Table 1.

Summary of existing ART models, by date of publication.

Study	Model structure	Setting	Assumptions	Key outcomes (pertaining to ART) and comments
Zaric et al 1998 [74]	Dynamic, difference equations	MSM and IDU, US cities/regions	Infection stratified into HIV and AIDS stages. Allows acquired and transmitted drug resistance. Rate of resistance evolution: 95% per year for non-adherents, 5% per year for adherents. Increased life expectancy due to ART: 1.5-fold for adherents, 1.2-fold for non-adherents, 1.2-fold for adherents infected with drug resistant HIV.	The most important factor affecting emergence of drug resistance is adherence to ART.
Aalen et al 1999 [17]	Linear	MSM, England and Wales, 1990s	Markov multi stage model (stage based on CD4 count). Explicit diagnosis and treatment. Estimated HIV incidence in the MSM population, which was fixed at 1200 cases/year for all but one scenario, where incidence was halved from 1995 onwards.	Decrease in AIDS incidence due to ART. Number receiving treatment will increase 50–100% by 2001 compared to pre-1996.
Wood et al 2000 [75]	Linear model	IDU, Vancouver, Canada 1999–2006	Treatment uptake: 80% (scenario 1), 20% (scenario 2). Median increase in life expectancy due to ART: 7 years. No drug resistance or stratification by infection stage or sexual activity class. Prevalence estimates used in DemProj, part of the Spectrum suite of models (information at http://www.futuresgroup.com/software/Goals/goals.pdf) (3 scenarios: prevalence reduced from 7% in 1999 to 5% in 2006, prevalence remains at 7%, prevalence increases to 9% in 2006.	Calculated life expectancy and AIDS deaths 1999–2006 for each scenario. Concluded that low level ART use is not sufficient to increase life expectancy in this population and called for expansion in ART coverage.
Wood et al 2000 [16]	Linear health economic model (based on previous model [75])	South Africa 2000–2005	Median increase in life expectancy due to ART: 6 years (range: 5–7). Treatment uptake: 25% of infected adults. Spectrum AIDS Impact model was used to adjust the population projections for current and projected HIV-associated mortality.	Providing ART for 25% of the infected population could prevent a 3.1 year decline in life expectancy and more than 430,000 incident cases, but with disproportionate expenditure ($19 billion at 2000 prices) compared to preventing mother-to-child transmission.
Blower et al 2000 [5]	Dynamic, deterministic	MSM, San Francisco, US, up to 2010	Changes in sexual behaviour: no change to doubling of risk. Treatment coverage rates: 50–90% uptake per year. ART reduces infectivity 2- to 100-fold. Acquired drug resistance: 10–60% per year (infections can revert back to ART-sensitive). Resistance is transmitted, but is less fit than wild type. No stratification by stage of infection or sexual activity class. Increased life expectancy due to ART: 1.5- to 3.0-fold.	Increasing ART usage would decrease the death rate and substantially reduce HIV incidence (wide range of results due to uncertainty in parameter estimations).
Blower et al 2001 [63]	Dynamic, deterministic (used previous model [5])	MSM, San Francisco, US, 1996–2005	Treatment uptake and drug resistance evolution rates as for [5]. No change in risk behaviour. Assumed no resistant strains could arise that were as transmissible as wild type. Transmissibility range: 1–90% as fit as wild type. Implicitly allows superinfection with wild type virus of subjects with primary resistance.	Prevalence of ART resistance is already high in San Francisco and will continue to increase substantially through 2005. Transmitted drug resistance will remain low, only increasing gradually, with a doubling time of around 4 years and a predicted median 15.6% (range 0.05–73.21%) new infections resistant to ARVs by 2005.
Freedberg et al 2001 [18]	Linear health economic model	US	Monte Carlo simulation of a hypothetical cohort of infected patients. Disease progression predicted by CD4 count (6 categories) and viral load (5 categories). Detailed description and associated costs of HIV-related morbidity, opportunistic infections and death. Virologic failure represented as 0.5 log increase in viral load for 2 consecutive months. Increased life expectancy due to ART: 2 years.	The cost-effectiveness ratio for ART was $13,000–$23,000 per quality-adjusted life year gained. Initial CD4 count and drug costs were the most important determinants of costs, clinical benefits, and cost effectiveness.
Tchetgen et al 2001 [76]	Dynamic, deterministic	MSM (assumes same population as Blower et al [5])	No stratification by sexual activity or stage of infection (model is for all stages except AIDS; progression to AIDS exits an individual from the model population). Models diagnosis separately from treatment initiation. No sexual behaviour change due to ART. Drug resistance emerges at 1.2–13.5% per year for adherent patients and 67.3–85.9% per year for non-adherent patients. Resistant strains are half as transmissible as wild type. Untreated resistant infections may revert to wild type infections (10% per year). 60% of treated patients adhere. Increased life expectancy due to ART: approximately 3-fold. ART reduces infectivity by 74%. Withdrawal rates also vary by adherence.	Although screening for adherence is likely to reduce levels of drug resistance compared to treating all patients, HIV and AIDS incidence rates are likely to increase unless screening accuracy is extremely high.
Dangerfield et al 2001 [77]	Dynamic, deterministic	MSM, UK 1981–1998	Five stages of infection with varying infectivity broadly corresponding to primary infection, incubation, pre-AIDS and early and late AIDS. Three levels of sexual activity with proportionate mixing. No drug resistance. Proportion initiating ART at each stage (models 1,2 and 3 respectively): incubation = 0%, 0%, 60%; preAIDS = 0%, 10%, 25%; early stage AIDS = 0%, 10%, 35%. No uptake for late stage AIDS, which is defined as the final few months of care – authors assume patients only reach this stage as a result of treatment failure. Infectivity decreases to a constant level for all those treated, which is 35–40-fold less than for pre-AIDS.	Three models were designed, differing by prognosis of patients experiencing treatment failure for models 1 and 2. Model 3 stratifies life expectancy on ART by stage of infection at which treatment is initiated.
Law et al 2001 [4]	Dynamic, deterministic	MSM, Australia 1996	Population-level changes in sexual behaviour: no change to doubling of risk. Decrease in infectivity due to ART: 10-fold (range: 100-fold to none). Proportion of individuals diagnosed and treated increases with progression of disease, as determined by CD4 count. HIV diagnosis modelled separately to ART initiation, median 2-fold decrease in risk behaviour upon diagnosis (range: 25–75% reduction). No stratification by sexual activity group. No incorporation of drug resistance. Stratified by stage of infection in terms of CD4 count (>500 cells/ml, 200–500, <200, AIDS). Proportion treated by disease stage: >500 = 35%, 200–500 = 52%, <200 = 72%, AIDS = 90%.	Changes in risk behaviour were linearly associated with increases in incidence, while decreases in infectivity were non-linearly associated with decreases in incidence. Decreases in infectivity of 2-, 5- and 10-fold would be counterbalanced (in terms of incidence) by increases in risk behaviour of 40, 60 and 70%, respectively.
Velasco-Hernandez et al 2002 [1]	Dynamic, deterministic (used previous model [5])	MSM, San Francisco, US,	Previous model [5] is used to derive an analytical expression for R0. Used assumptions as for the previous model. Changes in risk behaviour: 50% reduction to 100% increase (whole population). Relative fitness of resistant strains: 1% to "approximately as transmissible".	Median R0 = 0.90 if risky sex decreased, 1.0 if risky sex remained stable, and 1.16 if risky sex increased. R0 decreased as ART coverage increased. The probability of epidemic eradication is high (p = 0.85) if risky sex decreases (median 25% reduction), moderate (p = 0.5) if it remains stable, and low (p = 0.13) if it increases (median 50% increase). Concluded that ART can function as an effective HIV prevention tool, even with high levels of drug resistance and risky sex, and could eradicate a high prevalence (30%) HIV epidemic.
Law et al 2002 [78]	Dynamic, deterministic (extension of previous model [4])	MSM, Australia 1996	Incorporation of other sexually transmitted infections (STI), but not dynamically-assumed 100% increase in prevalence of STI among all MSM regardless of HIV status, due to increased risk behaviour as a result of ART introduction. STI infection increased HIV infectivity 3.5-fold (range: 2–5-fold).	Decreases in infectivity of 2-, 5- and 10-fold would be counterbalanced (in terms of incidence) by increases in risk behaviour of 30, 50 and 65%, respectively i.e. even more modest increases than in previous publication [4]. Even small increases in STI as a result of increased risk behaviour could have an important multiplicative effect increasing HIV incidence.
Johnson & Dorrington 2002 [79]	ASSA2000 Interventions Model (dynamic, deterministic spreadsheet model)	South Africa	Stages of infection: stages I to IV of the WHO clinical staging system, with decline in sexual activity at advanced stages. Includes voluntary counselling and testing (VCT) with a corresponding (though transient) decrease in risk behaviour for both infected and uninfected individuals. Reduction in viral load due to ART: 1.76 log10. Reduction in infectivity: 67% per log reduction in viral load. 4 sexual activity classes. Only AIDS patients qualify for treatment. Model assumes a phased roll-out achieving 90% coverage by 2006. First 6 months of ART: death rate = 8.2%, discontinuation rate = 9.1%. Thereafter: death rate = 5.8%/year, discontinuation rate = 5.8%. Resistance not explicitly modelled.	ART provision is highly effective at preventing new infections, through reduced infectivity and assumed impact of VCT, and the high coverage level. ART plus VCT reduces incidence of AIDS, but because of increasing numbers starting treatment, the overall number of AIDS cases increases to a peak in 2015. Approximately one million deaths would be averted between 2001 and 2015 if ART is added to a set of AIDS prevention initiatives.
Nagelkerke et al 2002 [80]	Dynamic, deterministic	Botswana and India	Stratified by gender and 2 sexual activity groups (higher group represents CSWs and their clients). No changes in sexual behaviour due to ART, but "effective counselling" of those on ART could decrease infectivity of those developing drug resistance by 50%. ART reduces infectivity to zero. Rate of acquired resistance: 25% per year (range: 5–25%). Transmitted resistance possible (resistant strains appear to be as transmissible as wild type). Rate of treatment uptake: all those infected are recruited at rate 50% per year. No stratification by stage of infection.	Compared impacts of an ART programmes to other HIV interventions. Concluded that after transient success, ART would be ineffective within 30 years due to widespread drug resistance. Assumes high treatment uptake rates and pessimistic assumptions regarding transmission of drug resistant strains.
Gray et al 2003 [2]	Dynamic, stochastic	Rakai, Uganda, 2000–2020	Assumes ART reduces HIV log viral load by 27.0–42.5%, representing decreases in log viral load from 5.32 to 3.06 log10 copies/ml [49], and 5.23 to 3.82 log10 copies/ml [48]. These generate an average decrease in infectivity of 95.7% (0.0023 to 0.0001 per coital act) and 43.5% (0.0023 to 0.0013) respectively. Sexual activity decreases with increasing viral load. Behavioural disinhibition: increased risk by 50–100% (among those on ART only). Treatment uptake: scenario 1: all with viral load >55,000 copies/ml; scenario 2: all subjects, irrespective of viral load (20% of infected persons in Rakai had viral loads >55,000 copies/ml [81]). Range of treatment coverage: 0–100%.	Concluded that ART alone cannot control mature HIV epidemics such as that in Rakai. Behavioural disinhibition would counter decreases in HIV infectivity due to ART.
Xiridou et al 2003 [82]	Dynamic, deterministic	Young MSM, Amsterdam, The Netherlands	Steady and casual partnerships. Stages of infection: primary, incubation, AIDS. Sexual activity assumed to cease after development of AIDS. 42% subjects in incubation stage are diagnosed. Diagnosis during incubation results in a 25% (0–50%) reduction in risky behaviour. ART reduces infectivity by 74.5%. Increased life expectancy (before development of AIDS) due to ART: 9.5 years.	A 75–99% reduction in infectivity due to ART will be counterbalanced by increases of 50% (range: 30–80%) in risky behaviour with steady partners, but not by increases of up to 100% with casual partners. Increasing HIV testing from 42% to 80% and ART coverage from 70% to 85%, would mean even a 100% increase in risk taking with steady partners would not outweigh the effect of ART on HIV incidence.
Xiridou et al 2004 [3]	Dynamic, deterministic (extension of previous model [82])	Young MSM, Amsterdam, The Netherlands	Extension of original model [3] to allow for initiation of ART during primary infection. Proportion of men diagnosed during incubation and successfully treated: 60–80%. Proportion initiating ART during primary infection: 1–10%. ART reduces infectivity during incubation by 50–99%. Population-level increase in risk behaviour for both steady and casual partnerships: 0–100%. Mean incubation time to AIDS for initiating ART during incubation: 15–30 years. Decreases in infectivity and increases in life expectancy for those initiating ART during primary infection were forced to be larger than for those initiating ART during incubation.	Investigates the role of primary infection in HIV transmission. Estimates that among all new infections only 11% occur during primary infection. The effect of ART during primary infection on transmission is therefore limited. However, in a community with higher risk behaviour among casual partnerships, the fraction of transmission attributed to primary infection increases to 25%.
Clements et al 2004 [38]	Dynamic, deterministic (based on previous models [4, 78])	MSM, Australia 1995–2006	Assumed a 10% annual increase in population-level risk behaviour from 1996. A stable proportion receive ART from 1998, which then declines from 70% in 2001 to a median of 50% of diagnosed on ART by 2006.	HIV incidence was predicted to have declined during 1996–1998 due to ART, with a slow increase 1998–2001 due to increased risk behaviour while ART usage remained fairly stable. From 2001, a continued increase in risk behaviour coupled with a moderate decline in ART use would lead to a 50% increase in incidence by 2006.
Auvert et al 2004 [26]	Linear	Township near Johannesburg South Africa, 2002	Used results from cross-sectional study. Under WHO guidelines, all with CD4 counts <200 initiated treatment. Under USDHHS guidelines, all with CD4 counts <350 or viral load >55,000 copies/mL initiated treatment. Reduction in infectivity due to ART calculated using infectivity estimates by viral load category used by Gray et al [2] and comparing change in distribution of viral load in the community with and without ART.	Investigated short term impact of ART on incidence. The proportion of infected subjects eligible for ART was 9.5% (95% CI 6.1–14.9%) under WHO guidelines and 56.3% (95% CI 49.1–63.2%) under USDHHS guidelines. The population impact of ART on HIV transmission is small (reduction in annual risk of transmission 11.9% (95% CI 7.1–17.0%)) under WHO guidelines, but higher under USDHHS guidelines (71.8% (95% CI 64.5–77.5%))
Boily et al 2004 [30]	Dynamic, deterministic	MSM population	STI (gonorrhoea) increasing HIV infectiousness is modelled dynamically. Stratified into 6 sexual activity groups with proportionate mixing. Two stages of HIV infection: incubation and AIDS. AIDS patients treated with ART resume the sexual activity of asymptomatic individuals within their activity class. ART reduces infectivity by 25% (pessimistic), 50–90% (moderate), 99% (optimistic). Treatment uptake rates: 10–90% per year, for AIDS patients only, or for all infected subjects Withdrawal rate (due to treatment failure, resistance and toxicity): 0–50% per year.	Zero to 55% new bacterial STI could be attributed to widescale ART use, due to more modest increases in risky behaviour (0–25%) at the population level. These increases have a negative impact on HIV if coverage is too low. Increasing ART coverage helps to prevent more HIV infections despite larger increases in risk behaviour and STI that is predicted to ensue. No individual-level increase in risk behaviour; population-level increases in risk behaviour over time are due to ART slowing the depletion of high-risk infected individuals, so these populations are replenished.
Salomon et al 2005 [22]	The Goals model (linear spreadsheet model) (based on previous models [20, 21])	Sub-Saharan Africa, calibrated to 3 regions: East, West/Central and Southern, up to 2020.	Goals model adjusts UNAIDS/WHO EPP (epidemic projection package) and Spectrum model incidence and prevalence estimates. 5 different risk groups (single and married men and women, and CSWs). Median increase in life expectancy due to ART: 3 years. No drug resistance. Includes STI transmission. 3 stages of infection: primary, incubation and symptomatic. ART reduces infectivity by 99% (optimistic) or 66% (pessimistic). Number of partners reduced by 50% plus 2 times higher condom use (optimistic) or no change (pessimistic) for those treated. Risk behaviour of the general population does not change (optimistic), or condom use declines by 10% (pessimistic). Treatment uptake: 50% ART coverage (of those in need) by 2005, increasing to and remaining at 80% from 2010–2020. This "treatment-centred" response, where little prevention activity occurs, was compared to a "prevention-centred" response where no ART scale-up occurred, and a "combined response", with optimistic and pessimistic assumptions of the effect of ART on prevention efforts being investigated.	Explored the potential impact of ART in the context of a broader strategy for HIV/AIDS control, comparing deaths and new infections averted to baseline projections without interventions. A prevention-centred strategy provides greater reductions in incidence and mortality reductions similar to those of treatment-centred strategies by 2020, but more modest mortality benefits over the next 5–10 years. If treatment scale-up leads to reduced effectiveness of prevention efforts, benefits (in terms of infections and HIV/AIDS deaths averted) are considerably smaller than for initiatives which complement each other. The number receiving ART in 2020 ranges from 9.2 million in a pessimistic treatment-only scenario, to 4.2 million in a combined response scenario with positive treatment-prevention synergies.
Wilson & Blower 2005 [19]	Spatial model	KwaZulu-Natal, South Africa	Incorporates heterogeneity in treatment accessibility with distance to health care facilities, and heterogeneous distribution of people infected with HIV.	Determining the optimal ART allocation strategy among health care facilities, aiming to maximise equity. Authors' strategy gave more equal access to ART than allocating therapy to the state capital only, or equal allocation to all health care facilities.