Download Contents Study Objective Agent Population Network

Supplemental Material for:
A C U TE HIV I N FE C TIO N T R A N S M IS S ION A M O N G P E OP LE W HO I N J EC T D R UG S
MA TU R E E P ID E M IC S E TT IN G
IN A
Daniel J ESCUDERO1, Mark N LURIE, PhD1, Kenneth H MAYER, MD2,3, Caleb WEINREB4,
Maximilian KING1, Sandro GALEA, MD5, DrPH, Samuel R FRIEDMAN, PhD6, Brandon DL
MARSHALL, PhD1
1.
2.
3.
4.
5.
6.
Department of Epidemiology, Brown University School of Public Health, Providence, RI, USA
Fenway Health, Boston, MA, USA
Beth Israel Deaconess Medical Center, Boston , MA, USA
Department of Systems Biology, Harvard Medical School, Boston, MA, USA
Boston University School of Public Health, Boston, MA, USA
National Development and Research Institutes, New York, NY, USA
This Supplemental Material includes additional information regarding the structure, calibration, and results
for the agent-based model.
Revsied: 7/1/16
Number of Supplementary Tables/Figures: 6
Word Count: 2,636
1
Contents
i.
Study Objective
ii.
Agent Population
iii.
Network Structure
iv.
Agent Behavior
v.
HIV Disease Progression and Treatment
vi.
HIV Transmission
vii.
Model Calibration
2
Study Objective
The agent-based model (ABM) was developed to examine the role of transmission during acute
HIV infection (AHI) in relation to total incidence among people who inject drugs (PWID) in a
mature epidemic setting. The importance and potential impact of this work is outlined in the
manuscript. Briefly, the contribution of this early and highly-infectious stage to overall
transmission among PWID may influence the effectiveness of certain prevention strategies, in
particular treatment as prevention (TasP). Due to the inherent difficulties of identifying, treating,
and virally suppressing cases before AHI has elapsed, it seems unlikely that TasP strategies will
be able to curb significant levels of transmission during AHI; therefore, this investigation has
been undertaken to deteremine the extent to which incident cases arise from those who are acutely
infected. Although the contribution of AHI to overall transmission has been investigated and
discussed heavily in the scientific literature [1-4], the focus has been almost exclusively on
epidemics driven by sexual risk behaviors, limiting generalizability to PWID.
Our model is adapted from previous versions of the ABM [5, 6], which have investigated the
roles of combination prevention strategies and treatment programs on the HIV epidemic (i.e.,
incidence) among PWID within the New York Metropolitan Statistical Area.
Agent Population
The ABM consists of individual agents (or ‘nodes’) that represent individuals within a virtual
population. Agents are stratified in three ways: drug use status (non-drug user [ND], non-injection
drug user [NIDU], and people who inject drugs [PWID]); sex (male, female); and sexual
orientation (woman who have sex with women [WSW], heterosexual women [HW], heterosexual
men [HM], and men who have sex with men [MSM]). Drug use status is defined as the following:
3
PWID – an agent that is actively injecting drugs (i.e., injected an illicit drug in the past year);
NIDU – an agent that is actively using hard drugs (i.e., crack, herion, cocaine, or
methamphetamine) by non-injection routes; ND – an agent that does not engage in either of these
behaviors. Heterosexual agents only engage in sexual relationships with those of the opposite sex.
In contrast, some MSM and WSW are able to form relationships with either sex, while other
MSM and WSW form relationships exclusively with other MSM and WSW, respectively. For the
purposes of this analysis, sex and sexual orientation assignment for each agent is presumed to be
time invariant. Agents may be characterized by any non-mutually exclusive set of the
fundamental strata (drug use status, sex, sexual orientation); for instance, an agent may be an
MSM PWID or a HW NIDU.
The probability of being assigned a given set of characteristics (i.e., sex, sexual orientation, and
drug-use status) is determined by the prevalence of these populations as estimated from empirical
data from NYC and other large urban settings in the United States during the study period (i.e.,
1996-2012). The distribution of these population characteristics at model initialization are
presented in Table S1. For instance, in this analysis, the prevalence of PWID in the agent
population at model initialization was assumed to be 1.9%; therefore, each agent has an
approximately 1.9% chance of being assigned drug-use status as a PWID. However, due to
changes in agent behavior and mortality, the PWID prevalence may change over the course of the
model study period.
Network Structure
At model intialization there are 100,000 agents within the virtual population, at which point they
begin forming connections with other agents (i.e., via an ‘edge’) that represent one of three
4
potential relationships: sexual, sexual and injecting, or injecting only. After initialization, the
model moves forward through time in discrete time-steps that represent a month of elapsed time.
During these transitions between time-steps, agents stochastically form, dissolve, or maintain
their current relationship connections. For instance, if Agent X is connected at time-step t to one
other agent (Agent Y), at time-step t+1 Agent X may form another concurrent relationship with
one or more of the remaining 99,998 agents in the model, dissolve the relationship with Agent Y,
or maintain a monogomaus relationship with Agent Y.
In addition to the dynamic nature of network connections (forming and dissolving of edges),
drug-using behaviors are also updated. Agents have the opportunity at each monthly time-step to
transition out of their current drug-using class into another (see section entitled Agent Behavior
below). Specifically, all three drug-using classes have the opportunity over time to transition to
one of the two other classes (however, NDs must first initiate non-injection drug use before they
can transition to injection drug use, and vice versa). Furthermore, risk behaviors for PWID are
updated at each time-step based on whether an agent has access to a needle and syringe program
(NSP), has enrolled in substance abuse treatment, or has been diagnosed with HIV after seeking
testing. For instance, an agent enrolled in a substance abuse treatment program will have a 50%
reduction in the baseline risk of HIV transmission, based on empirical data (see Table S2) [7, 8].
The probability of enrollment in substance abuse treatment for PWID or discontinuation from
such treatment were estimated from observational studies [9-12].
To construct the network (i.e., form relationships between agents), the program assigns a value
𝑘𝑖,𝑡 to each index agent 𝑖, where 𝑘𝑖,𝑡 is defined as the number of partnerships with other agents
5
per time step 𝑡. The value 𝑘𝑖,𝑡 is determined by a random sampling procedure from negative
binomial (NB) distribution functions, i.e.:
𝐾𝑖,𝑡 ~𝑁𝐵(𝑝, 𝑟) =
(𝑘𝑖,𝑡 + 𝑟 − 1)! 𝑟
𝑝 (1 − 𝑝)𝑘𝑖,𝑡 ,
(𝑟 − 1)! 𝑘𝑖,𝑡 !
𝑘𝑖,𝑡 ∈ ℵ0
with mean given by:
𝑚=
𝑝𝑟
1−𝑝
for all agents per time step. This method of partner formation means that partners are acquired
with probability p until r suitable partners are found. A previous version of the ABM has used
negative binomial distributions to determine partnership formation [5], and the use of NB
distributions have been shown by other studies to provide reasonable approximations of realworld partnership networks, in which the variance of the distribution is greater than would be
expected assuming constant-rate function (e.g., Poisson) [13].
We define different NB distribution functions for PWID agents and for non-PWID agents. The
functions were approximated by the authors based on available data from surveys of sexual and
injection relationship partnerships. The majority of these values are extrapolated from studies
with published annual estimates, and calibrated to fit the ABM’s monthly time-steps. The NB
distribution functions parameters for PWID and non-PWID agents are available in Tables S2-S4.
Figure S1 shows the approximate monthly distribution of unique partners for PWID and nonPWID agents, based on their distribution functions. To avoid overestimating the number of
unique partners over consecutive monthly sample drawings, we assigned a partner turnover
function that assumes each agent experiences a potential partner turnover event (where they
6
redraw from the partnership distribution) on average once a year. This method ensures that most
agents will not form an unrealistic number of unique partnerships over a given time period.
Agent Behavior
Agents who share a link in the network can engage in sexual and/or injecting behavior at each
time-step. A PWID-PWID agent dyad, for example, can engage in sexual activity exclusively,
injecting activity exclusively, or both, with probabilities 0.20, 0.60, and 0.20, respectively, based
on the published studies [14, 15]. The probability that any pair of PWID agents engage in
unprotected intercourse or share syringes are shown in Table S2. For other agent dyad
combinations, the probability that the pair engages in sexual risk behavior is shown in Tables S3
and S4. Probability functions assign agents to one or more prevention interventions at each time
step, which affects the likelihood of engagement in HIV risk behavior. For example, PWID
agents who use an NSP or enroll in substance abuse treatment are less likely to share syringes
(see Table S2). The number of sexual or needle sharing acts that a given dyad engage in (for a
specific time-step) is determined stochastically using a Poisson-distributed estimate, with a mean
of 2 sexual acts for MSM, 1.5 sexual acts for all other agents, and, for PWID, 1.3 injecting acts,
as determined by calibration procedures (see Model Calibration).
The probability of accessing HIV prevention interventions is interdependent, i.e., accessing one
affects the probability of accessing others in the same or future time steps. For example, PWID
agents using an NSP are more likely to access HIV testing during that time step, and also more
likely to initiate substance abuse treatment in later time steps. Agents also have specific
probability of cessation from prevention interventions, which represents relapse (in the case of
substance abuse treatment), or discontinuation of care (in the case of HAART).
7
Although sex and sexual orientation are time invariant characteristics (i.e., they do not change),
agents can initiate or cease drug use at any time step. PWID and NIDU have a 0.2% chance of
spontaneous drug use cessation, based on previous research [16], at which point they join the
NIDU and ND class of agents, respectively. Drug use initiation, however, is dependent on a given
agent’s current relationship(s), i.e., ND can transition to becoming a NIDU or a PWID only if the
ND has a current sexual relationship with a NIDU or PWID, respectively. In this manner, drug
use initiation is socially determined and explicitly a function of agent relationships. The
probabilities that an agent transitions to non-injection drug and injection drug use while in one of
these relationships were determined in previously model analyses, inductively from a calibration
procedure, that sought to reproduce empirical PWID and NIDU prevalence [6]. These
probabilities were transformed, as other previously calibrated parameters, to apply to monthly
rather than annual time steps.
In order to account for assortative mixing of the population, agents are more likely to form
connections to agents with whom their share characteristics. Agents are assortatively mixed based
on sex, sexual orientation, and drug use status. For example, PWID are four-times more likely to
form a relationship with other PWID (based on available data) [14, 15, 17], and NIDU are twice
as likely to for a relationship with NIDU, compared to other agent types.
HIV Disease Progression and Treatment
8
A detailed description of our HIV disease progression model has been published previously [6].
Following AHI, which lasts for 3 monthly time steps, based on previous data [18], HIV positive
agents in latent stage infection progress to AIDS at a rate dependent on treatment enrollment
status and adherence. This approach assures that there will be a large variation in time-to-AIDS
for HIV positive agent population, but also has a notable limitation in that all agents may progress
to AIDS with equal probability at each point following AHI, meaning that a very small portion
may progress to AIDS sooner than population-level estimate and clinical case-studies suggest
[19]. However, these instances of early progression are very rare. The probability of progression
to AIDS for each adherence category is listed in Tables S2-S4. There is a baseline probability of
all-cause mortality for each agent class, as well as an increased probability of all-cause mortality
for HIV-infected agents, based on their AIDS status and HAART adherence; these values are also
presented in Tables S2-S4. This means that the model does not directly estimate mortality as a
result of HIV infection or AIDS, rather it assigns unique values for all-cause mortality based on
disease and treatment statuses.
HIV Transmission
If an agent dyad consists of an HIV discordant pair (i.e., one agent is HIV-infected and one agent
is HIV-uninfected), then HIV transmission is possible, through either sexual or injection risk
behavior. During each time step in which the agents engage in risk behavior, the ABM
stochastically determines whether a transmission event will occur. To calculate the probability of
HIV transmission for each type of risk activity, we used population-level estimates of chronic
viral load set-point (approximately 4 log10 copies/mL), and late-stage infection (approximately
6.1 log10 copies/mL) values as baseline figures. We do not explicitly model partner roles in sexual
risk acts (i.e., receptive or insertive); rather, the HIV negative partner has a probability of
9
infection based on the average of receptive and insertive transmission probabilities. These values
were then input into meta-analytic data compiled by Baggaley et al,[20] and calibrated to
approximate HIV incidence among PWID in NYC during the study period [21]. Since reliable
estimates for per-act transmission risk from needle sharing, stratified by viral load levels, was not
available, we instead set needle-sharing transmission risk to approximately 0.01 for chronicallyinfected agents, and then calibrated the final value (0.0088) based on model output and metaanalytic data [22-24]. Since the main outcome of the study is the contribution of AHI to overall
transmission, the relative transmissibility of HIV during this stage compared to chronic infection
was considered based on the best available data, which contained diverse estimates. The best
available approximations for relative infectiousness (either explicitly calculated by other
investigators, or our team using per-act viral load specific estimates) ranged between about 2-fold
to 26-fold increased infectiousness of AHI to chronic infection [4, 18, 20, 25]. Subsequently, the
model assumes a 10-fold relative infectiousness for AHI, approximately the same ‘middle range’
value, of 9.2 used in the main analysis for another recent study by Eaton et al. examining acute
infection transmission [3]. HAART enrollment and the corresponding adherence classes each
attenuate the per-act probability of HIV transmission, and the resulting parameter estimates are
listed in Table S5.
Model Calibration
Calibration procedures for most model parameters, using an indirect iterative process, have been
described previously [5]. Since previous versions of the model (and their respective parameters)
were based on annual time-steps, all time-dependent parameters were scaled down to their best
monthly equivalents. All model inputs presented in Tables S1-S5 are the final values used for the
main analysis. Key model parameters (i.e., HAART initiation, AIDS mortality, mean injecting
10
acts, HIV transmission probabilities) were adjusted in an iterative fashion until model outputs
approximated estimates from available data among PWID in NYC (i.e., HAART enrollment, HIV
prevalence, HIV incidence) [21, 26-29]. For instance, initial model runs generated output
estimates significantly below empirical values for HAART enrollment among PWID in NYC,
above estimates of HIV prevalence among PWID after 1996, as well as HIV incidence greater
than observed among PWID. Per calibration protocol, we adjusted the input parameters believed
to mediate these output values, and for which there existed the greatest uncertainty for the input
values.
Specifically, HAART enrollment by the end of the 1996-2012 period had reached only 30%
among PWID, with initial initiation rates of 0.35% per month among those without access to
SAT, and 0.63% among those with access to SAT. These rates were incrementally increased (to
final values of 0.55% and 0.75%, respectively) until output on HAART coverage among PWID
closely matched empirical estimates in 2011 of 55% [29]. Similarly, HIV initial model outputs for
HIV incidence among PWID overestimated empirical data, and subsequently the mean value for
injection risk acts per partnership (originally 1.5 acts/partnerships) were decreased (to a final
value of 1.3 acts/partnership). We also decreased the per-act probability of HIV transmission via
needle-sharing acts (from 0.01 per unprotected act to 0.0088 per unprotected act) until model
output approximated empirical incidence [21]. Furthermore, the initial model output did not
reproduce the stark reductions in HIV prevalence observed among PWID in NYC following 1996
[27], believed to be in large part due to high AIDS mortality during this time. Since true all-cause
mortality for PWID with AIDS was difficult to estimate using available data [30-32], this input
was increased from the original estimate of 16.7 per 1,000 person-months, to 20.0 per 1,000
person-months, which resulted in improved approximation of HIV prevalence among PWID
11
throughout the study period. Although, as with previous analyses, this iterative calibration process
does not necessarily ensure model validity, they do ensure the elimination of parameter values
that prohibit the model from producing estimates highly disparate from published data.
12
Table S1: Population Distribution of the agent-based model at initialization
Male
PWID
NIDU
ND
Total
MSM
7.0%
7.8%
2.4%
3.0%
Female
HM
63.0%
57.2%
45.3%
47.0%
WSW
5.1%
6.0%
1.7%
2.5%
Total
HF
24.9%
29.0%
50.6%
47.5%
1.9%
6.4%
91.7%
100.0%
Abbreviations: HF – heterosexual female; HM – heterosexual male; PWID – people who inject drugs; MSM -men
who have sex with men; NIDU – non-injection drug users; NU – non-drug users; WSW – women who have sex with
women. Note: proportions estimated empirically from [26, 33-44].
13
Table S2: Parameter estimates for injection drug-using (PWID) agents.
Variable
Base Estimate
Source
MSM
HM
HF
WSW
Gender and sexual orientation distribution (%)
6
59
29
6
HIV prevalence (%)
22
12
11
14
AIDS prevalence (%)
13
Demographics
Proportion of HIV positive PWID on HAART (%)
7
[26, 34, 39, 45,
46]
[17, 46-48]
[49, 50]
20
[51-53]
Among HIV negative agents
1.25
[54-56]
Among HIV positive agents, not on HAART
8.33
[56, 57]
Among HIV positive agents, on HAART
1.66
[32, 56, 58]
All-Cause Mortality Rate (per 1,000 person-months)
Among Agents diagnosed with AIDS
20
[30-32]
Risk Behaviors
Unprotected intercourse‡ (probability for given act)
0.75
Reduction in sexual risk following HIV+ test (%)
10
Syringe sharing¶ (monthly probability)
[46, 47, 59, 60]
40
[52, 61, 62]
0.20
Reduction in injecting risk with SA treatment (%)
50
Injection drug use cessation (monthly probability)
0.00167
[46, 48, 63]
[7, 64]
[16]
Network Parameters
Number of monthly sexual and/or injecting partners*
NB(r = 7, p = 0.7)*
[14, 15, 17]
Behavior with partner(s) (annual probability)
[14, 15]
Sexual activity exclusively
0.20
Injecting activity exclusively
0.60
Sexual and injecting activity
0.20
Assortative mixing† (%)
50
80
50
[14, 15, 65, 66]
Substance Abuse Treatment (monthly probability)
Probability of initiation, given no NSP access
0.0077
[9, 10]
Probability of initiation, given NSP access
0.0161
[9, 11, 12]
Discontinuation§ at t = j, given initiation at t < j
0.0556
[9, 67]
Test for HIV, given no NSP access
0.0233
[68]
Test for HIV, given NSP access
0.0476
[68]
HAART initiation, given no SA treatment
0.0055
[69]
HAART initiation, given SA treatment
0.0075
[69, 70]
HAART discontinuation, given no SA treatment
0.0344
[69, 71, 72]
HIV Testing & Counseling (monthyly probability)
HIV Treatment Parameters (monthly probability)
Continues on next page
14
Table S2 Continued
Variable
Base Estimate
MSM
HAART discontinuation, given SA treatment
Proportion achieving ≥90% adherence to HAART (%)
#
HM
HF
Source
WSW
0.0182
[73]
60
[74]
Progression to AIDS (annual probability)
[75-77]
Not on HAART
0.1538
0% – 29% adherent to HAART
0.1538
30% – 49% adherent to HAART
0.1136
50% – 69% adherent to HAART
0.0087
70% – 89% adherent to HAART
0.0069
≥90% adherent to HAART
0.0020
Abbreviations: HAART – highly active antiretroviral therapy; HF – heterosexual female; HM – heterosexual male;
IDU – injection drug user; MSM – men who have sex with men; NB = negative binomial distribution; NSP – needle
and syringe exchange program; SA – substance abuse; WSW – women who have sex with women.
Notes: † – defined as proportion of partners from preferred sexual orientation and same drug use strata;
‡ – defined as <100% correct condom use between agent dyads; * – number of partners sampled from a negative
binomial distribution with parameters number of failures r = 7 and success probability p = 0.7;
¶ – defined as <100% sterile syringe use with injecting partners; § – agents who discontinue treatment at t = j can reinitiate treatment at some t > j with probability p = 0.0556; # – 60% of agents achieve ≥90% of adherence upon
initiating HAART (the remaining 40% are assigned to four other quartiles [0% - 29%, 30% - 49%, 50% - 69%, 70% 89%] with probability 0.10)
15
Table S3: Parameter estimates for non-injection drug-using (NIDU) agents.
Variable
Base Estimate
Source
MSM
HM
HF
WSW
Gender and sexual orientation distribution (%)
7
53
33
7
HIV prevalence (%)
28
7
[41, 42, 78-80]
AIDS prevalence (%)
14
4
[49, 50]
Demographics
Proportion of HIV positive NIDU on HAART (%)
15
[37, 40-44]
[51, 52]
All-Cause Mortality Rate (per 1,000 person-months)
Among HIV negative agents
.583
[55]
Among HIV positive agents, not on HAART
3.33
[49]
Among HIV positive agents, on HAART
Among Agents diagnosed with AIDS
1
[49, 76]
6.67
[49, 81]
Risk Behaviors
Unprotected intercourse‡ (monthly probability)
Reduction in sexual risk following HIV+ test (%)
0.55
0.85
0
40
Non-injection drug use cessation (annual probability)
[40, 42, 43, 82]
[83-85]
0.0016
[16]
Network Parameters
Number of monthly sexual partners
NB(r = 5, p = 0.8)*
Assortative mixing† (%)
90
Probability of IDU sex partner (per time step)
50
[14, 40, 42]
[40, 86-88]
0.015
[78, 89]
Probability of initiation
0.0075
[10]
Discontinuation§ at t = j, given initiation at t < j
0.0556
[90]
Substance Abuse (SA) Treatment (annual probability)
HIV Testing & Counseling
Test for HIV (monthly probability)
0.0280
0.0050
[88, 91]
HIV Treatment Parameters (annual probability)
HAART initiation, given no SA treatment
0.0067
[92]
Continues on next page
16
Table S3 Continued
Variable
Base Estimate
MSM
HM
HF
Source
WSW
HAART initiation, given SA treatment
0.0117
[92, 93]
HAART discontinuation, given no SA treatment
0.028
[71, 72]
HAART discontinuation, given SA treatment
0.0167
[73]
60
[74]
Proportion achieving ≥90% HAART adherence (%)#
Progression to AIDS (monthly probability)
[32, 75, 77]
Not on HAART
0.005
0% – 29% adherent to HAART
0.005
30% – 49% adherent to HAART
0.0039
50% – 69% adherent to HAART
0.0032
70% – 89% adherent to HAART
0.0025
≥90% adherent to HAART
0.0008
Abbreviations: HAART – highly active antiretroviral therapy; HF – heterosexual female; HM – heterosexual male;
IDU – injection drug user; MSM – men who have sex with men; NB = negative binomial distribution; SA –
substance abuse; WSW – women who have sex with women.
Notes: † – defined as proportion of partners from preferred sexual orientation and same drug use strata; ‡ – defined
as <100% correct condom use between agent dyads; * – number of partners sampled from a negative binomial
distribution with parameters number of failures r = 5 and success probability p = 0.8; § – agents who discontinue
treatment at t = j can re-initiate treatment at some t > j with probability p = 0.18; # – 60% of agents achieve ≥90% of
adherence upon initiating HAART (the remaining 40% are assigned to four other quartiles [0% - 29%, 30% - 49%,
50% - 69%, 70% - 89%] with probability 0.10)
17
Table S4: Parameter estimates for non-drug using agents.
Variable
Base Estimate
Source
MSM
HM
HF
WSW
Gender and sexual orientation distribution (%)
2.4
45.3
50.6
1.7
HIV prevalence (%)
16
Demographics
AIDS prevalence (%)
1
7
Proportion of HIV positive non users on HAART (%)
[33, 35,
36]
[41, 80,
94, 95]
[94]
30
24
[96]
All-Cause Mortality Rate (per 1,000 person-years)
Among HIV negative agents
0.417
[97]
Among HIV positive agents, not on HAART
3.333
[98]
Among HIV positive agents, on HAART
0.667
[32, 76,
99]
Among Agents diagnosed with AIDS
6.667
[76, 81]
Risk Behaviors
Unprotected intercourse‡ (prob per given act)
Reduction in sexual risk following HIV+ test (%)
0.40
0.70
0.75
0.
50
60
[40, 100103]
[83-85]
Network Parameters
Number of monthly sexual partners
NB(r = 5, p = 0.8)*
Assortative mixing† (%)
90
100
50
[35, 36,
88, 102105]
[36, 40,
87, 88]
HIV Testing & Counseling
Test for HIV (monthly probability)
0.0208
0.0050
[88, 91,
95]
HIV Treatment Parameters (monthly probability)
HAART initiation
0.0117
[93]
HAART discontinuation
0.0125
[106, 107]
Proportion achieving ≥90% adherence to HAART (%) #
60
[108]
Continues on next page
18
Table S4 Continued
Variable
Base Estimate
MSM
HM
HF
Progression to AIDS (annual probability)
Source
WSW
[32, 75, 77]
Not on HAART
0.005
0% – 29% adherent to HAART
0.005
30% – 49% adherent to HAART
0.0039
50% – 69% adherent to HAART
0.0032
70% – 89% adherent to HAART
0.0025
≥90% adherent to HAART
0.0008
Abbreviations: HIV – human immunodeficiency virus; HAART – highly active antiretroviral therapy; HF –
heterosexual female; HM – heterosexual male; MSM – men who have sex with men; NB = negative binomial;
WSW – women who have sex with women.
Notes: † – defined as proportion of partners from preferred sexual orientation and same drug use strata; ‡ – defined
as <100% correct condom use between agent dyads; * – number of partners sampled from an offset negative
binomial distribution with parameters number of failures r = 5 and success probability p = 0.8 for MSM, r = 1 and p
= 0.6 for WSW, and r = 1 and p = 0.75 for HF/HM; # – 60% of agents achieve ≥90% of adherence upon initiating
HAART (the remaining 40% are assigned to four other quartiles [0% - 29%, 30% - 49%, 50% - 69%, 70% - 89%]
with probability 0.10)
19
Table S5: Calibrated HIV transmission and disease progression parameters.
Variable
Not on
HAART
Adherence to HAART
0 – 29% 30 – 49% 50 – 69% 70 – 89%
Source
≥90%
HIV Disease Progression Parameters
0.0051
0.0051
0.0039
0.0032
0.0025
0.0008 [32, 77, 109]
Risk per syringe sharing act (chronic phase)
0.0088
0.0088
0.0070
0.0035
0.0018
0.0001 [22-24]
Risk per unprotected anal sex act (chronic phase)
0.0066
0.0066
0.0053
0.0026
0.0013
0.0001
Risk per unprotected vaginal sex act (chronic
phase)
0.0019
0.0019
0.0015
0.0008
0.0004
Progression to AIDS (monthly probability)
HIV Transmission Parameters
20
[20, 110,
111]
[20, 110,
0.0001
112-114]
Figure S1: Number of monthly sexual or injecting partners among agents within the agentbased model
0.35
0.3
Proportion of Agents
PWID
Non-PWID
0.25
0.2
0.15
0.1
0.05
0
0
1
2
3
4
5
6
7
8
9
10
Number of Partners
Abbreviations: PWID – people who inject drugs
Note: Among PWID agents, partners may be either sexual or injecting, however among nonPWID agents all partners are sexual
21
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