is it 1 syringe for every injection?11 Or is it the 60% coverage level recommended by United Nation Agencies?12 Unfortunately, the evidence in support of either coverage target is inconclusive, with few, if any, cities achieving the 60% target11,13-15 and other interventions reporting substantial decreases in HIV transmission with much lower coverage.16,17
Few studies have used mathematical modeling to consider the long-term effect of syringe distribution on HIV prevalence,18 and only 1 study has explicitly analyzed the effect of increasing syringe availability on HIV transmission.17 Kaplan's model assumed that IDUs use syringes randomly, with no personal ownership and, under increased syringe distribution, projected an associated reduction in HIV transmission among IDUs.19 However, evidence suggests that, given better access to sterile syringes, IDUs borrow and lend syringes less frequently20-23 and normally share just with close friends.24-26 Indeed, 1 of the main risk factors for sharing, not having a syringe,25,27 decreases with increased access to syringes.2,20,22
In this article, a mathematical model is developed to explore the relationship between an IDU population's endemic HIV prevalence and the coverage of syringe distribution. The model assumes that the frequency of syringe sharing is determined by the shortfall between the supply of syringes and the demand for injecting. The model is run using data from London (United Kingdom) and Svetlogorsk (Belarus).
A mathematical model was developed to estimate the impact of different intervention outcomes on an IDU population's HIV prevalence. To simplify the analysis, the model only simulates HIV transmission through syringe sharing. The coverage of syringe distribution is defined as the average number of syringes obtained by each IDU per year, divided by their average number of injections.
The model considers an IDU population that mixes randomly to form syringe-sharing partnerships. Each IDU receptively shares syringes with m IDUs per unit time with a frequency of n injections per IDU. The model assumes that infected IDUs inject for a duration D, and clean a proportion c of all used syringes, with efficacy e, before reuse. For a susceptible population, the number of IDUs infected by 1 infected IDU is given by the basic reproductive rate R028:
where β is the HIV transmission probability per syringe-sharing act. When the epidemic reaches an endemic state, the HIV prevalence is given by the formula p = 1 − 1/R0.28
Adjustment for IDUs that Do Not Share Syringes or Have Stable Sharing Networks
If only a proportion (s) of IDUs share syringes, then the endemic IDU HIV prevalence will be reduced by a factor s. In addition, if syringe sharing occurs in small stable networks, the transmission of HIV may be restricted to small segments of the IDU population.29 Indeed, if the IDU HIV prevalence was p0 when IDUs started sharing in isolated stable groups of size η, then there is a probability [1− (1 − p0)η] that a particular sharing group will contain at least 1 infected IDU if they were randomly distributed. If the current HIV prevalence was low at this point in time and η is small, then the endemic HIV prevalence p will be reduced to:
In reality, it is unlikely that infected IDUs will be randomly distributed but will be grouped together in specific sharing networks. Therefore, this assumption is likely to overestimate the proportion of IDUs connected to infected IDUs. To overcome this limitation and because of limited data on the size of sharing groups, the parameter η was varied to fit the model to observed HIV prevalence data.
Incorporating Syringe Distribution Coverage
The basic reproductive rate R0 in Eq. (2) can be approximated by Dmnβ (1 − ec) if n < 20 sharing acts per month. This expression includes the product mn, the number of receptive syringe-sharing events per IDU per unit time. If it is assumed that IDUs normally share syringes when they do not have any,20,22,25 and if improved syringe availability decreases sharing,2,20,22,30,31 then the frequency of sharing can be estimated by the shortfall between the frequency with which an IDU injects (T per unit time) and the product of the number of syringes distributed to the IDU (ε new syringes per unit time) and the number of times each syringe is used by that IDU (δ times before disposal). Note that we assume that injectors' personal reuse of their own syringe is safe. When this expression is substituted into Eq. (2), the following expressions for the required syringe distribution coverage (ε/T) or syringe-sharing rate (mn) needed to obtain a specific endemic HIV prevalence p are obtained:
where S = s(1 − (1 − p0)η).
Two settings, with contrasting HIV epidemics, are considered in this analysis: London (United Kingdom) and Svetlogorsk (Belarus). These populations were selected because of data availability32-36 and because the majority of syringes used by IDUs came from syringe distribution programs. In addition, coinciding with 1 of the main model assumptions, IDUs in London report having insufficient syringes as the main reason for sharing20,24,26 and that they keep and reuse their syringes to reduce syringe sharing.24 The model parameter values in Table 1 are based on data from these settings.32-39 The IDU population in London has lower levels of reported risk behavior, with half as many IDUs reporting syringe sharing and most reporting that they share with a small number of close friends.40
Table 1 also gives estimates for the HIV transmission probability per syringe-sharing event and the efficacy of syringe cleaning. A sensitivity analysis was undertaken to account for the uncertainty in these parameters.
HIV Prevalence and Syringe Sharing
Figure 1 shows the relationship between endemic HIV prevalence and the average syringe-sharing rate in a homogeneous IDU population where everyone shares syringes and there is no syringe cleaning. The figure suggests that, in such a scenario, the monthly sharing rate has to be less than 4 to reduce the endemic HIV prevalence to less than 10%, and it will be greater than 40% if each IDU shares more than 6 times a month.
Relationship Between HIV Prevalence and Syringe Distribution Coverage
Figure 2 shows a steplike relationship between syringe distribution coverage and the endemic HIV prevalence in each setting. That is, assuming that other factors remain equal, increasing syringe distribution coverage from a low level will have little effect on HIV prevalence until a threshold coverage is reached (15%-20% for Svetlogorsk and 20% for London), after which substantial decreases in HIV prevalence occur. The bold vertical line in each figure shows the current estimated coverage in each setting. The figure suggests what coverage may be required to reduce the IDU HIV prevalence caused by syringe sharing to negligible levels. For example, to reduce the IDU HIV prevalence in London to less than 1%, assuming that syringe reuse remains unchanged, the coverage of syringe distribution has to increase to 27%.
However, increased syringe availability may also lead to a decrease in syringe reuse,41,42 reducing the HIV impact of an increase in syringe distribution. For example, if in Svetlogorsk the frequency of syringe reuse decreases from 3.3 to 2.5 when coverage is increased by 50%, then the endemic HIV prevalence will decrease to 47% instead of reducing to negligible levels if syringe reuse had not changed.
Interestingly, Figure 2 suggests that, given equivalent syringe reuse, the coverage requirements for reducing the HIV prevalence to negligible levels are approximately equal for London and Svetlogorsk. This is due to the expression, 1/(β(1 − ec)DT), in Eq. (3), being small (<0.1), so the coverage required to reduce HIV prevalence to negligible levels is approximately the inverse of the number of times a syringe is used before disposal (1/δ). This corresponds to the coverage being high enough, at the current frequency of syringe reuse, to supply enough syringes to reduce syringe sharing to a sufficiently low level of approximately 2 sharing events per month.
Lastly, despite the similar coverage of syringe distribution in London and Svetlogorsk, there is a large disparity between their current IDU HIV prevalence (Fig. 2). This difference is primarily due to fewer IDUs sharing in London and that they share in small stable groups of 1 to 2 IDUs.24,40
HIV Prevalence and Other Factors
In Figure 3, the impact of other factors on the endemic HIV prevalence is examined. Data from Svetlogorsk are used for Figures 3A to C (the same relationships hold for London), and data from London are used for Figure 3D because the size of sharing networks only impacts on the endemic HIV prevalence in low-HIV prevalence settings.
The duration D that an infected IDU injects for incorporates cessation from injecting and mortality due to all causes. Figure 3A suggests that the impact of increasing the cessation rate is greater when coverage is higher, with the greatest impact achieved when coverage is close to the threshold level. Decreasing the frequency of injection should increase an intervention's effective coverage for the same quantity of syringes distributed (Fig. 3B) and so should also have little impact on the endemic HIV prevalence until a threshold is reached. As for the cessation rate, the impact of decreasing the injection frequency is greater for higher coverage. Figure 3C combines the consistency and efficacy of syringe cleaning into an overall measure of syringe-cleaning effectiveness. The figure suggests that syringe cleaning has significant impact if the syringe coverage is near the threshold (≥25%) or if the overall effectiveness of syringe cleaning is high (>50%). Figure 3D shows that the endemic HIV prevalence in London is sensitive to increases in the size of sharing networks, with very small sharing networks being required to maintain the HIV prevalence at less than 5%, even at high syringe coverage.
Uncertainty in the HIV transmission probability does not substantially affect the model's projections. For example, the required coverage to reduce the HIV prevalence to a negligible level in Svetlogorsk increases from 28% to 29% if the HIV transmission probability is 0.0141, instead of 0.0076, and reduces to 24% if the HIV transmission probability is 0.0029.
The endemic HIV prevalence is also fairly insensitive to changes in the overall effectiveness of syringe cleaning (Fig. 3C). Therefore, despite large uncertainty around the efficacy of syringe cleaning with water (37%-67%),43,44 the actual uncertainty in the overall effectiveness of syringe cleaning is smaller (11%-20% for Svetlogorsk), and Figure 3C shows that this has little impact on our predictions.
We developed a model to explore the relationship between syringe distribution coverage and the endemic HIV prevalence of an IDU population, while incorporating other factors important in the transmission and prevention of HIV. The model assumed that syringe sharing mainly occurs when IDUs have insufficient syringes and that the sharing frequency is determined by the shortfall between the demand and supply for syringes, assuming that each syringe is used a number of times by that IDU. In light of these assumptions, the model suggests that there are critical coverage thresholds for syringe distribution, which have to be reached to substantially reduce the IDU HIV prevalence. However, the results do not support the existence of a universal coverage target, although their usefulness for gauging intervention quality should not be underestimated.
The existence of these coverage thresholds follows on from our predictions that syringe sharing needs to be low (<4 times per IDU per month) before any substantial reduction in HIV prevalence can occur. This is due to the high HIV transmission probability per syringe-sharing event causing the HIV prevalence to be very sensitive to small increases in the monthly syringe-sharing rate and so also the syringe distribution coverage. In contrast, if the syringe-sharing rate increases much more than 4 times per month, then most IDUs connected to an infected IDU become infected, and so any further increase in syringe sharing or decrease in syringe distribution has little effect.
Model Findings and Interpretation
The model suggests that the coverage thresholds mainly depend on the level of "safe" use and reuse of an IDU's own syringes, with the coverage required to reduce HIV prevalence to negligible levels being approximately the inverse of the average frequency with which IDUs safely reuse their own syringes before disposal. Our interpretation of this finding is that syringe reuse can be protective. This finding concurs with advice given by syringe exchanges which recommends that IDUs reuse their own syringe if they run out of clean syringes. Policies or practices that discourage the safe reuse and/or carriage of syringes could reduce the impact of syringe distribution interventions.45-47 However, if syringe reuse is to be promoted, it is important to emphasize that using someone else's syringe is not "safe," and the reuse of one's own syringe can increase the risk of bacterial/wound infections.8,48 Furthermore, some epidemiological studies find an association between HIV and syringe reuse,17,49 probably because syringe reuse can be unsafe or coincide with a tendency to inject more frequently.34,41 These factors need to be considered when devising strategies to promote safer injection by encouraging IDUs to safely reuse their syringes in preference to sharing.
The model suggests that, in general, each IDU needs to share syringes in small stable groups (2-3 people) to limit the spread of HIV, as has occurred in London. Previous studies have also emphasized the importance of network structures50 and specifically small sharing networks in reducing the transmission of HIV among IDUs in New York.50 However, the high HCV incidence in London51 and signs of increasing HIV prevalence 32 imply that syringe sharing may not be as restricted as we thought. If so, there is no room for complacency because, at the current coverage and sharing rate, HIV could easily spread through London's IDU population.
Decreasing the frequency that IDUs inject is also important and should be a focus for health promotion. Equally, patterns of drug taking which increase injecting frequency, such as the rise in cocaine or crack-cocaine injecting,52 may increase HIV transmission and so should be a special target for syringe distribution interventions. Lastly, the results suggest that other factors, such as the rate of cessation of injecting and syringe cleaning, can play an important role in reducing HIV prevalence but only once the syringe distribution coverage is near the critical threshold.
Model Comparisons and Limitations
Although many studies have shown that syringe exchange interventions can decrease syringe sharing or HIV transmission,2 only 1 study from New York has shown that successive increases in syringe availability can lead to parallel decreases in HIV transmission.53 However, although the study also reported that initial increases in syringe distribution have less effect on HIV prevalence, no equivalent trends in syringe sharing or reuse and the size of sharing groups were reported, so limiting direct comparisons with our model. There is an urgent need for further quantitative and qualitative epidemiological studies on the relationship between syringe availability, injecting behavior, and HIV transmission.
Our model projections of the level of syringe sharing required to reduce the HIV prevalence to a low level corroborate with those produced by Murray et al.18 In addition, although not presented here, these results also agree with projections made using a more complex dynamic model, IDU 2.4.54,55 IDU 2.4 also predicted that it would take 10 to 15 years to reach the new endemic HIV prevalence after a reduction in syringe sharing. This highlights the importance of prolonged intervention activity for attaining substantial decreases in IDU HIV prevalence, as highlighted by the long-term impact of harm reduction activities in New York and London.16,53,56,57
Our findings offer a different picture to Kaplan's analysis, which strongly suggested that the impact of the New Haven syringe exchange was due to a reduction in the duration each syringe is used.17 In Kaplan's analysis, IDUs had no ownership of syringes, and so all syringe reuse was potentially unsafe because they could have been used by other IDUs. This assumption agreed with the observation in New Haven but does not reflect other IDU populations, where there is evidence that IDUs retain their syringes to reuse in preference to sharing,24 reduce and restrict syringe sharing when they have access to syringes,20-26 and only use someone else's syringe when they have difficulty obtaining syringes.20,27 Our model reflects these observations and will be relevant in settings where, broadly speaking, these patterns of behavior apply.
The analysis has several limitations and made a number of simplifying assumptions. First, the model assumed that IDUs only share syringes when they do not have their own syringes, although there is evidence that sharing occurs for other social reasons.40,58 Second, the model contains no heterogeneity in IDU risk behavior, and IDUs can only infect their direct sharing partner at each sharing event. Limited sensitivity analysis around these aspects of the model structure (not presented here) suggested that the model's coverage thresholds may be minimum estimates. Third, the model did not include sexual HIV transmission, which sometimes plays a large role in IDU epidemics.59
Despite the model's simplicity, our findings illustrate the importance of discouraging syringe sharing through increased syringe distribution, encouraging the safe reuse of an IDU's own syringes when clean syringes are not available, and supporting interventions that reduce the frequency of injection. In addition, in low HIV prevalence settings, special emphasis should be given to maintaining and encouraging IDUs to inject in small stable groups. Our analysis did not find any evidence for a universal coverage target, but did suggest the existence of coverage thresholds that are related to the frequency of (safe) syringe reuse. In practice, the feasibility of attaining these coverage levels is likely to depend on environmental factors, and optimum coverage targets will therefore be situation dependent.
1. Preventing HIV transmission-the role of sterile needles and bleach. In: Norman J, Vlahov D, Moses LE eds. Institute of Medicine
. Washington, DC: National Academy Press; 1995.
2. Gibson DR, Flynn N, Perales D. Effectiveness of syringe exchange programs in reducing HIV risk behavior and HIV seroconversion among injecting drug users. AIDS
3. Des Jarlais DC. Structural interventions to reduce HIV transmission among injecting drug users. AIDS
. 2000;14(suppl 1):S41-S46.
4. Hurley SF, Jolley DJ, Kaldor JM. Effectiveness of needle-exchange programmes for prevention of HIV infection. Lancet
5. Lurie P, Drucker E. An opportunity lost: HIV infections associated with lack of a national needle-exchange programme in the USA. Lancet
6. MacDonald M, Law MG, Kaldor JM, et al. Effectiveness of needle and syringe programmes for preventing HIV transmission. Int J Drug Policy
7. Taussig JA, Weinstein B, Burris S, et al. Syringe laws and pharmacy regulations are structural constraints on HIV prevention in the US. AIDS
. 2000;14(suppl 1):S47-S51.
8. Strathdee SA, van Ameijden EJ, Mesquita F, et al. Can HIV epidemics among injection drug users be prevented? AIDS
. 1998;12(suppl A):S71-S79.
9. United Nations. General assembly declaration of commitment on HIV/AIDS. 2001. Available at: http://www.un.org/ga/aids/docs/aress262.pdf
. Accessed June 2005.
10. Jones TS, Vlahov D. Use of sterile syringes and aseptic drug preparation are important components of HIV prevention among injection drug users. J Acquir Immune Defic Syndr
. 1998;18(suppl 1):S1-S5.
11. Strathdee S, Vlahov D. The effectiveness of needle exchange programs: a review of the science and policy. AID Science
12. WHO. Task force for the urgent response to the epidemics of sexually transmitted infections in eastern Europe and central Asia. 2000. WHO regional office for Europe.
13. Monterroso ER, Hamburger ME, Vlahov D, et al. Prevention of HIV infection in street-recruited injection drug users. The Collaborative Injection Drug User Study (CIDUS). J Acquir Immune Defic Syndr
14. Parsons J, Hickman M, Turnbull PJ, et al. Over a decade of syringe exchange: results from 1997 UK survey. Addiction
15. Anonymous. Update: syringe exchange programs-United States, 1998. MMWR Morb Mortal Wkly Rep
16. Des Jarlais DC, Marmor M, Friedmann P, et al. HIV incidence among injection drug users in New York City, 1992-1997: evidence for a declining epidemic. Am J Public Health
17. Kaplan EH, Heimer R. A circulation theory of needle exchange. AIDS
. 1994;8(5):567-574. [editorial].
18. Murray JM, Law MG, Gao Z, et al. The impact of behavioural changes on the prevalence of HIV and hepatitis C among injecting drug users. Int J Epidemiol
19. Kaplan E, O'Keefe E. Let the needles do the talking! Evaluating the New Haven needle exchange. Interfaces
20. Donoghoe MC, Stimson GV, Dolan K, et al. Changes in HIV risk behaviour in clients of syringe-exchange schemes in England and Scotland. AIDS
21. Des Jarlais C, Perlis T, Friedman SR, et al. Behavioral risk reduction in a declining HIV epidemic: injection drug users in New York City, 1990-1997. Am J Public Health
22. Hartgers C, Buning EC, van Santen GW, et al. The impact of the needle and syringe-exchange programme in Amsterdam on injecting risk behaviour. AIDS
23. Bluthenthal RN, Kral AH, Gee L, et al. The effect of syringe exchange use on high-risk injection drug users: a cohort study. AIDS
24. Rhodes T, Davis M, Judd A. Hepatitis C and its risk management among drug injectors in London: renewing harm reduction in the context of uncertainty. Addiction
25. McKeganey N, Abel M, Taylor A, et al. The preparedness to share injecting equipment: an analysis using vignettes. Addiction
26. Donoghoe M, Dolan K, Stimson G. Life-style factors and social circumstances of syringe sharing in injecting drug users. Br J Addict
27. Wood E, Tyndall MW, Spittal PM, et al. Factors associated with persistent high-risk syringe sharing in the presence of an established needle exchange programme. AIDS
28. Anderson R, May RM. The basic model: dynamics. In: Infectious Diseases of Humans: Dynamics and Control
. Oxford, UK: Oxford University Press, 1992:122-143.
29. Friedman SR, Kottiri BJ, Neaigus A, et al. Network-related mechanisms may help explain long-term HIV-1 seroprevalence levels that remain high but do not approach population-group saturation. Am J Epidemiol
30. Des Jarlais C, Friedman S, Sotheran JL, et al. Continuity and change with an HIV epidemic. JAMA
31. Schoenbaum EE, Hartel DM, Gourevitch MN. Needle exchange use among a cohort of injecting drug users. AIDS
32. Hope VD, Judd A, Hickman M, et al. HIV prevalence among injecting drug users in England and Wales 1990 to 2000: evidence for increased transmission in recent years. AIDS
33. Judd A, Hickman M, Jones S, et al. Incidence of hepatitis C virus among new injecting drug users in London-prospective cohort study. Br Med J
34. Judd A, Hutchinson S, Wadd S, et al. Prevalence of, and risk factors for, hepatitis C virus infection among recent initiates to injecting in London and Glasgow-cross sectional analysis. J Viral Hepat
35. Vickerman P, Watts CH. The impact of an HIV prevention intervention for injecting drug users in Svetlogorsk, Belarus: model predictions. Int J Drug Policy
36. Hickman M, Higgins V, Hope VD, et al. Injecting drug use in Brighton, Liverpool, and London: best estimates of prevalence and coverage
of public health indicators. J Epidemiol Community Health
37. Hickman M, Higgins V, Hope V, et al. Injecting drug use in Brighton, Liverpool, and London: best estimates of prevalence and coverage
of public health indicators. J Epidemiol Community Health
38. Prins M, Hernandez Aguado IH, Brettle RP, et al. Pre-AIDS mortality from natural causes associated with HIV disease progression: evidence from the European Seroconverter Study among injecting drug users. AIDS
39. Pezzotti P, Galai N, Vlahov D, et al. Direct comparison of time to AIDS and infectious disease death between HIV seroconverter injection drug users in Italy and the United States: results from the ALIVE and ISS studies. AIDS link to intravenous experiences. Italian Seroconversion Study. J Acquir Immune Defic Syndr Hum Retrovirol
40. Hunter GM, Donoghoe MC, Stimson GV, et al. Changes in the injecting risk behaviour of injecting drug users in London, 1990-1993. AIDS
41. Frischer M, Bloor M, Green S, et al. Reduction in needle sharing among community wide samples of injecting drug users. Int J STD AIDS
42. Bluthenthal RN, Malik MR, Grau LE, et al. Sterile syringe access conditions and variations in HIV risk among drug injectors in three cities. Addiction
43. Abdala N, Crowe M, Tolstov Y, et al. Survival of human immunodeficiency virus type 1 after rinsing injection syringes with different cleaning solutions. Subst Use Misuse
44. Abdala N, Gleghorn A, Carney JM, et al. Can HIV-1-contaminated syringes be disinfected? Implications for transmission among injection drug users. J Acquir Immune Defic Syndr
45. Blumenthal RN, Kral A, Lorvick J, et al. Impact of law enforcement on syringe exchange programs. Med Anthropol
46. Burris S. Law as a structural factor in the spread of communicable disease. Houston Law Review
47. Rhodes T, Mikhailova L, Sarang A, et al. Situational factors influencing drug injecting, risk reduction and syringe exchange in Togliatti City, Russian Federation: a qualitative study of micro risk environment. Soc Sci Med
48. Hope VD, Goldberg D, de Souza L, et al. Shooting up infections among injecting drug users in the United Kingdom, 2002. An update: December 2003. Health Protection Agency, SCIEH, NPHSW, CDSCNI, CRDHB, UASSG 2003.
49. Heimer R, Khoshnood K, Bigg D, et al. Syringe use and reuse: effects of syringe exchange programs in four cities. J Acquir Immune Defic Syndr
. 1998;18(suppl 1):S37-S44.
50. Des Jarlais DC, Perlis T, Arasteh K, et al. "Informed altruism" and "partner restriction" in the reduction of HIV infection in injecting drug users entering detoxification treatment in New York City, 1990-2001. J Acquir Immune Defic Syndr
51. Judd A, Hickman M, Jones S, et al. Incidence of hepatitis C virus and HIV among new injecting drug users in London: prospective cohort study. BMJ
52. Hope VD, Hickman M, and Tilling K. Capturing crack-cocaine use: estimating the prevalence of crack-cocaine use in London using capture-recapture with covariates. Addiction
53. Des Jarlais DC, Perlis T, Arasteh K, et al. HIV incidence among injection drug users in New York City, 1990 to 2002: use of serologic test algorithm to assess expansion of HIV prevention services. Am J Public Health
54. Kumaranayake L, Vickerman P, Walker D, et al. The cost-effectiveness of HIV preventive measures among injecting drug users in Svetlogorsk, Belarus. Addiction
55. Vickerman P, Kumaranayake L, Balakireva O, Guinness L, et al. The cost-effectiveness of expanding harm reduction activities for injecting drug users in Odessa, Ukraine. Sex Transm Dis
. 2006. In press.
56. Des Jarlais DC, Perlis T, Friedman SR, et al. Declining seroprevalence in a very large HIV epidemic: injecting drug users in New York City, 1991 to 1996. Am J Public Health
57. Stimson GV, Hunter GM, Donoghoe MC, et al. HIV-1 prevalence in community-wide samples of injecting drug users in London, 1990-1993. AIDS
58. Zule WA. Risk and reciprocity: HIV and the injection drug user. J Psychoactive Drugs
59. Strathdee S. Sexual HIV transmission in the context of injection drug use: implications for interventions. Int J Drug Policy
60. Kaplan EH, Heimer R. A model-based estimate of HIV infectivity via needle sharing. J Acquir Immune Defic Syndr
61. Hudgens MG, Longini IM Jr, Vanichseni S, et al. Subtype-specific transmission probabilities for human immunodeficiency virus among injecting drug users in Bangkok, Thailand. Am J Epidemiol