JAIDS Journal of Acquired Immune Deficiency Syndromes:
Epidemiology and Social Science
Potential Impact of Antiretroviral Therapy on HIV-1 Transmission and AIDS Mortality in Resource-Limited Settings
Abbas, Ume L. MD*; Anderson, Roy M. PhD†; Mellors, John W. MD*
From the *Division of Infectious Diseases, School of Medicine, University of Pittsburgh, Pittsburgh, PA; and †Department of Infectious Disease Epidemiology, Imperial College, Faculty of Medicine, University of London, London, United Kingdom.
Received for publication May 10, 2005; accepted October 21, 2005.
R.M. Anderson acknowledges grant support from the Wellcome Trust. J.W. Mellors acknowledges support from the Bristol Myers Squibb Research Foundation and grants from the National Institute of Allergy and Infectious Diseases (U01AI38858) and from the National Cancer Institute (Science Applications International Corporation (SAIC) contract 20XS190A).
Reprints: Ume L. Abbas, Division of Infectious Diseases, University of Pittsburgh School of Medicine, Falk Medical Building, Suite 3-A, 3601 Fifth Avenue, Pittsburgh, PA 15213 (e-mail: firstname.lastname@example.org).
Objective: To estimate the potential impact of antiretroviral therapy on the heterosexual spread of HIV-1 infection and AIDS mortality in resource-limited settings.
Methods: A mathematic model of HIV-1 disease progression and transmission was used to assess epidemiologic outcomes under different scenarios of antiretroviral therapy, including implementation of World Health Organization guidelines.
Results: Implementing antiretroviral therapy at 5% HIV-1 prevalence and administering it to 100% of AIDS cases are predicted to decrease new HIV-1 infections and cumulative deaths from AIDS after 10 years by 11.2% (inter-quartile range [IQR]: 1.8%-21.4%) and 33.4% (IQR: 26%-42.8%), respectively. Later implementation of therapy at endemic equilibrium (40% prevalence) is predicted to be less effective, decreasing new HIV-1 infections and cumulative deaths from AIDS by 10.5% (IQR: 2.6%-19.3%) and 27.6% (IQR: 20.8%-36.8%), respectively. Therapy is predicted to benefit the infected individual and the uninfected community by decreasing transmission and AIDS deaths. The community benefit is greater than the individual benefit after 25 years of treatment and increases with the proportion of AIDS cases treated.
Conclusions: Antiretroviral therapy is predicted to have individual and public health benefits that increase with time and the proportion of infected persons treated. The impact of therapy is greater when introduced earlier in an epidemic, but the benefit can be lost by residual infectivity or disease progression on treatment and by sexual disinhibition of the general population.
The benefit of antiretroviral treatment of HIV-infected individuals is undisputed.1 Because the level of viremia correlates with the likelihood of sexual transmission of HIV-1,2,3 suppression of viremia by treatment is also likely to reduce HIV-1 spread.4 Although guidelines for treatment of HIV-1 infection in resource-limited settings have been issued,5 the approach that would yield maximum individual and public health benefit is not defined.
Several studies have explored the potential effect of antiretroviral therapy on HIV-1 epidemics using mathematic models.6-25 Most of these models, however, have focused on monotherapy and on epidemics in developed nations among men who have sex with men (MSM). Much less attention has been directed to the impact of antiretroviral therapy on heterosexual epidemics in resource-limited settings.19-25 We therefore developed a transmission model of the HIV-1 epidemic to estimate the individual and public health benefit of antiretroviral therapy in resource-limited settings.
We used a deterministic system of 20 differential equations to represent the natural history of HIV-1 infection, heterosexual transmission of HIV-1, and impact of antiretroviral therapy (Fig. 1). A staged progression model, based on CD4 cell decline,26 was used to make explicit the timing of treatment initiation. The model parameter set was chosen to mimic an epidemic in a sub-Saharan African nation reaching an endemic prevalence of 40% in the sexually active population 15 to 49 years of age. Parameter assignments were made from recent literature on HIV-1 disease progression,27,28 infectivity,29 sexual behavior,30-32 and response to antiretroviral therapy33 in resource-limited settings. Model parameters are shown in Table 1, and model equations and details are provided in the Appendix.
We analyzed the model numerically34 and by time-dependent uncertainty and sensitivity analyses.35-37 We determined the following epidemiologic outcomes: HIV-1 prevalence, HIV-1 incidence, cumulative new HIV-1 infections, and cumulative deaths from AIDS. To measure the impact of treatment, we made comparisons between the treated and untreated epidemics at each simulation time step and calculated the percent change in outcomes.
We simulated the effect of antiretroviral therapy using the World Health Organization (WHO) criteria5 for treatment initiation in resource-limited settings (CD4 count <200 cells/mm3) at 3 different phases of the epidemic, defined by HIV-1 prevalence levels of 5% (early), 20% (intermediate), and 40% (late/endemic equilibrium). At these epidemic phases, AIDS cases comprised 12%, 13%, and 18% of the total HIV-1-infected population, respectively. Treatment was administered to 100% of AIDS cases. We assumed that (1) the sexual activity level (number of sexual partners and total sexual acts per year) of AIDS cases was 70% of that for the general population29,38,39 and was not changed by treatment; (2) 60% of the individuals initiating treatment would maintain viral suppression for 3 years,33 corresponding to an average treatment failure rate of 17% per year (and a median time to failure of 4 years)40; and (3) disease progression was stopped and infectivity reduced to nil during virus suppression.
We also explored different levels of treatment coverage of AIDS cases and incremental coverage of individuals in successively less advanced disease stages. Analyses were performed using the Runge-Kutta 4 integration method with a fixed time step of one fiftieth of a year.41
Individual Versus Population Benefit
We determined the population-level benefit of antiretroviral therapy and contrasted this with benefit exclusive to infected individuals by assuming 2 scenarios. For scenario I, we assumed that the decrease in infectivity on treatment was 100%. For scenario II, we assumed that the decrease in infectivity on treatment was 0%. For each scenario, we varied the proportion of AIDS cases on treatment from 10% to 100%. Other assumptions were as described for the base-case scenario. We calculated the benefit of antiretroviral therapy as the percent change in cumulative AIDS deaths. The difference between the untreated epidemic and scenario II defined the individual benefit (direct effect attributable to improved patient survival), whereas the difference between scenario II and scenario I defined the population benefit (effect attributable to reduced transmission).
Uncertainty and Sensitivity Analyses
We performed uncertainty analyses to define the magnitude of variability in model output arising from uncertainty in model input parameter values. We performed sensitivity analyses to identify the relative contribution of specific input parameters to variability in model output.35-37
We performed time-dependent uncertainty analyses using Latin hypercube sampling (LHS)42 and 1000 simulation runs, as follows. First, we varied at random a set of 19 input parameters (see Table 1) to confirm that the results of our base-case scenario analysis were within the 95% prediction interval of the uncertainty analysis. Second, we varied only the input parameters that directly affected treatment outcome as follows: (1) treatment-mediated decreases in infectivity and disease progression were varied from 50% to 100%; (2) the treatment failure rate per year was varied from 12% to 23%, representing a median time to failure of 3 to 5 years;33,43-48 and (3) the sexual activity level of the individuals with AIDS on treatment ranged from 85% to 100% of that in the general population.49 We performed this uncertainty analysis for 2 scenarios: a conservative scenario with no increase in the sexual activity level in the general population and a sexual disinhibition scenario with sexual activity increasing from 0% to 20%. Third, we repeated the uncertainty analysis for the conservative scenario with treatment coverage of AIDS cases ranging from 10% to 100%.
After confirming monotonicity37 and rank transformation of data,50 we performed multivariate regression and derived the standardized rank regression coefficients.51
When antiretroviral therapy was implemented early in the epidemic (at 5% prevalence) and administered to 100% of AIDS cases, the predicted decrease in cumulative new HIV-1 infections was 25.8% after 5 years, 29.4% after 10 years, and 32% after 15 years (Fig. 2A). The predicted decrease in cumulative deaths from AIDS was 68% after 5 years, 58.4% after 10 years, and 56.1% after 15 years (see Fig. 2B). After 15 years, HIV-1 incidence had declined by 35.6% but prevalence had only declined by 4.4% because of longer survival of treated individuals.
Table 2 quantifies the predicted impact of antiretroviral therapy for South Africa and sub-Saharan Africa as a whole, where HIV-1 prevalence in adults is 18.5% and 7.4%, respectively. In South Africa, up to 1.2 million new HIV-1 infections and 1.3 million AIDS deaths could be averted over 10 years by treating 100% of AIDS cases. For sub-Saharan Africa, the projections are 6.9 million new HIV-1 infections and 9.3 million AIDS deaths averted.
A smaller effect of therapy is predicted with lower treatment coverage of AIDS cases. With 50% treatment coverage, the predicted decreases in cumulative new HIV-1 infections and AIDS deaths after 10 years were 15.6% and 32.7%, respectively. Treatment of at least 25% of AIDS cases was required to achieve approximately a 10% or greater decline in cumulative AIDS deaths at 10 years.
When all infected individuals were treated early in an epidemic (5% prevalence), the reduction in cumulative AIDS deaths was 67% after 10 years (data not shown). The residual AIDS mortality is attributable to treatment failure and subsequent disease progression. The decrease in cumulative new HIV-1 infections after 10 years rose to 78.1% with maximum treatment coverage. With 100% treatment coverage of individuals with CD4 counts <350 cells/mm3, there was a 45.1% reduction in HIV-1 incidence and a 41.2% reduction in cumulative new HIV-1 infections after 10 years. The corresponding figures after late (40% prevalence) treatment introduction were 28.2% and 36.5%, respectively. The disease stages for which treatment coverage was most influential in decreasing cumulative new HIV-1 infections were recent infection and chronic infection with a CD4 count >500 cells/mm3 (data not shown).
Population Versus Individual Benefit
Figure 3 shows the predicted individual and population benefit after 5 to 25 years of antiretroviral therapy for 10% to 100% of AIDS cases as the relative contribution to decline in cumulative AIDS deaths. A population benefit was observed at all times after treatment implementation, although the benefit was small initially. For example, 5 years after early implementation of therapy, the population benefit accounted for only approximately 1% of the decrease in AIDS deaths. After 25 years, however, the population benefit accounted for 70.6%, 55.4%, and 52.3% of the decrease in AIDS deaths after early, intermediate, and late implementation of therapy, respectively (see Fig. 3). Thus, the population benefit exceeded the individual benefit of therapy after 25 years.
Analysis of Uncertainty
Figures 4A and B show the uncertainty analysis of the effect of treating 100% of AIDS cases under the conservative scenario (no generalized sexual disinhibition). After 10 years, the decline in cumulative deaths from AIDS was always positive and had a median value of 33.4% for early (see Fig. 4B), 30.7% for intermediate, and 27.6% for late treatment implementation. The decline in cumulative new HIV-1 infections was also largely positive, although a few simulation runs predicted an increase after the first few years of treatment because of increased sexual activity and extended life of HIV-1-infected individuals. The median decline in HIV-1 infections after 10 years was 11.2% for early (see Fig. 4A), 10.7% for intermediate, and 10.5% for late treatment implementation, respectively.
Uncertainty analysis of the sexual disinhibition scenario showed a progressive increase in cumulative new HIV-1 infections and HIV-1 prevalence. Specifically, after 10 years, the median change in cumulative new HIV-1 infections was +12% for early (see Fig. 4C), +2.7% for intermediate, and −0.5% for late treatment implementation, respectively. By contrast, cumulative deaths from AIDS declined over time, because individual benefit of treatment was still realized (see Fig. 4D).
When the conservative scenario was assumed, the decline in cumulative new HIV-1 infections was most sensitive to the effect of treatment on infectivity, whereas the decline in cumulative deaths from AIDS was most sensitive to the effect of treatment on disease progression. Uncertainty in the effect of treatment on infectivity explained more than 90% of the variance in the predicted decline in cumulative HIV-1 infections, regardless of the time of treatment introduction or duration of treatment use. Approximately 96% of the variance in predicted cumulative deaths from AIDS after 5 years was explained by uncertainty in the effect of treatment on disease progression.
Generalized sexual disinhibition emerged as a key factor negatively influencing the effect of antiretroviral therapy on new HIV-1 infections. At 15 years, uncertainty in sexual disinhibition explained 49.7% and 24% of the variance in decline of cumulative infections for early and late treatment introduction, respectively.
Antiretroviral therapy unequivocally benefits HIV-infected individuals by reducing HIV-related morbidity and mortality.1 The public health benefits of therapy are uncertain, however, and optimal treatment strategies are debated.5,52,53 Using a simple but well-parameterized deterministic model of HIV-1 spread, we found that antiretroviral therapy benefits the infected individual by decreasing AIDS deaths and the uninfected community by producing a net reduction in transmission (population benefit). The population benefit became greater than the individual benefit for a major part of the simulated epidemic. Larger individual and population benefits were observed when treatment was introduced early into the epidemic, before peak infection rate and prevalence were reached. Our findings are in line with the more general rule for control of infectious disease epidemics-early intervention has a greater impact than later efforts.54 It is important to note, however, that late implementation of treatment was only modestly inferior to early treatment and considerably better than no treatment, because there was a persistent and sustained decrease in cumulative deaths from AIDS at early and late intervention times.
Simulations showed greater benefit with higher rates of treatment coverage of AIDS cases, at the individual and population levels, in terms of cumulative deaths from AIDS averted. Again, all levels of treatment coverage were superior to no treatment. The benefit in terms of reduction in cumulative new HIV-1 infections was modest, however, even when 100% of AIDS cases were treated according to WHO guidelines for resource-limited settings. This is likely because AIDS cases contribute a relatively small fraction of transmission compared with acute infection or other earlier stages of HIV-1 disease progression.
Our model predicted incremental reductions in cumulative new HIV-1 infections and deaths from AIDS when individuals at earlier stages were treated. In keeping with this, Auvert and colleagues55 predicted that over a 3-year period, the reduction in the annual risk of HIV-1 transmission using the WHO treatment strategy (CD4 count <200 cells/mm3) would be 12%, whereas that using the US Department of Health and Human Services (DHHS) 2001 through 2003 strategy (CD4 count <350 cells/mm3 or plasma HIV-1 RNA level >55,000 copies/mL)56 would be 72%. The median plasma HIV-1 RNA level in their population (South African township) was 55,750 copies/mL. For comparison, Gray et al,20 using a stochastic epidemic model, predicted that 100% treatment coverage by DHHS criteria (HIV-1 RNA level >55,000 copies/mL) in Rakai, Uganda would decrease HIV-1 incidence by 19%. Eligibility for treatment was based on serum HIV-1 RNA levels in Rakai, which has median values of 15,649 copies/mL in men and 9655 copies/mL in women.2 HIV-1 RNA levels in serum are known to be 30% to 80% lower than when measured in plasma.57,58 Thus, only 20% of the chronically infected individuals were eligible for treatment (HIV-1 RNA level >55,000 copies/mL) in the model by Gray et al.20 Furthermore, these authors assumed that treatment reduced viremia by only 27% to 44% and that cumulative 3-year treatment discontinuation was 55%. By comparison, our model predicted a 45.1% reduction in HIV-1 incidence and a 41.2% reduction in cumulative new HIV-1 infections after 10 years, with 100% treatment coverage of individuals with a CD4 count <350 cells/mm3 (DHHS 2004-2005 criteria53) and early (5% prevalence) treatment introduction. The corresponding figures after late (40% prevalence) treatment introduction were 28.2% and 36.5%, respectively. Thus, differences in the proportion of individuals eligible for treatment and in treatment efficacy are likely to account for the more favorable results in our model.
A decrease in the HIV-1 infection rate after widespread availability of potent antiretroviral therapy has been empirically observed. Porco and colleagues59 attributed the decreasing HIV-1 seroincidence in a cohort of MSM in San Francisco to a 60% decline in per partnership probability of HIV-1 transmission after widespread use of antiretroviral therapy. Six years after providing free antiretroviral therapy, the rate of HIV-1 transmission in Taiwan decreased by 53%.60 Similarly, heterosexual transmission of HIV-1 decreased by 80% in a Spanish cohort of 393 steady couples.4 These observations support reduced infectivity of individuals on antiretroviral therapy, as we have modeled. Additional studies are being conducted to define the impact of antiretroviral therapy on infectivity better.61
Our analyses identified persistent infectivity or disease progression on treatment and sexual disinhibition in the general population as key variables that could potentially undermine the beneficial effect of therapy. These findings are in general agreement with earlier models.12,17,20,23
Sub-Saharan Africa has 64% of the HIV-infected population of the world, totaling 23 million adults.62 Although a heterogeneous variety of epidemics are affecting this region,63 most of the Africans are not yet infected with HIV. Thus, effective treatment and prevention strategies are urgently needed. Our analyses indicate that roughly 3 to 7 million new HIV-1 infections and 5 to 9 million AIDS deaths could be averted in sub-Saharan Africa over the next 10 years if 100% of AIDS cases (approximately 4 million persons) are given treatment and sexual disinhibition is prevented. The corresponding estimates for South Africa alone are 0.4 to 1.2 million infections and 0.7 to 1.3 million AIDS deaths averted if 100% of AIDS cases (approximately 0.8 million persons) are treated. This enormous individual and public health benefit would require sustained access to antiretroviral therapy beyond the near-term goal of the WHO "3 by 5" program (3 million persons treated globally by 2005).64 In addition, the integration of treatment programs with voluntary counseling and testing services and prevention programs (eg, promotion of condom use and identification and treatment of sexually transmitted diseases) is key in controlling the spread of HIV-1.65
Others investigators have forecasted the effect of antiretroviral treatment rollout in resource-limited settings using simple mathematic models.21-25 Blower and colleagues23,24 used a model that included emergence of drug resistance but not the natural history of HIV-1 infection to predict that if 10% of the total HIV-infected population were treated (US global HIV/AIDS treatment strategy66), the decrease in HIV-1 incidence would be less than 5%24 after 10 years and that coverage of 10% to 50% would prevent 8.5% (range: 5.1%-31.5%) of cumulative new HIV-1 infections.23 Although these investigators assumed a 50% to 99% reduction in infectivity and a 1.5- to 3-fold increase in survival on treatment, they also assumed a 50% average increase in the sexual activity of the general population, which is much higher than the 10% increase we assumed for the sexual disinhibition scenario. Salomon et al25 used a more detailed model to predict the effect of treatment in sub-Saharan Africa.64 They simulated coverage of 50% of individuals with advanced disease by 2005 (WHO s 3 by 5 target), with extension to 80% by 2010 and beyond. Under different scenarios of sexual behavior and reduced transmission with treatment, their model predicted a −4% to +5% change in cumulative new adult HIV-1 infections and a 22% decline in cumulative adult deaths from AIDS through 2010.
The results of our base-case and conservative scenarios are more optimistic. This is because we simulated treatment according to WHO guidelines5 and our model incorporates recent data on HIV transmission29 and outcomes of treatment in sub-Saharan Africa.33 Furthermore, our model also stratified infected individuals according to disease progression,26-28,67 which made explicit the implementation and analysis of different treatment strategies. Despite differences in model structure and assumptions and scenarios of treatment use, our predictions confirm the general insights derived from earlier models, namely, that WHO s 3 by 5 program is likely to have a small public health benefit. Greater treatment coverage of the HIV-infected population is needed to achieve more substantial public health benefit.
The precise quantitative detail of our predictions will be affected by various refinements of the model structure. More complex stochastic models that incorporate, for example, sexual network structure, concurrent partnerships, age, and gender, together with complex treatment issues, can be easily formulated, and their properties can be analyzed using numeric methods. This is an important next step for the research reported in this article to increase the accuracy of model predictions. It is important to note, however, that the relatively simple structure used in the present analysis contains 55 parameters. With more complex models, parameter numbers spiral quickly as complexity increases, especially in connection with human sexual behavior. Because of limited knowledge, the problem of making parameter assignments is thus greatly exacerbated as complexity and realism are increased. Simple deterministic models can provide important and robust insights of a qualitative nature into the impact of control interventions for a wide variety of infectious agents.34 Our results must be interpreted with these caveats in mind, in terms of the relative merits of simplicity versus complexity.
U.L. Abbas is grateful to Bob Eberlein, Bard Ermentrout, and Michael McKay for helpful discussions and constructive suggestions and to Debbie Bradshaw and Leigh Johnson for providing the 2004 HIV/AIDS estimates for South Africa.
1. Palella FJ Jr, Delaney KM, Moorman AC, et al. Declining morbidity and mortality among patients with advanced human immunodeficiency virus infection. HIV Outpatient Study Investigators. N Engl J Med
. 1998;338: 853-860.
2. Quinn TC, Wawer MJ, Sewankambo N, et al. Viral load and heterosexual transmission of human immunodeficiency virus type 1. Rakai Project Study Group. N Engl J Med
3. Gray RH, Wawer MJ, Brookmeyer R, et al. Probability of HIV-1 transmission per coital act in monogamous, heterosexual, HIV-1-discordant couples in Rakai, Uganda. Lancet
4. Castilla J, Del Romero J, Hernando V, et al. Effectiveness of highly active antiretroviral therapy in reducing heterosexual transmission of HIV. J Acquir Immune Defic Syndr
6. Anderson RM, Gupta S, May RM. Potential of community-wide chemotherapy or immunotherapy to control the spread of HIV-1. Nature
7. Velasco-Hernandez JX, Hsieh YH. Modelling the effect of treatment and behavioral change in HIV transmission dynamics. J Math Biol
8. Hsieh YH, Velasco-Hernandez JX. Community treatment of HIV-1: initial stage and asymptotic dynamics. Biosystems
9. Garnett GP, Anderson RM. Antiviral therapy and the transmission dynamics of HIV-1. J Antimicrob Chemother
. 1996;37(Suppl B): 135-150.
10. Hsieh YH. A two-sex model for treatment of HIV/AIDS and behaviour change in a population of varying size. IMA J Math Appl Med Biol
11. Yang HM, Ferreira Junior WC. A population model applied to HIV transmission considering protection and treatment. IMA J Math Appl Med Biol
12. Blower SM, Gershengorn HB, Grant RM. A tale of two futures: HIV and antiretroviral therapy in San Francisco. Science
13. Hsu Schmitz S. Effects of treatment or/and vaccination on HIV transmission in homosexuals with genetic heterogeneity. Math Biosci
14. Hsieh YH, Sheu SP. The effect of density-dependent treatment and behavior change on the dynamics of HIV transmission. J Math Biol
15. Dangerfield BC, Fang Y, Roberts CA. Model-based scenarios for the epidemiology of HIV/AIDS: the consequences of highly active antiretroviral therapy. Syst Dyn Rev
16. Velasco-Hernandez JX, Gershengorn HB, Blower SM. Could widespread use of combination antiretroviral therapy eradicate HIV epidemics? Lancet Infect Dis
17. Law MG, Prestage G, Grulich A, et al. Modelling the effect of combination antiretroviral treatments on HIV incidence. AIDS
. 2001; 15:1287-1294.
18. Clements MS, Prestage G, Grulich A, et al. Modeling trends in HIV incidence among homosexual men in Australia 1995-2006. J Acquir Immune Defic Syndr
19. Garnett GP, Bartley L, Grassly NC, et al. Antiretroviral therapy to treat and prevent HIV/AIDS in resource-poor settings. Nat Med
. 2002;8: 651-654.
20. Gray RH, Li X, Wawer MJ, et al. Stochastic simulation of the impact of antiretroviral therapy and HIV vaccines on HIV transmission; Rakai, Uganda. AIDS
21. Over M, Heywood P, Gold J, et al. HIV/AIDS Treatment and Prevention in India: Modeling the Cost and Consequences
. Washington, DC: World Bank; 2004.
22. Dorrington R, Bradshaw D, Johnson L, et al. The demographic impact of HIV/AIDS in South Africa. National indicators for 2004. Centre for Actuarial Research, South African Medical Research Council and Actuarial Society of South Africa. 2004. Available at: http://www.mrc.ac.za/bod/demographic.pdf
. Accessed September 18, 2005.
23. Blower S, Ma L, Farmer P, et al. Predicting the impact of antiretrovirals in resource-poor settings: preventing HIV infections whilst controlling drug resistance. Curr Drug Targets Infect Disord
. 2003; 3: 345-353.
24. Blower S, Bodine E, Kahn J, et al. The antiretroviral rollout and drug-resistant HIV in Africa: insights from empirical data and theoretical models. AIDS
25. Salomon JA, Hogan DR, Stover J, et al. Integrating HIV prevention and treatment: from slogans to impact. PLoS Medicine
26. Longini IM Jr, Clark WS, Gardner LI, et al. The dynamics of CD4+
T-lymphocyte decline in HIV-infected individuals: a Markov modeling approach. J Acquir Immune Defic Syndr
27. Morgan D, Malamba SS, Orem J, et al. Survival by AIDS defining condition in rural Uganda. Sex Transm Infect
28. Morgan D, Mahe C, Mayanja B, et al. HIV-1 infection in rural Africa: is there a difference in median time to AIDS and survival compared with that in industrialized countries? AIDS
29. Wawer MJ, Gray RH, Sewankambo NK, et al. Rates of HIV-1 transmission per coital act, by stage of HIV-1 infection, in Rakai, Uganda. J Infect Dis
30. Cleland J, Ferry B, eds. Sexual Behaviour and AIDS in the Developing World
. New York: Taylor & Francis; 1995.
31. United States Agency for International Development and Macro International. Demographic and health surveys. Available at: http://www.measuredhs.com
. Accessed September 18, 2005.
32. Konings E, Blattner WA, Levin A, et al. Sexual behaviour survey in a rural area of northwest Tanzania. AIDS
33. Laurent C, Ngom Gueye NF, Ndour CT, et al. Long-term benefits of highly active antiretroviral therapy in Senegalese HIV-1-infected adults. J Acquir Immune Defic Syndr
34. Anderson RM, May RM. Infectious Diseases of Humans: Dynamics and Control
. Oxford: Oxford University Press; 1991.
35. Blower SM, Dowlatabadi H. Sensitivity and uncertainty analysis of complex-models of disease transmission-an HIV model, as an example. Int Stat Rev
36. Iman RL, Helton JC. An investigation of uncertainty and sensitivity analysis techniques for computer models. Risk Anal
37. Saltelli A, Chan K, Scott EM, eds. Sensitivity Analysis
. New York: John Wiley & Sons; 2000.
38. Deschamps M-M, Pape JW, Hafner A, et al. Heterosexual transmission of HIV in Haiti. Ann Intern Med
39. Moatti JP, Prudhomme J, Traore DC, et al. Access to antiretroviral treatment and sexual behaviours of HIV-infected patients aware of their serostatus in Cote d Ivoire. AIDS
. 2003;17(Suppl 3):S69-S77.
40. Miller DK, Homan SM. Determining transition probabilities: confusion and suggestions. Med Decis Making
41. Press WH, Flannery BP, Teukolsky SA, et al. Numerical Recipes in C: The Art of Scientific Computing
. 2nd ed. Cambridge: Cambridge University Press; 1992.
42. McKay MD, Beckman RJ, Conover WJ. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics
43. Casado JL, Perez-Elias MJ, Antela A, et al. Predictors of long-term response to protease inhibitor therapy in a cohort of HIV-infected patients. AIDS
44. Lucas GM, Chaisson RE, Moore RD. Highly active antiretroviral therapy in a large urban clinic: risk factors for virologic failure and adverse drug reactions. Ann Intern Med
45. Deeks SG, Hecht FM, Swanson M, et al. HIV RNA and CD4 cell count response to protease inhibitor therapy in an urban AIDS clinic: response to both initial and salvage therapy. AIDS
. 1999;13(Suppl): F35-F43.
46. Lucas GM, Chaisson RE, Moore RD. Survival in an urban HIV-1 clinic in the era of highly active antiretroviral therapy: a 5-year cohort study. J Acquir Immune Defic Syndr
47. Gallant JE, Staszewski S, Pozniak AL, et al. Efficacy and safety of tenofovir DF vs stavudine in combination therapy in antiretroviral-naive patients: a 3-year randomized trial. JAMA
48. Saag MS, Cahn P, Raffi F, et al. Efficacy and safety of emtricitabine vs stavudine in combination therapy in antiretroviral-naive patients: a randomized trial. JAMA
49. Crepaz N, Hart TA, Marks G. Highly active antiretroviral therapy and sexual risk behavior: a meta-analytic review. JAMA
50. Iman RL, Conover WJ. The use of the rank transform in regression. Technometrics
51. Hofer E. Sensitivity analysis in the context of uncertainty analysis for computationally intensive models. Comput Phys Commun
. 1999;117: 21-34.
52. Yeni PG, Hammer SM, Hirsch MS, et al. Treatment for adult HIV infection: 2004 recommendations of the International AIDS Society-USA Panel. JAMA
53. Panel on Clinical Practices for Treatment of HIV Infection. Guidelines for the use of antiretroviral agents in HIV-1-infected adults and adolescents. Department of Health and Human Services and Henry J. Kaiser Foundation. October 29, 2004. Available at: http://www.aidsinfo.nih.gov/guidelines/adult/archive/AA_102904.pdf
. Accessed September 18, 2005.
54. Rowley JT, Anderson RM, Ng TW. Reducing the spread of HIV infection in sub-Saharan Africa: some demographic and economic implications. AIDS
55. Auvert BMDP, Males S, Puren AMDP, et al. Can highly active antiretroviral therapy reduce the spread of HIV?: a study in a township of South Africa. J Acquir Immune Defic Syndr
56. Panel on Clinical Practices for Treatment of HIV Infection. Guidelines for the use of antiretroviral agents in HIV-1-infected adults and adolescents. Department of Health and Human Services and Henry J. Kaiser Foundation. February 5, 2001. Available at: http://www.aidsinfo.nih.gov/guidelines/adult/archive/AA_020501.pdf
. Accessed September 18, 2005.
57. Lew J, Reichelderfer P, Fowler M, et al. Determinations of levels of human immunodeficiency virus type 1 RNA in plasma: reassessment of parameters affecting assay outcome. TUBE Meeting Workshop Attendees. Technology Utilization for HIV-1 Blood Evaluation and Standardization in Pediatrics. J Clin Microbiol
. 1998;36(6): 1471-1479.
58. Fremont-Smith K. A study in rural Uganda of heterosexual transmission of human immunodeficiency virus. N Engl J Med
. 2000;343: 364. [author reply: 364-365].
59. Porco TC, Martin JN, Page-Shafer KA, et al. Decline in HIV infectivity following the introduction of highly active antiretroviral therapy. AIDS
60. Fang C-T, Hsu H-M, Twu S-J, et al. Decreased HIV transmission after a policy of providing free access to highly active antiretroviral therapy in Taiwan. J Infect Dis
61. Celum CL, Robinson NJ, Cohen MS. Potential effect of HIV type 1 antiretroviral and herpes simplex virus type 2 antiviral therapy on transmission and acquisition of HIV type 1 infection. J Infect Dis
. 2005;191 (Suppl 1):S107-S114.
63. Asamoah-Odei E, Garcia Calleja JM, Boerma JT. HIV prevalence and trends in sub-Saharan Africa: no decline and large subregional differences. Lancet
65. Abdool Karim SS, Abdool Karim Q, Baxter C. Antiretroviral therapy: challenges and options in South Africa. Lancet
67. Mellors JW, Munoz A, Giorgi JV, et al. Plasma viral load and CD4+ lymphocytes as prognostic markers of HIV-1 infection. Ann Intern Med
68. Fideli US, Allen SA, Musonda R, et al. Virologic and immunologicdeterminants of heterosexual transmission of human immunodeficiency virus type 1 in Africa. AIDS Res Hum Retroviruses
. 2001;17: 901-910.
69. Serwadda D, Gray RH, Wawer MJ, et al. The social dynamics of HIV transmission as reflected through discordant couples in rural Uganda. AIDS
70. Allen S, Tice J, Van de Perre P, et al. Effect of serotesting with counselling on condom use and seroconversion among HIV discordant couples in Africa. BMJ
71. May RM, Anderson RM. The transmission dynamics of human immunodeficiency virus (HIV). Philos Trans R Soc Lond B Biol Sci
72. Ho DD, Neumann AU, Perelson AS, et al. Rapid turnover of plasma virions and CD4 lymphocytes in HIV-1 infection. Nature
. 1995;373: 123-126.
73. Chene G, Sterne JA, May M, et al. Prognostic importance of initial response in HIV-1 infected patients starting potent antiretroviral therapy: analysis of prospective studies. Lancet
74. Oxenius A, Price DA, Gunthard HF, et al. Stimulation of HIV-specific cellular immunity by structured treatment interruption fails to enhance viral control in chronic HIV infection. Proc Natl Acad Sci USA
. 2002; 99:13747-13752.
75. Morens DM. Serological screening tests for antibody to human immunodeficiency virus-the search for perfection in an imperfect world. Clin Infect Dis. 1997;25:101-103.
76. Mylonakis E, Paliou M, Lally M, et al. Laboratory testing for infection with the human immunodeficiency virus: established and novel approaches. Am J Med
77. Hethcote HW, van Ark JW. Modeling HIV Transmission and AIDS in the United States, vol. 95. Berlin: Springer-Verlag; 1992.
To model the effect of antiretroviral therapy within an HIV-1 epidemic, we classified the population into 4 groups: susceptible (X), infected and treatment naive (I), infected and on treatment (T), and infected and off treatment (F). After acquisition of HIV-1, each individual passed through 6 successive stages of infection, followed by death from AIDS. The stages included (1) acute infection, (2) recent infection, (3) chronic infection with a CD4 count >500 cells/mm3, (4) chronic infection with a CD4 count of 350 to 499 cells/mm3, (5) chronic infection with a CD4 count of 200 to 349 cells/mm3, and (6) AIDS (CD4 count <200 cells/mm3). Each stage was characterized by a stage-transition rate (disease progression) and a probability of transmission per sex act (infectivity). The model allowed for initiation and termination of treatment by infected individuals. The treatment discontinuation rate represented a composite of all causes of treatment failure (virologic failure and discontinuation for drug toxicity). Retreatment was not modeled, because second-line regimens are often not available in resource-limited settings.
The mathematic model is described by the following set of differential equations:
Equation (Uncited)Image Tools
The recruitment of susceptible individuals to the sexually active class occurs at a constant net rate, μN0, where N0 is the population size of sexually active adults in the absence of infection. Individuals leave the model after an average duration of sexual activity, 1/μ. Subscript s refers to the stage of HIV-1 infection based on the natural history of HIV-1 infection and CD4 cell count. For the 3 infected groups I, T, and F, the rates of progression through different stages of HIV-1 disease are represented by δs, ηs, and σs, respectively, with δ6, η6, and σ6 being the respective death rates from AIDS. The per capita rates of treatment initiation and discontinuation are represented by α and κ, respectively. The rate of infection (incident HIV-1 cases per unit time) is the product of the number of susceptible individuals, X, and the risk of infection per susceptible individual, λ. Also known as the force of infection, λ is given by the following equation:34
Equation (Uncited)Image Tools
Here, c is the average rate of sexual partner change. The subscripts s and τ represent the stage of infection and treatment status of the infected individuals, respectively. Y is the sum of all infected individuals (I, T, and F), and N is the total population. The probability of transmission of HIV-1 infection per partnership from an infected individual in disease stage s and treatment status τ to a susceptible individual is βsτ. The probability, βsτ, depends on the number of sex acts (a) and the probability of transmission per sex act (γsτ) and is given by the expression:
Equation (Uncited)Image Tools
Women comprise half of the HIV-infected population worldwide and approximately 60% in Africa,62 where the efficiency of female-to-male transmission is similar to that for male-to-female transmission.2,3,68-70 We therefore assumed symmetry in sexual behavior and infectivity for both sexes.71 The stage-specific probabilities of transmission per heterosexual act used in our model were based on the rates of transmission per coital act estimated in a study of serodiscordant couples in Rakai, Uganda29 and the known heterogeneity in plasma HIV-1 RNA level among infected individuals.67
We assumed a dichotomous (and relatively pessimistic) treatment outcome: (1) treatment success with nil/reduced disease progression and transmission and (2) treatment failure with discontinuation of therapy and resumption of disease progression and transmission at pretreatment level. The rationale for this assumption is that antiretroviral therapy exerts its beneficial effects by suppressing HIV-1 replication,72 which delays disease progression73 and lowers infectivity,2,4,59,60 and that discontinuation of therapy leads to rebound of viremia to pretreatment levels,74 and to capture in a single composite rate (treatment failure at a rate κ) the different mechanisms of treatment failure over the entire simulation time period for individual patients. By assuming a median time to failure of 3 to 5 years with no retreatment and resumption of disease progression in, and transmission from, cases failing treatment, we tried to define a simple scenario for antiretroviral therapy. This obviated the need for assumptions regarding (1) the yet unknown long-term effects of antiretroviral therapy on survival and infectivity of infected individuals and (2) the rates of emergence of drug resistance, patient adherence in resource poor settings, temporary treatment discontinuations, and regimen changes.
The HIV-1 epidemic was initiated by allowing a single infected individual in the primary stage of HIV-1 infection at the beginning of simulation. Simulation was continued until a steady (endemic) stage was reached.
antiretroviral therapy; HIV-1 epidemic; mathematic model; transmission; developing countries; public health
© 2006 Lippincott Williams & Wilkins, Inc.
What does "Remember me" mean?
By checking this box, you'll stay logged in until you logout. You'll get easier access to your articles, collections,
media, and all your other content, even if you close your browser or shut down your
To protect your most sensitive data and activities (like changing your password),
we'll ask you to re-enter your password when you access these services.
What if I'm on a computer that I share with others?
If you're using a public computer or you share this computer with others, we recommend
that you uncheck the "Remember me" box.
Highlight selected keywords in the article text.
Data is temporarily unavailable. Please try again soon.