The Effect of Antiretroviral Therapy on Secondary Transmission of HIV among Men Who Have Sex with Men

Abstract

Background

Antiretroviral therapy (ART) reduces human immunodeficiency virus (HIV) RNA load and the probability of transmitting HIV to an HIV-uninfected partner. However, the potential reduction in secondary transmission associated with ART may be offset by the longer duration of infectiousness.

Methods

To estimate the effects of ART on the secondary transmission of HIV among men who have sex with men, we used a previously published state-transition model of HIV disease to simulate the clinical and virologic course of HIV infection among 2 cohorts of men who have sex with men: (1) a cohort of individuals who were not receiving ART and (2) a cohort of individuals treated with US guideline–concordant ART. The model tracked the number of acts of unprotected insertive anal intercourse, transmission risk per act as determined by HIV RNA level, and the number of secondary cases generated in each cohort.

Results

The estimated mean number of secondary transmissions from an HIV-infected individual after 10, 20, and 30 years of infection were 1.9, 2.5, and 2.5, respectively, in the untreated cohort, compared with 1.4, 1.8, and 2.3, respectively, in the treated cohort. The total number of transmissions for the treated cohort began to exceed the total number of transmissions for the untreated cohort 33 years after infection; over the entire course of infection, treatment with ART led to a 23% increase in secondary infections. All estimates of the impact of ART on secondary transmission were sensitive to changes in risk behaviors.

Conclusions

These results suggest that ART must be accompanied by effective HIV-related risk reduction interventions. Programs that target prevention to decrease further HIV transmission are crucial to epidemic control.

It is uncertain whether treatment of HIV infection with antiretroviral therapy (ART) will slow the US HIV epidemic. Because ART is associated with a reduction in HIV RNA levels in both blood and semen [1–3], and because lower levels of HIV RNA are correlated with lower HIV transmission rates [4, 5], ART might curb transmission from individuals receiving therapy. However, because ART does not eradicate HIV RNA [1, 3, 6], the potential reduction in secondary transmission by ART may be offset by the longer duration of infectiousness [7], which may be compounded if HIV-infected individuals do not fully adhere to therapy or reduce their HIV risk behavior.

HIV transmission may occur during every stage of disease, from primary infection to late-stage AIDS. Levels of HIV RNA are highest during primary HIV infection [8, 9]. However, the duration of time spent in this high-infectivity stage is low. One recent report [10] suggests that late-stage disease may also play an important role in transmission. These offsetting dynamics must be taken into account in evaluating the overall impact of ART on HIV transmission.

Several mathematical models have been developed to determine the effect of ART on HIV transmission by estimating the basic reproductive number (R₀), which represents the number of individuals that a single infectious person will infect when introduced into a completely susceptible population [11–14]. These models are limited by their simplification of the biological, clinical, and behavioral components of HIV transmission. To address these issues, we modified an existing state-transition model to simulate HIV transmission from HIV-infected individuals to un-infected individuals, accounting for the relationships between ART, HIV RNA level, disease progression, behavioral changes, and transmission risk.

METHODS

Analytic Overview

Cost-effectiveness of preventing AIDS complications model (CEPAC)

We employed a previously published [15] state-transition simulation model of HIV disease, CEPAC, to estimate the effects of ART on HIV transmission. Primary infection was analyzed separately from chronic and late-stage infection. For chronic infection, men enter the model with a mean CD4⁺ cell count of 744 cells/mm³ and an HIV RNA level close to set-point, as determined by the Multicenter AIDS Cohort Study [16]. Men were defined as having late-stage infection when they had a CD4⁺ cell count <50 cells/mm³ and were not receiving ART or when they had a CD4⁺ cell count <50 cells/mm³ and had experienced failure of their most recent ART regimen.

In CEPAC, HIV RNA level determines the rate of CD4⁺ cell count decrease, and CD4⁺ cell count determines the monthly risk of opportunistic infection (OI) and AIDS-related mortality. Simulations within CEPAC may include various treatment regimens, including both OI prophylaxis and ART. When ART reduces the HIV RNA level of an individual, the CD4⁺ cell count increases at a rate reported in clinical trials [17–19]. When ART fails (defined by virologic rebound, decrease in CD4⁺ cell count, or a new OI), HIV RNA level slowly reverts to set point, until a new ART regimen is initiated [20].

For each simulated individual, the model tallies the number of months spent in each health state, the number of clinical events, the time spent in each HIV RNA level stratum, and the time of death. After the entire simulated cohort has cycled through the model, life expectancy and mean time spent in each HIV RNA level stratum are estimated. Data on disease progression, ART initiation, and ART efficacy are based on previously published data [21]. We included sequential lines of ART, each with decreasing efficacy of HIV RNA level suppression and CD4⁺ cell count reconstitution (tables 1 and 2).

Table 1.

Summary of input parameters for the model: HIV RNA distribution and CD4⁺ cell count decrease by HIV RNA level.

HIV RNA level, copies/mL	Proportion of cohorta	Monthly decrease in CD4+ cell count, mean cells/mm3b
0–500	0.2573	3.025
501–3000	0.2502	3.733
3001–10,000	0.2521	4.600
10,001–30,000	0.1633	5.400
>30,000	0.0771	6.375

NOTE. The initial mean value (±SD) for CD4⁺ cell count was 744 ± 279 cells/mm³. The mean age (± SD) of the patients was 33 ± 9.78 years.

^aData are from the Multicenter AIDS Cohort Study [16].

^bData are from Mellors et al. [45] and the Multicenter AIDS Cohort Study [16].

Table 2.

Summary of input parameters for the model: efficacy of antiretroviral therapy

Therapy regimen	Study	Drugs	HIV RNA level<400 copies/mL, percentage of patients	CD4+ cell count increase, mean cells/mm3	Duration of therapy, weeks
1st	Gallant et al. [34]	Efavirenz + tenofovir diso- proxil fumarate + 1 NRTI	80	169	48
2nd	Nieto-Cisneros et al. [35]	Lopinavir-ritonavir + 2 NRTIs	82	121	24
3rd	DeJesus et al. [36]	Atazanavir-ritonavir + 2 NRTIs	56	110	48
4th	Clotet et al. [37]	Enfuvirtide + OBR	30	91	48

NOTE. Antiretroviral therapy was initiated at a CD4⁺ cell count of <350 cells/mm³. The initial mean value (±SD) for CD4⁺ cell count was 744 ± 279 cells/mm³. The mean age (±SD) of the patients was 33 ± 9.78 years. NRTI, nucleoside reverse-transcriptase inhibitor; OBR, optimized background regimen.

Estimation of $R_0^t$

We used the notation $R_0^t$ to denote the cumulative number of secondary transmissions from a typical infectious individual by t years after infection, if all contacts were with susceptible individuals. In this notation, $R_0^{\infty }$ would be equivalent to the traditional basic reproductive number; we consider the cumulative transmission by a given time after infection to focus attention on the nearer (more predictable) term. To estimate $R_0^t$ of HIV under different treatment strategies in a population of HIV-infected men who have sex with men (MSM), we added a transmission-tracking component to CE-PAC. Monthly acts of unprotected insertive anal intercourse (UIAI) were determined by CD4⁺ cell count and summed across the entire course of infection. The model then multiplied the number of acts by the probability of HIV transmission per act, which is driven by HIV RNA level at the time of the act. This formula, (number of acts) × (transmission per act) = transmitted cases, generates the number of secondary cases per person per month. R₀ was calculated as the mean number of secondary cases up to time t after infection for a cohort of 1 million individuals. Because of the uncertainty of future ART regimens, we focused the primary analysis on the first 10 years after infection, but we also present results for 20 years after infection, 30 years after infection, and the lifetime of the infected cohort.

To estimate the portion of the basic reproductive number attributable to chronic infection, we ran the model under 2 conditions: with no ART and with ART for individuals with CD4⁺ cell counts <350 cells/mm³. We then added the number of secondary infections attributable to primary infection.

Model Parameters

Transmission probability parameters

Because the study population consisted of MSM, we estimated transmission probabilities for unprotected anal intercourse, the primary means of HIV transmission in this population [22], by HIV RNA level. Using data [23] collected from discordant heterosexual partners, we categorized per-contact heterosexual transmission probabilities by HIV RNA level (table 3). To estimate the probability of transmission during primary and late-stage infection, we used estimates from Wawer and colleagues [24, 25]. We compared these heterosexual transmission probabilities to the estimates of per-contact infectivity for UIAI obtained from Vittinghoff et al. [26] and DeGruttola et al. [27] and estimated the probability of HIV transmission during UIAI in MSMs to be 8-fold higher than the probability of transmission observed for male-to-female vaginal intercourse (table 3).

Table 3.

Transmission model parameters: transmission probability per act of unprotected insertive anal intercourse (UIAI).

	Transmission probability per act of UIAI
Variable	Heterosexuala	MSMb
HIV RNA level, copies/mL
0–500	0.0001	0.0008
501–3000	0.0011	0.0088
3001–10,000	0.0012	0.0096
10,001–30,000	0.0014	0.011
>30,000	0.0023	0.018
Primary infection	0.0081	0.065
Late-stage infection	0.0043	0.0344

^aData on the probability of transmission in the heterosexual population are adapted from Gray et al. [23] for HIV RNA level and from Wawer et al. [25] for primary and late-stage infection.

^bData on the probability of transmission in the MSM population are adapted from Vittinghoff et al. [26], DeGruttola et al. [27], and Gray et al. [23].

Sexual behavior parameter estimates

We determined, using the Multicenter AIDS Cohort Study public use dataset [16, 28], that CD4⁺ cell count, not HIV RNA level, was related to the probability of being sexually active and engaging in insertive anal intercourse. To estimate the number of unprotected sex acts among MSMs stratified by CD4⁺ cell count, we used data from the Boston Partners Study [22, 29] (table 4).

Table 4.

Transmission model parameters: number of acts of unprotected insertive anal intercourse (UIAI) per month.

Variable	UIAI, no. of acts per person per month
CD4+ cell count, cells/mm3
0–50	0.81
51–100	1.45
101–200	0.55
201–300	2.69
301–500	1.11
500	1.25
Primary infection	1.87

NOTE. The number of acts of UIAI was estimated from the MSM population of the Boston Partners Study [22, 29].

Because sexual behavior may differ during primary infection, defined as the first 3 months after seroconversion [30, 31] with HIV RNA level >100,000 copies/mL [30, 32], we obtained a separate estimate of the mean monthly number of acts of UIAI during this period. We estimated this number from data for the 6 months prior to the first positive HIV test result [33]; the estimate was similar to the number of acts in most of the CD4⁺ cell count categories (table 4). Because sensitivity analyses showed that smoothing out the relationship between CD4⁺ cell count and the number of acts per month had very little impact on the overall results, we used actual data gathered from the Boston Partners Study categorized by CD4⁺ cell count. Because we were particularly interested in estimating the effect of primary infection on secondary transmission, we kept primary infection as a separate category.

For the analyses, we assumed that each act of UIAI occurred with a different partner. Although it is unlikely that all individuals change partners with each sexual encounter, the number of transmission events “double-counted” in our analysis should be small because of the rapid rate of partner turnover in the population of interest. In the untreated population, the annual probability of transmission was ~0.25; if transmission events were randomly distributed, this would amount to ~4 years between transmissions. This is ~16 times the mean duration of a partnership (3 months) in the Boston Partners Study [22, 29].

Sensitivity Analyses

To evaluate the relative impact of the assumptions in the model, we conducted a number of sensitivity analyses. First, we used previously published values for the efficacy of therapy [34–37] and performed sensitivity analyses to evaluate the effect of ART failure rates on the number of secondary transmissions. Second, we explored the effect of varying the 8:1 ratio of MSM to heterosexual per-contact transmission probability for all disease stages, including primary and late-stage HIV infection. Third, we considered departures from the primary analysis assumption that men did not change their sexual risk behavior after initiation of therapy. Thus, we evaluated the impact of a potential increase or decrease in the frequency of UIAI both after ART initiation for an individual and after the availability of ART to the population. Fourth, a secondary case that occurs early in the course of infection would contribute more to the epidemic than a case that occurs later [38]. Therefore, we explored the effect of decreasing the impact of secondary cases exponentially with time, so that a case occurring earlier in the epidemic is weighted more than a case occurring later in the epidemic. Finally, because in some studies risky sexual behavior has been found to be negatively associated with age [39–41], we examined the effect of exponentially decreasing risk behavior with age on the lifetime estimates—an analysis that was technically equivalent to that which reduced the impact of secondary cases exponentially with time. We examined these parameters both individually and jointly to understand their impact.

RESULTS

Baseline model results

On average, the untreated cohort of MSM had a much shorter survival (mean survival, 145.4 months), compared with the cohort treated with ART (mean survival, 366.7 months), and engaged in fewer total lifetime acts of UIAI (5). For both the untreated and treated cohorts, an average of 0.36 secondary cases occurred per person during primary infection. Within the first 10 years of infection, primary infection accounted for 19% of the secondary cases transmitted by the untreated cohort, compared with 26% of the secondary cases transmitted by the treated cohort. With ART still widely used 10 years after infection, <0.01% of secondary cases occurred during the last 6 months of life, compared with 5% in untreated men (table 5).

Table 5.

Ten-year and lifetime projected outcomes for untreated and treated cohorts per 1 million population.

Variable	Untreated cohort	Treated cohort
Survival
Mean months	145.4	366.7
Median months (range)	139.5 (1–544.5)	381.5 (1–969.5)
10 Years after infection
No. (%) of secondary cases, by HIV RNA level
0–500 copies/mL	8566 (0.5)	45,241 (3.2)
501–3000 copies/mL	198,007 (10.3)	153,472 (11.0)
3001–10,000 copies/mL	323,905 (16.9)	231,665 (16.5)
10,001–30,000 copies/mL	359,459 (18.8)	243,213 (17.4)
>30,000 copies/mL	570,457 (29.8)	365,328 (25.8)
Primary infection	361,432 (18.9)	361,432 (25.8)
Late-stage infectiona	91,939 (4.8)	90 (0)
$R_0^{10}$	1.9	1.4
Lifetime of infection
No. (%) of secondary cases, by HIV RNA level
0–500 copies/mL	15,939 (0.6)	196,152 (6.4)
501–3000 copies/mL	315,702 (12.6)	407,083 (13.2)
3001–10,000 copies/mL	443,663 (17.7)	574,445 (18.7)
10,001–30,000 copies/mL	444,081 (17.7)	577,609 (18.8)
>30,000 copies/mL	643,729 (25.7)	843,084 (27.4)
Primary infection	361,432 (14.4)	361,432 (11.8)
Late-stage infectiona	278,107 (11.1)	114,846 (3.7)
$R_0^{\infty }$	2.5	3.1

^aOnce an individual is defined as having late-stage infection, they are no longer counted in any of the CD4⁺ cell count strata.

Secondary transmissions from an untreated cohort and a treated cohort

We estimated an untreated $R_0^{10}$ of 1.9 and a treated $R_0^{10}$ of 1.4, suggesting that ART reduces transmission in the first 10 years after infection. ART has a strong, beneficial impact on secondary transmissions over the first 20 years after infection, with an untreated $R_0^{20}$ of 2.5, compared with a treated $R_0^{20}$ of 1.8. However, at longer time horizons after infection, the benefit of treatment decreased, because viral load reductions were offset by longer duration of infectiousness (untreated $R_0^{30}=2.5$ and treated $R_0^{30}=2.3$ at 30 years), assuming that no new HIV treatments become available. The treated and untreated $R_0^t$ were equivalent at 33 years, because of the eventual failure of ART and the longer survival in the treated cohort. Over the entire lifetime of the 2 cohorts, treatment led to a 23% increase in $R_0=R_0^{\infty }$ (figure 1).

Figure 1.

The basic reproductive number (R₀) by year in the untreated (thick blue line) and treated (red line) cohorts are shown to compare the time required to reach a given R₀. The proportion of the original cohort that is alive in the untreated (thin blue line) and treated (pink line) cohort and the proportion of the original cohort receiving ART in the treated cohort (green line) are also shown. This graph is truncated at 60 years after infection.

The graph of $R_0^t$ (figure 1) shows that, in the untreated cohort, $R_0^t$ increases steadily but begins to level off as individuals die, reaching a plateau by 26 years. In contrast, the $R_0^t$ for the treated cohort shows initial, steady growth similar to that of the $R_0^t$ for the untreated cohort; growth then slows after ~10 years, as individuals begin treatment and their HIV RNA level decreases. The slope of $R_0^t$ begins to increase again after ~20 years of infection, as a large proportion of individuals exhaust available treatment options.

Sensitivity analyses

Because most of the assumptions that we tested were similar across both treated and untreated populations, they had no effect on the relative magnitude (ratio) of $R_0^t$ for untreated and treated cohorts. Changing the rate ofART failure had little effect on the number of secondary transmissions at 10 years after infection (table 6). Population-wide changes in sexual activity levels increased or decreased R₀ by the same factor regardless of ART use, as did changes in the assumption that per-contact infectivity of UIAI was 8-fold higher than vaginal intercourse. The probability of transmission during primary, chronic, and late-stage infection had a multiplicative effect on the number of secondary cases during each of these disease stages (table 6). However, changing the overall probability of transmission during primary infection and late-stage infection had little effect on the number of secondary cases, because together they account for ~25% of all secondary cases that occurred within the first 10 years of infection. Comparatively, there was a greater impact on transmission when we increased or decreased the probability of transmission during the chronic stage of infection, because the majority of secondary cases arise during this long disease stage.

Table 6.

Sensitivity analyses.

	10 Years after infection, $R_0^{10}$		20 Years after infection, $R_0^{20}$		30 Years after infection, $R_0^{30}$		Lifetime, $R_0^{\infty }$
Variable	Untreated	Treated	Untreated	Treated	Untreated	Treated	Untreated	Treated
Baseline estimate	1.9	1.4	2.5	1.8	2.5	2.3	2.5	3.1
ART failure ratea
Decrease 10%	…	1.4	…	1.8	…	2.2	…	3.0
Decrease 20%	…	1.4	…	1.7	…	2.2	…	3.0
Increase 10%	…	1.4	…	1.9	…	2.4	…	3.1
Increase 20%	…	1.4	…	1.9	…	2.5	…	3.2
Probability of transmission during primary infection
Decrease 25%	1.9	1.3	2.4	1.7	2.4	2.2	2.4	3.0
Increase 25%	2.0	1.5	2.5	1.9	2.6	2.4	2.6	3.2
Probability of transmission during chronic infection
Decrease 25%	1.6	1.1	2.0	1.4	2.0	1.8	2.0	2.4
Increase 25%	2.3	1.7	2.9	2.1	3.0	2.8	3.0	3.7
Probability of transmission during late-stage infection
Decrease 25%	1.9	1.4	2.4	1.8	2.4	2.3	2.4	3.1
Increase 25%	2.0	1.4	2.5	1.8	2.6	2.3	2.6	3.1
Annual age-related decrease in sexual activity
1%	1.9	1.4	2.3	1.7	2.4	2.1	2.4	2.6
2%	1.8	1.3	2.2	1.6	2.2	2.0	2.2	2.3
3%	1.8	1.6	2.1	1.6	2.1	1.8	2.1	2.0
Yearly decrease in the impact of secondary cases
1%	1.9	1.4	2.3	1.7	2.4	2.1	2.4	2.6
2%	1.8	1.3	2.2	1.6	2.2	2.0	2.2	2.3
3%	1.8	1.6	2.1	1.6	2.1	1.8	2.1	2.0
Change in risk behavior when ART is available
Decrease 50%	…	0.7	…	0.9	…	1.2	…	1.6
Increase 100%	…	2.8	…	3.6	…	4.7	…	6.2
Change in risk behavior when ART is initiated
Decrease 50%	…	1.4	…	2.1	…	2.6	…	2.9
Increase 100%	…	1.5	…	2.4	…	3.0	…	3.4

NOTE. $R_0^t$ denotes the cumulative number of secondary transmissions from a typical infectious individual by t years after infection, if all contacts were with susceptible individuals (see Methods). ART, antiretroviral therapy.

^aWe changed the efficacy of each therapy regimen by increasing or decreasing the failure rate by the corresponding percentage (e.g., for the first regimen, a 10% decrease reduced the ART failure rate from 20% at 48 weeks to 18% at 48 weeks).

Changes in risk behavior because of the availability of ART or because of starting ART had a substantial effect on $R_0^t$ in the treated group (table 6). For example, if all of the men in the treated cohort decreased risky sexual behavior by 50%, compared with the untreated cohort, simply because ART was available and regardless of whether they had yet begun treatment, $R_0^{10}$ would decrease to 0.7, indicating a 63% decrease in secondary cases, compared with no treatment. If these men doubled their risky sexual behavior, there would be a mean of 2.8 secondary cases per person after 10 years (i.e., 1.5 times the number of cases found without treatment). However, the effects of changing sexual behavior were not as substantial over a 10-year period if we assumed that only the men receiving therapy changed their behavior (table 6).

When we assumed that individuals decrease their sexual activity as they age, there was a disproportionate reduction in secondary cases among patients in the treated cohort, who live longer and generate relatively more secondary cases at older ages. The overall difference in the number of secondary cases in the treated cohort, compared with the untreated cohort, decreased with greater decreases in sexual activity with age, until—at a 3% annual decrease in sexual activity—there were more secondary cases in the untreated cohort than in the treated cohort (table 6). These same analyses could assess the impact of changes in secondary transmission in the context of a growing epidemic [8, 38] (table 6).

DISCUSSION

Using a detailed natural history and treatment model of HIV disease, combined with monthly probabilities of sexual activity and per-act transmission risk, we estimated that the use of ART resulted in a reduction in the number of secondary HIV transmissions from 1.9 to 1.4 transmissions per person during the initial 10 years after infection, assuming no increase in risk behavior and no changes in available therapy. These results support more-aggressive and more-active case-finding approaches, such as routine voluntary HIV screening and appropriate ART. However, much of this benefit may be reduced over the lifetime of HIV-infected patients because of the combined effect of increased survival and the eventual failure of ART, increasing from 2.5 to 3.1. However, this increase is not R₀ inevitable and may be attenuated by the identification of new and effective ART regimens and other effective treatment options, as well as by decreased sexual activity resulting either from the aging of the ART cohort or from specific risk-reduction interventions.

An alternative to estimating R₀ would be to estimate the effects of ART on incidence. Although these estimates are closely related, the effects of treatment on incidence depend on a number of additional factors, such as the current phase of the epidemic, the types of sexual mixing in the population, and other aspects of the epidemic in a particular population. We have chosen to limit our analysis to effects on R₀ to make use of the detailed natural history model CEPAC to calculate a single measure of infectiousness.

The values of R₀ obtained here (and in other existing estimates of treatment effects) represent averages across the population. It is well known that behavioral heterogeneity increases the effective value of R₀ above its mean value in the population, because highly sexually active individuals are more likely to become infected and to transmit infection [42]. As with many of the other uncertainties in model inputs, this issue affects the magnitude of R₀ in both treated and untreated populations, but it should not affect the relationship between them.

A published mathematical model has concluded that widespread ART use could eradicate the HIV epidemic in the MSM population in San Francisco [12, 13] if the incidence of unsafe sexual behavior remained stable. Velasco-Hernandez et al. [13] assumed a 2-fold to 100-fold decrease in infectivity for individuals treated with ART and estimated an R₀ of 1.0 with the assumption of no change in sexual risk behavior. Our model provided a more detailed method for estimating time-dependent reductions in infectiousness and the increased duration of infectiousness achieved by ART by explicitly incorporating biological, clinical, and behavioral components. Our results, although still predicting that treatment would reduce infectiousness over the first 10 years, are less optimistic than earlier efforts regarding the likelihood of HIV eradication [43].

Gray et al. [14] estimated a 10-year R₀ of 1.44 for an untreated population, which decreased to 1.09 when HIV-infected individuals with HIV RNA levels >55,000 copies/mL were treated with ART. Our 10-year estimates of R₀ differed from those reported by Gray et al. [14], who simulated a heterosexual population and modeled ART use as a function of HIV RNA level rather than of CD4⁺ cell count.

Several studies have focused on the impact of primary [8, 9] and late-stage infection [10] on transmission. We found that the number of secondary cases that occurred during primary infection was a small percentage of the total number of secondary cases that occurred during the first 10 years of infection. Late-stage infection contributes even fewer secondary cases. Therefore, the extended duration of chronic infection contributes the largest proportion of secondary cases and provides more opportunities for preventive interventions.

We assumed that all sexual acts were with a seronegative partner consistent with the definition of R₀. To calculate the expected number of secondary cases in a population in which only a percentage of partners were seronegative, $R_0^t$ in both untreated and treated individuals would be multiplied by the same percentage if we assume the probability of encountering a seronegative partner is equal in the treated and untreated cohorts. Thus, the ratio of secondary transmissions for an untreated versus treated cohort remains the same over the cohort’s lifetime.

Another important assumption in the model was that the number of acts of UIAI each month does not decrease with age. Variations in this assumption had the largest effect on lifetime estimates of R₀. Because treated individuals live longer, a decrease in sexual activity with increasing age has a more powerful impact on the treated population. Sexual activity would have to decrease by ~3% per year before the R₀ of the treated cohort is less than that of the untreated cohort.

Because a secondary case early in the course of infection contributes more to future cases than does a case that occurs later [8, 38], the same sensitivity analysis used for age could be used to consider the impact of time-weighted transmission. In the context of an epidemic that is growing by ≥3% per year (but in the absence of age-related behavior change), the contribution of a treated person to epidemic growth would be less than that of an untreated person. Put another way, the benefits of treatment are greater in a growing epidemic, because the delay in transmission by treated persons reduces their contribution to the epidemic, even in situations in which the total number of secondary cases resulting from transmission from a treated person might be greater.

An implicit assumption of this model is that the relationship between plasma HIV RNA level and per-contact infectiousness was the same for treated and untreated individuals. Among individuals receiving ART, HIV RNA levels have been shown to be lower in semen than in plasma [44]; if this phenomenon can be confirmed, the effect of treatment in reducing secondary transmission might be greater than was observed in our model, which was driven by reductions in plasma HIV RNA level. A priority for future research would be to measure the probability of transmission given seminal HIV RNA levels.

In conclusion, the relationship between ART and lifetime infectiousness is complex, with an initial benefit over the short term but an eventual increase in total infections transmitted over the lifetime of an HIV-infected cohort. Our best estimate of R₀ in patients receiving ART always exceeds 1.0, suggesting that ART alone will not eradicate the HIV epidemic. Thus, it will be important to implement complementary programs that target reduction in secondary transmission, in addition to ART, to further decrease HIV transmission.