Software package

We used the Evonet_HIV package (https://github.com/EvoNetHIV), a stochastic, agent-based HIV epidemic model that accounts for a broad set of virological, immunological, behavioral, and epidemiological phenomena [33–35]. Each agent has attributes such as age, sex, HIV status, viral load, CD4 count (discretized into 5 bins), and HIV diagnosis status. Partnership lists and agent attributes (such as viral load and CD4 counts) were updated sequentially each day. The formation and dissolution of sexual partnerships were modeled using separable temporal exponential random graph model (STERGM) terms [36]. Since the model accounts for changes in behavior with age (e.g., young people having shorter relationships and preferentially forming attachments with other young people) and infection status (e.g., AIDS patients dying and/or having lower probabilities of sex) the model can be classified as a time-evolving adaptive network. The R package includes modules for HIV testing; viral load changes within hosts; age-dependent relationship durations; age- and viral load-dependent CD4 decline; CD4-dependent probabilities of sex; the effect of treatment on viral load; age- and diagnosis-dependent condom use; and age-, sex-, condom-, circumcision-, and viral load-dependent transmission rates. Different modules (sexual relational formation, viral load updates, etc.) were updated sequentially each time step.

Within-host viral dynamics, CD4 progression patterns, probabilities of dying of AIDS, testing procedures, and transmission probabilities were, for the most part, identical to those in previous studies using Evonet_HIV [33–35]. In the sections below, we summarize features that differ from these previous studies and/or that relate specifically to age (i.e., the key assumptions of this study). Additional details about the software are given in S1 Supplementary Methods and at github.com/EvoNetHIV.

Data sources

We have derived most of the parameters from studies of sub-Saharan countries (mainly South Africa); however, we have used parameters from other regions when they were of significantly better quality and/or more applicable to our model. We give more details about data sources, algorithms, and network estimation procedures in the Supplemental Methods.

Age-specific relationship durations

To approximate the tendency of young people to have short-term relationships [22–26], we divided the population into two groups: agents in group 1 (primarily composed of young people) tend to form short-term partnerships (default 2 years), agents in group 2 (primarily composed older people) tend to form long-term partnerships (default 10 years). We assumed that 90% of agents entering the sexually active population at age 16 belong to group 1. Agents in group 1 (median age 27) were assumed to have a small probability (default 0.00011 per day = ~5.5% per year) of transitioning to group 2 (median age 44). That is, agents exhibit a tendency to have longer partnerships as they age. These values were chosen so that the mean duration for people under 25 will approximate the midpoint of estimates in refs [23, 37, 38] and so that the ratio of the number partners per unit time for people under 25 to those over 40 is consistent with refs 23–26 (however, see below for caveats). Relationships between people from different groups were assumed to break up each day with probability 1/(365*AveDur), where AveDur is the geometric mean of each partner’s duration tendency. Use of the geometric mean (i.e., the square root of the product) means that relationship durations are determined more strongly by the partner with the shorter relationship tendency. With the parameters given above, relationships will last an average of ~6 years in a typical simulation, with ~40% and ~60% of agents, respectively, belonging to groups 1 and 2.

We are aware that our age-specific relationship terms provide but a loose approximation to a broad, but heterogeneous (and potentially unreliable) swath of data. Nguyen et al. [37], for example, show that estimates can vary 3-fold depending on methods used to analyze the data. Fortunately, we are able to show below that our main results do not depend on the exact values. Rather than trying to create a more complex model or trying to fit of this model to additional data, we have elected to stick with these approximate values and then examine the effect of changing the relationship duration terms in sensitivity tests (including tests in relationship durations are assumed to be completely independent of age).

Age- and sex-specific relationship formation terms

To represent age-disparate relationships, we added a network term that pushes the average age difference between men and women to equal a specified value (default: women partner with men who are, on average, 4 years older [12, 13, 39]). To mimic the tendency of people to partner with others who are about the same age, we added an additional term that forces the average age difference in the population (after adjusting for the average male-female age difference) to equal a specified value (default 4 years). With these default values, 20-year-old women will typically partner with men between 20 and 28. In Fig 1, we give an example age-age plot from one of our simulations.

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Fig 1. Ages of sexually active males plotted against the age of their sexually active female partners.

While the model allows for partnerships between people of different ages, the majority of people partner with someone who is about the same age after accounting for age-disparate relationships. The red line is a lowess fit to the data. The blue line is the y = x line that would occur if women partnered only with men who were exactly the same age. This graph shows data from a simulation in which treatment had reduced incidence to zero.

https://doi.org/10.1371/journal.pcbi.1007561.g001

To increase prevalence in young women relative to young men [26], we also added network terms for the sex-specific cross-sectional prevalence of relational concurrency [40, 41] (defaults: Men 0.24, Women 0.04).

Age-dependent probabilities of coitus

Following data in refs [25–28], we modeled declining probabilities of coitus, P_sex, with age as follows: where AveAge is the average age of the partners and P_sex19 (default 0.2 per day) is the probability of having coitus if AveAge = 19.

Age- and sex-dependent probabilities of transmission

We assumed that women have a higher (default 2-fold) per act probability of infection [11]. Following an adaptation of data from Hughes et al. [31] used in our previous studies [33–35], we also assumed that the relative per-act risk of transmission is higher when the susceptible partner is young (default: RR 1.492 for each decade under 46).

Age-dependent progression rates

We followed the general strategy used in our previous studies [33–35] in which the initial placement into a CD4 category (1 = CD4>500 units, 2 = 350<CD4<500, 3 = 200<CD4<350, 4 = CD4<200, 5 = died of AIDS) and the daily probability of transitioning to a different CD4 category depend on set point viral load (SPVL) and treatment status. However, we modified the SPVL-dependent probability of progression to a higher CD4 category, in the absence of ART, to reflect the slower disease progression observed in people infected at younger ages [35] (Table 1).

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Table 1. Effect of age on progression in the absence of therapy.

https://doi.org/10.1371/journal.pcbi.1007561.t001

Age-specific condom usage

Based on reports of condom usage in developing countries [15–18], we modeled decreasing per act probabilities of using a condom, P_condom, with age as follows: where P_condom16 (default 0.8) is the probability that two 16-year-olds will use a condom, Age₅₀ (default 35) is the age at which condom usage drops to 0.5 * P_condom16, and AveAge is the average age of the partners.

Demographic setup

HIV-negative people were assumed to enter the sexually active population in our model at age 16 and die of natural causes according to age-specific mortality tables; the arrival rate was set so that the population will increase by ~1% per year in the absence of HIV-induced mortality. We set the initial age distribution so that the age distribution will be stable in the absence of HIV-induced mortality. Because our TERGM-based network model is computationally time-consuming, we set the initial population size (N) to 2,000. Simulations yielding interesting or important results were then re-run with N = 10,000 or 20,000. Since key transmission rate parameters, such as the average number of partners per person, are independent of population size for sexually transmitted diseases [42, 43], our results should generalize to larger populations.

Treatment cascade

We assume a certain percentage of the population (default 95%) is linkable; i.e., could become virally suppressed in response to a TasP campaign. We assumed that 100% of the linkable population is tested annually but only a subset of diagnosed people, the size of which we vary in our simulations, were linked to effective care, resulting in a suppressed viral load. In our default runs, individuals remained in care indefinitely even if they were originally linked to care due to a factor (e.g., youth) that no longer applies.

Rollout of ART prior to targeted TasP campaigns

To establish the presence of suppressive ART in the population prior to our targeted TasP campaign, we modeled both gradual and sudden rollout schemes where the number of people receiving suppressive ART increases linearly from zero treated, starting either 9 years (gradual) or 1 year (sudden) prior to the targeted TasP campaign, to where S_targ is the percentage of people who will be targeted in response to the subsequent targeted TasP campaign, I_pre is the number of infected people at the start of the pre-TasP rollout. The “/2” in the equation above signifies that the subsequent TasP campaign will roughly double the number of people receiving suppressive therapy in our model. Under both the gradual and sudden pre-TasP rollout schemes, random subsets of agents received suppressive ART. While gradual rollouts are more realistic, sudden rollouts allow for more precise statements about the percentage of people receiving ART at the start of the TasP campaign. That is, under a gradual rollout, the percent of people receiving ART prior to the TasP campaign is a complex function of other dynamic variables (e.g., the age distribution and the percentage of people in the two relationship-length groups). We focused, therefore, on sudden pre-TasP rollouts for summary figures with S_targ in the x-axis.

Parameter tuning

While most of the parameters are based directly on data, we adjusted the maximum probability of infection (default 0.0025), mean degree (default 0.75), and the male- and female-specific concurrency parameters (defaults 0.25 and 0.04) to give prevalence and incidence values and male-to-female infection ratios that fall within ranges seen in sub-Saharan epidemics. [1, 2, 26, 44].

Simulated TasP campaigns

Following the pre-TasP ART rollout, we introduced a targeted TasP campaign that increases the number of HIV+ people receiving suppressive ART ~2-fold to S_targI₀, where I₀ is the number of infected people at the start of the TasP campaign. (This will be an exact doubling if the number of infected people does not change between the start of the pre-TasP rollout and the start of the TasP campaign). To allow us to make more precise statements about the percentage of people treated, we stipulated for our default runs that the TasP campaign was implemented instantly (as we did for the pre-TasP rollout). After the TasP target has been hit, the absolute number of individuals receiving suppressive ART was assumed to grow annually at rate r (default 2% per year) to account for population growth and general increases in public health expenditures. That is, we capped the number of people receiving ART at S_targI₀(1+r)^t, where t is the number of years since the start of the TasP campaign.

Under the targeted TasP campaigns, different categories of individuals were targeted for linkage to effective care in different scenarios. Targeting strategies included: age (e.g. “under age 25”), immunological status (e.g., “CD4<500”), combinations of age and immunological status (e.g., “Under 25, CD4 < 500”), viral load (e.g., “SPVL”), and no targeting at all (“random”) (Table 2). Several of the strategies include a targeting hierarchy within the primary target range. “Under age 30”, for example, targets those under age 25 first, and then those between ages 25 and 30. In these cases, agents are linked to care at random within each successive target group until the overall treatment limit is reached. To ensure that equal numbers are treated under all strategies (prior to one strategy linking 100% of people to effective care), all strategies included a final “random” (untargeted) component that is applied once all of the people in the target groups have been linked to effective care.

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Table 2. Key TasP strategies modeled in this paper.

https://doi.org/10.1371/journal.pcbi.1007561.t002

In the era of test-and-treat, the treatment strategies employed in Sub-Saharan African countries now most closely reflect the randomized treatment model we use in the United States. We included two additional non-random strategies, SPVL- and CD4-based targeting in order to understand how age-based strategies perform against other strategies that have the potential to outperform random (untargeted) TasP. Doing so allows us to separate the general effect of having a structured, targeted campaign from the specific effects of focusing on younger age groups. We are aware that SPVL, as defined in Table 2, has never been used and that CD4-based targeting, while once used, is no longer recommended. We are, furthermore, aware that “CD4<500” and “SPVL”, respectively, assume access to information that will be inconsistently or rarely available.

For the simulations with “sudden” pre-TasP rollouts, we quantified impacts as a function of S_targ, the percent of infected people linked to effective care in response to the TasP campaign. We note that S_targ gives the percentage of HIV+ people receiving suppressive therapy at a single point in time (i.e., just after the TasP target has been hit). For a TasP campaign that succeeds in reducing the number of untreated people, the percentage of HIV+ people receiving ART will exceed S_targ as the treatment expands at the annual post-TasP rate, r. For a TasP campaign that fails to reduce the number of untreated people, the percentage of HIV+ people receiving ART will remain at or fall below S_targ depending on how fast the epidemic expands compared to the post-TasP expansion rate r.

For each value of S_targ, we quantified the impact of TasP campaigns using: mean incidence 20–25 years after campaign initiation; the total number of AIDS deaths and person-years of therapy during the first 25 years of the campaign; the percentage of the population initiating suppressive ART that was not a part of a target group; and the percentage of untargeted infected people receiving suppressive ART. Since strategies that do not suppress viral load in a significant percentage of people outside the target group could be considered unethical, we used the two last measures as screening tools to help us decide which strategies to investigate in more detail.

For strategies for which we noted a conflict between short- and long-term AIDS death rates, we calculated time-discounted AIDS deaths—a measure that quantifies the tendency of people to prefer strategies that minimize deaths in current years over strategies that minimize deaths in later years.

We also considered a gradual version of the TasP rollout, in which the absolute number of people being treated increased linearly (without any cap) beginning 9 years before the start of the targeted TasP campaign. To prevent 100% of newly treated people belonging to a target group in the first few years of the TasP campaign, we modified these gradual simulations so that 40% of newly treated people were automatically treated at random and the other 60% were treated according to the targeting rules in Table 2 after the start of the TasP campaign. This capped the percentage of newly treated people who were treated specifically because they belonged to the target group at 60% of HIV+ people receiving ART.

Sensitivity analyses

To test the dependence of our results to parameter values, we conducted a series of sensitivity analyses in which we altered or removed parameters. For these sensitivity analyses, we focused on the TasP target (S_targ value) needed to reduce long-term incidence (i.e., incidence 20–25 years after the start of the TasP campaign) 20-fold compared to a no-ART control. In preliminary work, we found that this 20-fold reduction allows for more meaningful comparisons than an absolute cutoff (e.g., incidence less than 0.1 infections/100 person-years) because parameter changes can dramatically change the baseline incidence rate. Given our 2% annual post-TasP increase in viral suppression, we found in preliminary work that a 20-fold reduction in incidence led to eventual viral eradication in all of the scenarios studied here. For sensitivity tests in which the parameter perturbation resulted in a substantially weakened epidemic, we increased an unrelated parameter (baseline transmission rate) to create a more realistic epidemic and reduce run-to-run variation.

As a part of these sensitivity analyses, we explored the effect of allowing 10% of treated individuals to discontinue treatment each year [46–49]. We did not include this in the default model because members of a target group who discontinue ART are more likely to be relinked to care than those who are not. This effect could, in principle, cycle an increasing percentage of people into the target group into ART as people outside the target group drop out.

Statistics and replication

Error bars in the figures represent standard deviations using n-1 degrees of freedom where n is the number of replicates. Experiments shown in the figures and tables were replicated either 16 (default) or 32 (marked by ++ signs in the summary table below) times. For some of the experiments described in the text, we replicated the simulation 120 times.

Epidemic

Our base model gives a pre-TasP epidemic that reproduces broad features of sub-Saharan African epidemics [1, 44], namely: an initial prevalence of ~10% and a decline in incidence, though not necessarily prevalence, following a ramp-up in treatment (Fig 2A and 2B, years -0 to 10). Prior to the TasP campaign reducing incidence, the model predicts 2- to 3-fold higher prevalence in young women than young men and higher prevalence in people between 25 and 50 than in people under 25 or over 50, as reported by Shisana et al. [26]. In our model, women under 30 tend to get infected by older men (S1 Fig), while men over 30 tend to get infected by younger women (S2 Fig). Importantly, our model predicts that adolescents will typically get infected by partners who are under 30 (S1 Fig). This suggests that treating people under 30 could help to protect uninfected adolescents. Consistent with data in ref [50], our base model predicts a median inter-infection time of ~2.4 years (S3 Fig). Although considerably lower than it is in the presence of a very-high-risk group (see the section on sensitivity analyses below), our baseline model has a greater-than-random percentage of agents with many partners (S4 Fig).

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Fig 2.

Simulations showing the percent of the population that is HIV+ (panels a-c, red lines), HIV+ and receiving treatment (panels a-c, blue lines), and HIV+ and receiving treatment specifically due to being part of a target group (panels a-c, purple lines); incidence (panels d-f); and AIDS death rates (panels g-h) following our “CD4<500” (left-side), “random” (middle), and “under age 30” (right side) treatment-as-prevention (TasP) strategies. To account for existing treatment, we assume a linear increase in the number of people receiving suppressive therapy beginning nine years before the TasP campaign. The TasP campaign immediately increases the percentage of HIV+ people receiving therapy to ~60%. Once the TasP campaign starts, the model uses the CD4-, random- or age-based strategies to link a subset of unsuppressed diagnosed people to care. The 2%/yr increase in the number treated after the campaign reflects population growth and generalized increases in health care efficiency or expenditures. Thick lines give the mean of 16 independent replicates; thin dashed lines show individual runs. The decline in prevalence of treated people after year 15 in panel c (blue lines) occurs because prevalence decreases once all infected agents are treated. The black lines in panels h and i give the means from the CD4<500 simulations in panel g (to highlight differences between short- versus long-term effects of “CD4<500” and “Under age 30”). For these simulations, we set the initial population size to 20,000 to reduce run-to-run variation.

https://doi.org/10.1371/journal.pcbi.1007561.g002

Advantages to youth-focused TasP

We compared age-based TasP strategies to untargeted TasP (random), a theoretical strategy (SPVL-based) and a historical (CD4-based) strategy (see Table 2 for definitions). In Fig 2 we show the number of infected, the number treated, incidence, and AIDS death rates under the “CD4<500”, “random”, and “under age 30” targeting strategies in a simulation in which ~60% of infected people received suppressive therapy as a result of the TasP campaign. In contrast to the “CD4<500” strategy and random (untargeted) TasP, where the final mean incidences were ~0.65 and ~0.3, respectively, incidence in the “under age 30” strategy dropped to less than 0.1 infections/100 person-years in all (16/16) replicate simulations ~15 years after the start of the TasP campaign.

The increase in prevalence under the "CD4<500" targeting strategy in Fig 2A is due primarily to HIV-infected people living longer and the failure of this strategy to reduce incidence to zero. However, we note that demographic shifts (AIDS deaths reducing the number of people between ages 30 and 50) also contribute to increasing prevalence in this and other simulations. This attrition increases the proportion of people who have a higher risk of getting infected (i.e., young adults) in the first 20 years of the TasP campaign. Also, because our baseline model includes comparatively favorable conditions for the spread of virus, the average SPVL increases by about ~0.1 logs between years 0 and 20 (due to a well-known evolutionary tradeoff verified in earlier versions of our software [34]). This small increase in the average SPVL contributes somewhat to the increasing prevalence during this period.

The purple lines in Fig 2A and 2C give the percent of the population that was treated specifically due to their having CD4 counts below 500 and being under age 30, respectively. For the “Under age 30” strategy, the percent of treated people who were treated specifically due to being <30 peaked at ~38% after ~6 years, then declined slowly to ~32% at year 15 (after which ~100% of people were virally suppressed). For the “CD4<500” strategy, the percent of treated people who were treated specifically due to having a low CD4 count increased monotonically from ~44% at year 1 to ~83% at year 25. This indicates that the “under age 30” strategy succeeded in reducing incidence despite being significantly less exclusionary that the historical “CD4<500” strategy.

Fig 3 presents results for a broader range of strategies and for multiple values of S_targ (percent infected people linked to effective care in response to the TasP campaign) demonstrating the range of scenarios over which age-based strategies convey an advantage. Fig 3A (average incidence 20–25 years after implementing the TasP campaign) shows that S_targ had to be set to 70% and 80%, respectively, to reduce incidence rates to negligible levels for the “random” and “CD4<500” targeting strategies. Under the age-based targeting strategies, by contrast, incidence could be reduced to negligible levels using S_targ values of 40% to 60%. Age-based strategies also resulted in fewer AIDS deaths over 25 years than random or “CD4<500” (Fig 3B). The SPVL strategy gave results comparable to the age-based strategies for S_targ > = 50%, but somewhat worse results for S_targ < 50%. With the exception of the “CD4<500” strategy, which resulted in more person-years of therapy for S_targ between 60 and 80%, the total number of person-years of treatment over the course of the simulation was similar for all strategies (Fig 3C). This shows that the success of the age-based strategies is not due to these strategies treating more people. In particular, it shows that this success is not due to the longer lifespan of younger people starting therapy (relative to old people starting therapy) increasing the number of person years of therapy.

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Fig 3.

Effect of targeting strategy and the TasP target (S_targ) on: (a) incidence 20–25 years after the TasP campaign, (b) AIDS deaths between years 0 and 25, (c) person-years of therapy (included to demonstrate that the age-based strategies did not inadvertently result in more people being treated), and (d) the percentage of HIV+ people initiating treatment at the start of the TasP campaign who were not a member of a target group. For random (untargeted) TasP, the values in panel d will always be 100% (data omitted from graph). The apparent decline in panel d between 90% and 100%, a decline not seen in other experiments, reflects statistical noise accentuated by the fact that only 95% of the population is linkable in this simulation (i.e., S_targ = 100% translating to 95% suppression). Each point is the mean of 16 replicates. Bars give standard deviations (SDs). For normally distributed data, 95% confidence intervals would be ~55% the width [since t_0.025,15 *SD/sqrt(15) = ~0.55*SD]. For this simulation, we set the initial population size to 10,000. In this and subsequent figures we assumed sudden pre-TasP rollouts so that the TasP campaign will roughly double the number of virally suppressed people.

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Fig 3A and 3B also show that the benefit of age-based targeting depends on the percentage of the overall population that can be virally suppressed. For high levels of suppression (i.e., S_targ > = 80%), the advantage to age-based targeting largely disappears. A similar effect can be seen using our alternative (gradual) rollout strategy in which the number of people being treated increases linearly with time: age-based targeting is highly effective when rollouts are slow or moderate (S5 Fig, left and middle columns); however, the advantage to age-based targeting disappears when treatment ramps up quickly (S5 Fig, right column).

We note that Figs 2 and 3 assume that 95% of any given target group could be reached during the treatment campaign. We kept this value high in order to demonstrate the underlying potential of age-based TasP. In the Sensitivity Analysis section below, we report on what happens when this percentage is altered.

Inclusivity / exclusivity of strategies

A targeting strategy that focuses the majority of resources on a single group is not an acceptable strategy due to the ethical issues of potentially leaving a proportion of the population without access to care. Of the five “non-random” strategies in Fig 3, the percentage of the HIV+ population initiating suppressive therapy at the start of the TasP campaign that was not a member of a target group was highest under the “under age 25” and “under age 30” strategies (Fig 3D).

For S_targ = 60% and the “under age 25” strategy, for example, ~87% of people initiating suppressive therapy at the start of TasP campaign fell outside the target group—a result that can be attributed to there being relatively few HIV+ people under the age of 25. For the “under age 30”, “under age 35”, “SPVL”, and “CD4<500” strategies, the percentages outside the targeted group were 58%, 35%, 7% and 0%, respectively (Fig 3D). If we were to include people who were virally suppressed prior to the TasP campaign, the percentage of treated people who were not a member of the target group for the “under age 25”, “under age 30” “under age 35”, “SPVL”, and “CD4<500” strategies, would jump slightly (to ~90%, ~70%, ~50%, ~25%, and ~10%, respectively). In subsequent simulations, we focus mainly on comparing the “under age 25” and “under age 30” strategies and variants thereof with the “random” and/or “CD4<500” strategies.

The y-axis in Fig 3D is similar to S_targ in that it quantifies “inclusivity” at a single point in time (i.e., just after the TasP target has been hit). For TasP campaigns that reduced prevalence, the percentage of untargeted infected individuals receiving suppressive therapy increased over time (as can be inferred from the narrowing difference between the red and blue lines in Fig 2C). However, for the TasP campaigns that failed to reduce prevalence, the percentage of untargeted individuals receiving suppressive therapy either decreased or remained roughly constant (Fig 2C before prevalence flattened around year 20) or in subsequent years. In other words, the successful TasP campaigns became more inclusionary over time, while unsuccessful TasP campaigns either became more exclusionary or retained similar levels of inclusivity over time.

Fortunately, our simulations suggest that one will not have to wait long to find out whether a campaign will succeed. For the successful “under age 30” strategy shown in Fig 2, for example, we observed a ~2-fold drop in incidence within 2 years of starting the TasP campaign. While drops in incidence are unlikely to be as rapid under more realistic scale-ups, incidence is a highly sensitive measure that can, with the aid of an epidemiological model, predict whether an in-progress TasP campaign is likely to reduce prevalence. In cases where incidence cannot easily be calculated, age-based TasP can be assessed from HIV prevalence in cohorts of young people who become sexually active after starting the TasP campaign. For our “under age 30” strategy in Fig 2, for example, we observed a 4.8-fold drop in prevalence in those under 25 six years into the TasP campaign.

Increases in S_targ above a specific threshold (given by points in Fig 3D in which the lines intersect the x-axis) result in treatment being directed almost entirely to people outside the target group. For the “under age 25” and “under age 30” strategies we observed continued benefits (e.g., reductions in AIDS deaths) as S_targ increased beyond this threshold (Fig 3A and 3B). For the “under age 25” strategy in Fig 3A, for example, we observed lower incidence and fewer AIDS deaths for S_targ = 20% than for S_targ = 10% (the value of S_targ at which all reachable agents under the age of 25 have been linked to care). While not surprising, this is important for broader discussions about age-based TasP (see last paragraph of discussion).

Time-discounted AIDS death rates

While age-based targeting greatly reduces the number of deaths over the long-term, it comes at the cost of slightly more AIDS deaths relative to CD4-based targeting in the years immediately following the TasP campaign (as illustrated in Fig 2I). This tradeoff can be quantified using time-discounted AIDS deaths; i.e., a measure of AIDS deaths that gives less weight to future deaths than current deaths. In S6 Fig, we show that, for discount rates between 0 and 7% per year, age-based targeting reduces time-discounted AIDS deaths compared to the other strategies in Fig 3.

Sensitivity analyses

To test the extent to which our results depend on parameter values and functional forms, we conducted a series of sensitivity analyses in which we altered parameters identified a priori as being likely to contribute to the success of age-based TasP targeting (see methods for details). In Table 3, we demonstrate continued benefits of age-based targeting when: (i) the probability of transmission was increased; (ii) all agents have the same average relationship duration; (iii) young and old people have the same coital frequency; (iv) young people no longer have a higher per-act risk of infection; (v) the average age difference between male and female partners increased to 8 years; (vi) the average difference in ages after accounting for the male-female age difference has increased to 8 years; (vii) the age-related homophily term was removed in its entirety so that young people no longer preferentially form relationships with other young people; (viii) the percentage of people who could potentially be linked to HIV-1 treatment services was decreased; (viii) testing rates were varied; (ix), treated people have a small per-day probability of discontinuing treatment; (x) all agents have the same SPVL, and (xi) in a triple-perturbation experiment in which relationship durations, transmission rates, and probabilities of coitus were all independent of age (Fig 4 and Table 3, perturbation 14) (though in this case only "Under age 30" and "Under age 35" performed substantially better than untargeted TasP). We also observed benefits to age-based TasP when condom use was independent of age, though this is not surprising since our baseline model assumes that young people use condoms more often.

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Fig 4. Performance of age-based TasP in sensitivity experiment in simulations [Table 3, perturbation 14] in which all of the primary age-related risk factors except for age-related homophily were removed (i.e., in a model in which relationship durations, transmission rates, and probabilities were all independent of age).

(a) Incidence 20–25 years after the TasP campaign. (b) AIDS deaths between years 0 and 25. (c) Person-years of therapy. (d) Percentage of HIV+ people initiating treatment at the start of the TasP campaign who were not a member of a target group. Error bars present standard deviations based on 32 replicates.

https://doi.org/10.1371/journal.pcbi.1007561.g004

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Table 3. Sensitivity experiments in which we varied key age-related and epidemiological parameters.

https://doi.org/10.1371/journal.pcbi.1007561.t003

To keep our focus on normal age-related risks, we did not include a very-high-risk group in our base model. To explore the effect of adding a "very-high-risk" group to our model, we did a series of perturbation experiments in which we manipulated relationship durations for groups 1 and 2, made these groups age-independent, and/or changed the proportion of agents in the two groups. Table 3 (perturbations 3–6) gives some representative results. We found that age-based TasP greatly outperformed random (untargeted) TasP when members of group 1 have very high risks and do not transition to group 2 (Table 3, perturbation 3), as well as when a greater percentage of people belong to group 1 and in which a group 1 has moderately or greatly elevated risks (Table 3, perturbations 4 and 5, respectively). (We note that the coloring in Table 1 understates effects when percentages are high: in perturbations 4 and 5 age-based TasP doubled the number of people who did not have to treated in order to drive incidence to zero.) These perturbations, therefore, show that age-based TasP can be highly effective in a model with a risk group that results in a heavy-tailed partnership-distribution curve (S4 Fig).

However, when we pushed incidence even higher by reducing relationship durations in both groups and increasing the proportion of agents in group 1 (Table 3, perturbation 6), we found that none of the strategies could reduce incidence to zero despite 100% of eligible agents (i.e., 95% of all agents) receiving suppressive therapy. While incidence was unrealistically high, this establishes that TasP (age-based or not) is not assured of controlling the epidemic.

Age-based TasP also failed to provide an advantage over untargeted TasP in a “zero age risks” perturbation in which we eliminated age-related homophily and made relationship durations, transmission rates, and probabilities of coitus independent of age (Table 3, perturbation 15). While not surprising, this provides re-assurance that age-based TasP did not outperform the other strategies due to some unappreciated aspect of our model.

Contrary to our initial expectations, SPVL variation had little effect on the efficacy of age-based TasP (Table 3, perturbation 20). We found that untreated HIV+ people under the age of 30 have SPVLs that are roughly double those of untreated HIV+ people over 50, an increase that should translate to ~25% increase in the infectivity of untreated young people. However, this is proved to be fairly small compared to other age-based risks shown to have modest effects in Table 3. The probability of sex, for example, will be roughly halved by age 50, and yet we continued to a large advantage to age-based TasP when the term for age-based coital frequency was removed from the model (Table 3, perturbations 7 and 8).

The largest and most informative reductions in the efficacy of age-based TasP relative to random (untargeted) TasP occurred in perturbations in which we removed the age-related homophily term (Table 3, perturbations 13 and 15) and in which we reduced the maximum percentage of people who could be linked to care to 60–70% (Table 3, perturbations 17 and 18 and Fig 5). We note that neither age-based homophily nor overall linkage to care directly affects the susceptibility of a young person. Instead, they affect the probability that a young person’s partners will be infectious. Together these results point to a substantial contribution of age-specific herd immunity (ASHI) to the success of age-based TasP: in order for ASHI to work, a sufficient percentage of the partners of HIV- adolescents entering the sexually active population need to be virally suppressed.

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Fig 5. Performance of age-based TasP in simulations [Table 3, perturbation 17] in which only 70% of HIV+ people could be linked to care (i.e., only 70% would get tested and treated under a vigorous treatment campaign).

(a) Incidence 20–25 years after the TasP campaign. (b) AIDS deaths between years 0 and 25. (c) Person-years of therapy. (d) Percentage of HIV+ people initiating treatment at the start of the TasP campaign who were not a member of a target group. Error bars present standard deviations based on 32 replicates.

https://doi.org/10.1371/journal.pcbi.1007561.g005

While decreasing the maximum percentage of people who could be linked to care reduced the efficacy of age-based TasP, we found it remarkable that age-based TasP could succeed (albeit not as dramatically) in a model in which only 60% to 70% of agents could be linked to care (Fig 5 and Table 3, perturbations 17 and 18). Three factors that contributed to this success. First, the percentage of people who are not linkable decreases over time in the face of HIV-induced mortality. Second, and more interestingly, surviving HIV+ people who are not linkable became less infectious over time due to increases in their average age (since age-based TasP reduces incidence in young people) and reductions in their average viral load (since people infected with high SPVL viruses die sooner in the absence of therapy).

In most of the simulations in Table 3 where the value of S_targ needed to drive incidence to zero following age-based TasP was the same or only slightly lower than random (untargeted) TasP, we continued to see advantages to age-based TasP for lower values S_targ. For S_targ < 55 in Fig 5, final incidence and total AIDS deaths continued to be lower for the age-based strategies than for our “random” and “CD4<500” strategies. For some of these simulations, “SPVL” (which doesn’t depend on ASHI) reduced final incidence and AIDS deaths more than "under age 25” for selected S_targ values. However, we have not considered “SPVL” further because it is, as defined in Table 2, a theoretical strategy introduced for purposes of comparison. “SPVL” furthermore did not perform as well as “under age 30” in our baseline simulations (Fig 3A and 3B), and is considerably more restrictive (Figs 3D, 4D, and 5D).

Hybrid strategies combining age with CD4 status or sex

Our analyses have focused so far on strategies that consider age, sex, and CD4 status in isolation. We also studied strategies that integrated these in various combinations. Although we hypothesized that combining age and CD4 status for targeting might yield even better results than either factor in isolation, we did not see any clear advantages to strategies combining “under age 25” and either “CD4<500” or “CD4<200.” (S7 and S8 Figs). [For these simulations we first considered combinations of “Under age 25” and “CD4<500”, but these strategies were so exclusive (S7 Fig) that we switched to “CD4<200”-age hybrids.] CD4-based strategies that utilized age as a secondary criterion performed about the same as those that used only CD4 status, while age-based strategies that utilized CD4 status as a secondary strategy performed about as well as strategies that used only age (S7 and S8 Figs). Although there was a weak trend for “Under 25, CD4<200” to reduce time-discounted AIDS deaths relative to “Under age 25” for S_targ between 50 and 60% using a 7% discount rate, CD4-age hybrids did not reduce time-discounted AIDS deaths using the standard 3% discount rate (S9 Fig). These tests, in other words, failed to support our hypothesis that combining age and CD4 status would yield significantly better outcomes compared to straight age-based or CD4-based targeting.

Since young women tend to get infected by older men, we hypothesized that including a higher target age for men (e.g., men < 30, women < 25) might enhance the effectiveness of age-based TasP relative to sex-independent cutoffs; however, we did not see any significant advantages of “men <30, women<25” compared to “men <25, women < 30 (S10 Fig). The “men <30, women<25” and “men <25, women < 30” strategies, while considerably better than random, generated incidence rates and AIDS deaths that fell between the “under age 25” or “under age 30” strategies.