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RESEARCH ARTICLE
Agent-Based Model Forecasts Aging of the
Population of People Who Inject Drugs in
Metropolitan Chicago and Changing
Prevalence of Hepatitis C Infections
Alexander Gutfraind
1,2,3☯
*, Basmattee Boodram
1☯
, Nikhil Prachand
4
,
Atesmachew Hailegiorgis
5
, Harel Dahari
2,6‡
, Marian E. Major
3‡
*
1 Division of Epidemiology and Biostatistics, School of Public Health, University of Illinois at Chicago,
Chicago, Illinois, United States of America, 2 The Program for Experimental & Theoretical Modeling,
Department of Medicine, Loyola University Medical Center, Maywood, Illinois, United States of America,
3 Center for Biologics Evaluation and Research, Food and Drug Administration, Silver Spring, Maryland,
United States of America, 4 STI/HIV Surveillance, Chicago Department of Public Health, Chicago, Illinois,
United States of America, 5 Department of Computational Social Science, George Mason University, Fairfax,
Virginia, United States of America, 6 Theoretical Division, Los Alamos National Laboratory, Los Alamos,
New Mexico, United States of America
☯ These authors contributed equally to this work.
‡ HD and MM are joint senior authors.
* marian.major@fda.hhs.gov (MM); agutfrai@uic.edu (AG)
Abstract
People who inject drugs (PWID) are at high risk for blood-borne pathogens transmitted dur-
ing the sharing of contaminated injection equipment, particularly hepatitis C virus (HCV).
HCV prevalence is influenced by a complex interplay of drug-use behaviors, social networks,
and geography, as well as the availability of interventions, such as needle exchange pro-
grams. To adequately address this complexity in HCV epidemic forecasting, we have devel-
oped a computational model, the Agent-based Pathogen Kinetics model (APK). APK
simulates the PWID population in metropolitan Chicago, including the social interactions that
result in HCV infection. We used multiple empirical data sources on Chicago PWID to build a
spatial distribution of an in silico PWID population and modeled networks among the PWID
by considering the geography of the city and its suburbs. APK was validated against 2012
empirical data (the latest available) and shown to agree with network and epidemiological
surveys to within 1%. For the period 2010–2020, APK forecasts a decline in HCV prevalence
of 0.8% per year from 44(±2)% to 36(±5)%, although some sub-populations would continue
to have relatively high prevalence, including Non-Hispanic Blacks, 48(±5)%. The rate of
decline will be lowest in Non-Hispanic Whites and we find, in a reversal of historical trends,
that incidence among non-Hispanic Whites would exceed incidence among Non-Hispanic
Blacks (0.66 per 100 per years vs 0.17 per 100 person years). APK also forecasts an
increase in PWID mean age from 35(±1) to 40(±2) with a corresponding increase from 59
(±2)% to 80(±6)% in the proportion of the population >30 years old. Our studies highlight the
importance of analyzing subpopulations in disease predictions, the utility of computer
PLOS ONE | DOI:10.1371/journal.pone.0137993 September 30, 2015 1/23
OPEN ACCESS
Citation: Gutfraind A, Boodram B, Prachand N,
Hailegiorgis A, Dahari H, Major ME (2015) Agent-
Based Model Forecasts Aging of the Population of
People Who Inject Drugs in Metropolitan Chicago and
Changing Prevalence of Hepatitis C Infections. PLoS
ONE 10(9): e0137993. doi:10.1371/journal.
pone.0137993
Editor: Lars Kaderali, University Medicine
Greifswald, GERMANY
Received: July 29, 2015
Accepted: August 16, 2015
Published: September 30, 2015
Copyright: This is an open access article, free of all
copyright, and may be freely reproduced, distributed,
transmitted, modified, built upon, or otherwise used
by anyone for any lawful purpose. The work is made
available under the Creative Commons CC0 public
domain dedication.
Data Availability Statement: The source code of
APK and all related tools can be accessed on the
website [https://github.com/sashagutfraind/apk]. The
software includes compiled binaries (available from
https://zenodo.org/record/21714) that could be run on
any system that supports Java 7 SE and simulated
PWID databases to enable experimentation with
APK. The authors are unable to provide direct access
to the underlying PWID databases because they are
considered Protected Health Information under
institutional, state and federal laws. The Institutional
simulation for analyzing demographic and health trends among PWID and serve as a tool for
guiding intervention and prevention strategies in Chicago, and other major cities.
Introduction
HCV is a major public health threat with 130–150 million chronic cases worldwide [1], includ-
ing 2.7–3.9 million in the U.S. [2], and is the leading cause of cirrhosis, liver cancer, liver failure,
and liver transplantation [3]. In the U.S., mortality related to viral hepatitis exceeded that for
human immunodeficiency virus (HIV) between 1999 and 2007 [4]. Every year, 7,000–43,000
new cases of HCV infection are estimated to occur in the U.S. [2]and2–4millionnewcases
worldwide [5]. In developed countries, the primary mode of HCV transmission is illicit drug use
[6], with an estimated 60% of all HCV infections in the U.S. attributable to drug injection [7].
The injecting drug population in the U.S. has been experiencing a long-term demographic
shift that impacts HCV transmission and prevalence in complex ways. For at least a decade,
multiple studies in Chicago, Illinois and other areas have documented a shift in the racial/eth-
nic composition of the U.S. drug-user population [8–10]. These data consistently show that
young persons initiating into injection drug use are increasingly likely to be non-Hispanic
Whites from suburban communities rather than the urban, low-income minority populations
that have typified people who inject drugs (PWID) since at least 1950 [9]. These studies are fur-
ther supported by high incidence of HCV infection [11] and outbreaks among younger PWID
[12–14] while HIV [15 ] and HCV [16] prevalence have steadily declined in older populations.
Factors contributing to HCV infection acquisition and successful intervention among PWID
are complex and occur at the individual, social and geographic levels (e.g., risk behaviors, injec-
tion networks and interaction locations, respectively). The impact of these trends on HCV epi-
demics over time has not been adequately considered in forecasting and planning.
Dynamic modeling is a useful method for simultaneously accounting for the aforementioned
complexities inherent in forecasting HCV transmission and prevalence among PWID and can be
divided into two main categories—Compartmental Models (CM) and Agent-Based or Individ-
ual-Based Models (ABMs/IBMs) [17]. Compartmental models are the most commonly used class
for modeling HCV epidemics among PWID [17]. The CM approach is usually a set of differential
equations that assign the PWID population into compartments based on their HCV infection
state (e.g. susceptible, infected, recovered), along with other attributes such as enrollment in anti-
viral/vaccine treatment, harm reduction programs, or imprisonment [18,19]. For simplification,
these models consider homogenous populations of PWID within a given compartment although
it is known that PWID populations are highly heterogeneous. The ABMs/IBMs approach
addresses this limitation and offers a more realistic modeling strategy that accounts for the vari-
ability of individual characteristics and behaviors [20]. These models may include factors antici-
pated to vary between individuals based on empirical studies, including injection network [21–
23], age, length of time since initiating injection drug use, injection behaviors (e.g. sharing of
injection equipment) and geographic locations [24–27]. ABMs have been previously applied to
study HCV infections among PWID [28–31] and other infections such as influenza [32–34].
In the current study, we applied the ABM methodology [20
] to study the approximately
32,000 PWID who reside in metropolitan Chicago, IL, U.S. [35] and undertook to forecast HCV
prevalence among this group. Our software is termed the Agent-based Pathogen Kinetics model
(APK) and it represents a novel computational modeling platform. In APK, each PWID per-
forms drug-related daily activities, has a state of HCV infection (if infected), location of residency
Agent-Based Model for Hepatitis C in People Who Inject Drugs
PLOS ONE | DOI:10.1371/journal.pone.0137993 September 30, 2015 2/23
Review Board of the University of Illinois (CNEP,
YSN) and the Chicago Department of Public Health
(NHBS) prohibit direct sharing of these data as they
contain protected health information (PHS), including
age and residence, about PWID.
Funding: Support was provided by National
Institutes of Health [http://www.nih.gov/] grant P20-
GM103452 and R01-AI078881 to HD, Food and Drug
Administration (FDA) Center for Biologics Evaluation
and Research (CBER) intramural research funds
[http://www.fda.gov/AboutFDA/CentersOffices/
OfficeofMedicalProductsandTobacco/CBER/default.
htm] to MM, University of Illinois at Chicago (UIC)
Areas of Excellence Award [http://www.uic.edu/uic/]to
BB. Computational experiments were supported
through the National Science Foundation’s[www.nsf.
gov] XSEDE supercomputing system through grant
number OCI-1053575 to AG. Portion of this work
were done under the auspices of the U.S.
Department of Energy under contract DE-AC52-
06NA25396. Additional computing training and
resources were awarded by TACC at the University of
Texas at Austin to AG. The funders had no role in
study design, data collection and analysis, decision to
publish, or preparation of the manuscript.
Competing Interests: The authors have declared
that no competing interests exist.
and could maintain a drug sharing network with other PWID. APK was designed using highly-
detailed empirical networks and geospatial Chicago-based data from large epidemiological
empirical datasets to model the PWID population in each neighborhood; capturing associations
between demographic characteristics (e.g. age, race/ethnicity) and drug use risk behaviors.
The main novelty of APK is the detailed simulation of four aspects of the drug lifestyle: demo-
graphic, behavioral, social and geospatial. Whereas previous studies introduced social networks
and behavioral simulations, few have explored how they are influenced by geographic and
demographic processes [17]. In addition, APK is based on unique multi-annual surveys of the
Chicago drug epidemic, which have not been previously studied using agent-based models [17].
We used APK to forecast long-term trends in HCV incidence and prevalence among PWID
in metropolitan Chicago. We validated the forecast with empirical data and predict a number
of trends over the next decade, including aging of the PWID population and the persistence of
high HCV prevalence among certain sub-groups of PWID.
Materials and Methods
Epidemiological and Network Datasets
Four datasets were used for these studies that contained information from surveys performed
with people who inject drugs. All data were analyzed anonymously. Three of these studies have
been published previously. All study procedures for the Needle Exchange Program and Young
Social Networks studies were approved by the Institutional Review Board of the University of
Illinois at Chicago and the use of the NHBS data was approved through a data agreement with
the Chicago Department of Public Health.
The five main datasets used in developing APK are described below; the use of each dataset
in the development is shown in Fig 1.
The COIP Needle Exchange Program (CNEP) Survey. The base dataset for APK came
from the ongoing Community Outreach Intervention Projects (COIP) Needle Exchange Pro-
gram (NEP) that operates at four Chicago storefront locations and at multiple urban locations
through a mobile outreach unit. COIP has provided harm reduction supplies such as sterile
syringes/needles and counseling, as well as collecting extensive research data on metropolitan
Chicago PWID since 1996. About 1,500 registered PWID regularly visit one of COIP’s store-
front locations or mobile units each year. The ongoing COIP Needle Exchange Program
(CNEP) survey [36] collects data at the enrollment visit of each participant, including demo-
graphic characteristics, place of residence, injection drug use practices and behaviors, and
health status. We accessed more than 6,000 CNEP questionnaires collected from 2006–2013
from clients residing throughout the Chicago metropolitan area. The large size and wide geo-
graphic coverage of the NEP provides the most comprehensive data on the metropolitan Chi-
cago PWID population and was used to map the distribution of PWID.
The CDC-sponsored National HIV Behavioral Surveillance (NHBS) survey for Chicago
(years 2009 and 2012). Through a data agreement with the Chicago Department of Public
Health, we obtained the NHBS surveys for 2009 and 2012 specific to metropolitan Chicago
PWID. In the 2009 survey [37], 545 eligible PWID were enrolled using respondent-driven sam-
pling, a type of chain referral sampling that has been shown to be effective in finding hidden pop-
ulations such as PWID who may live across a wide geographic area [38]. The interviews were
conducted between August 12, 2009 and November 24, 2009. NHBS includes data on HCV risk
and HCV antibody prevalence. The NHBS 2012 (n = 209) applied the same methodology as the
NHBS 2009 between October 18, 2012 and December 21, 2012. We used the 2009 HCV antibody
prevalence data as an estimate of the HCV prevalence at the start of our simulation (January 1,
2010) and the 2012 NHBS HCV antibody prevalence to validate the simulation.
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The Young PWID Social Networks Study. The Young Social Networks survey (2013) is
an unpublished study led by the Division of Epidemiology and Biostatistics, School of Public
Health, UIC, Chicago, IL (Boodram, personal communication) which collected information
regarding demographic characteristics (e.g. age, race/ethnicity), place of residence(s), injection
related risk practices (e.g. sharing needles), and self-reported HIV and HCV status data on 164
young (ages 18–30 years) PWID and the people they injected drugs with most frequently (core
network) in the prior 6 months. We used these data to calibrate and validate the construction
of APK’s social risk network.
Geography data. The Chicago metropolitan area has an area of 28,120 km
2
and had a
population of 9.7 million in 2010. The City of Chicago had a 2010 population of 2.7 million
and can be divided into th ree large areas with distinct demographics—the North, West and
South sides. The metropolitan Chicago area is represented in APK with over a hundred geo-
graphic zones using postal (ZIP) codes from the 2010 U.S. Census. The location of drug mar-
kets was based on multiple data sources from COIP researchers [24,39–41]. Fig 2 shows the
geographic layout of a subset (1%) of these data as a screen shot of the APK PWID in the city
and connections between them based on locations.
Fig 1. Schematic representation of APK design. The empirical data is represented by five main datasets. The incorporation of each dataset in the
development of APK is shown by arrows. The locations of specific data outputs in the form of Tables and Figures are shown in Red type. CNEP: Community
Outreach Intervention Projects (COIP) Needle Exchange Program (NEP); NHBS: National HIV Behavioral Surveillance; YSN: Young Social Networks;
CNEP+: Enhanced CNEP population generated for APK.
doi:10.1371/journal.pone.0137993.g001
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HCV Infection Stages
Each in silico individual may be at any given time in one of the following HCV infection stages
(Fig 3): (1) naïve (or susceptible), (2) primary acute, (3) recovered phase (spontaneously
Fig 2. APK screen showing the Chicago metropolitan area. The screen shows people who inject drugs
(PWID, small squares), geographic zones (gray regions) and relationships (straight black lines). PWID are
colored based on their hepatitis C status: Red—HCV- Infected, Blue—naïve, and Green—HCV-recovered.
For clarity, this simulation displays just 320 agents, 1% of the entire APK PWID population. Orange circles—
major drug markets.
doi:10.1371/journal.pone.0137993.g002
Fig 3. Stages in the progression of infection with HCV. The duration of each stage is indicated (if temporary) together with the probability of transition to
another state of HCV infection. Probabilities are shown as representative values (details in Table 1).
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cleared the virus until re-infected), (4) non-primary acute phase (i.e., re-infected), and (5)
chronic viremic phase (life-long). Primary acute infection (Stage 2) usually results in chronic
life-long infection (Stage 5), but about 20% of cases experience spontaneous recovery (Stage 3).
If an individual spontaneously clears HCV during the acute stage (recovers) then some nat ural
immunity is attained, which leads to a modified infection upon re-exposure [42,43]. Recovered
individuals have improved outcomes if they acquire HCV again, including shorter duration of
acute infection (Stage 4) and a lower risk of developing chronic HCV infection. HCV infection
parameters, values and sources [30, 42–46] for these values are shown in Table 1. We based the
values for duration of HCV infection (primary and secondary infections) and clearance rates
on empirical data obtained from our meta-analysis of 99 chimpanzees [42], which have been
shown to be comp arable to data from human studies [43].
Generation of the Synthetic Population
We calculated that approximately half of the estimated 32,000 PWID [35] in metropolitan Chi-
cago are similar to those enrolled in harm reduction programs. We used the large CNEP data-
set (n~6,000) to construct the harm reduction-based population and developed an algorithm
(described in S1 Text) to construct the non-harm reduction-based population. Briefly, since we
expect harm reduction and non-harm reduction to be demographically similar [ 36], we con-
structed the non-harm reduction profiles based on CNEP, but adjusted for reported differences
[36] in risky behaviors and health status. The resulting synthetic PWID population (termed)
CNEP+ was used to generate the in silico initial population, i.e. the population on January 1,
2010. We expect that the non-parametric process (i.e. population modeling process that draws
from a large database) represents the spatially complex and internally correlated structure of
the PWID population, including e.g. correlations of age and race, with greater accuracy than
alternatives based on parametric models (e.g. [28]). The param eters used in this process are
shown in Table 2 based on [42, 47–50]. The values of the parameters and the range of values
were rigorously reviewed by the team of co-authors that include an epidemiologist, virologist,
and hepatologist against additional empirical studies in their respective areas of expertise to
align with literature beyond the scope and breadth of the datasets.
At the start of the simulation, the population consists of the approximately 32,000 PWID
(parameter initial_PWID_count), which are drawn from the CNEP+ data. New PWID (i.e.
newly-initiating) enter the population over 2010–2020 and they represent those who are begin-
ning injection drug careers. We expect that these individuals would be subtly different from the
CNEP+ population since the existing population represents a wider range of injection career
Table 1. HCV infection parameters.
Parameter Description Value Range Refs
mean_days_acute_naive Duration of acute infection in a naïve individual 102 77–127 [42,44]
mean_days_acute_rechallenged Duration of acute infection in a recovered individual 28 8–48 [42]
mean_days_naive_to_infectious Time taken for an infected individual to become infectious 3 2–4[42]
prob_clearing Probability of a recovered individual clearing virus upon re-exposure
a
0.85 0.75–0.95 [42,43]
prob_self_limiting_female Probability of spontaneous viral clearance upon first exposure- females 0.346 0.30–0.40 [45]
prob_self_limiting_male Probability of spontaneous viral clearance upon first exposure—males 0.121 0.10–0.14 [45]
transmissibility Probability that a naive PWID will be infected in a receptive sharing event with an
infected PWID
0.01 0.0005–
0.05
[30,46]
a
, regardless of gender
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histories. To account for these differences, we modeled the newly-initiating PWID using a non-
parameteric data-driven approach, i.e. newly-initiating PWID are patterned after PWID in
CNEP+ who have been engaging in injection drug use for a relatively short time (e.g. < 5years)
(parameter PWID_maturity_threshold). We assume that the majority of the newly-initiating
PWID are HCV-uninfected since they enter the simulation when they initiate into injection drug
use. However, we assigned 5% of the newly-initiated PWID as acutely infected (parameter pro-
b_infected_when_arrive) to account for other modes of HCV acquisition, which may include
sharing non-injection equipment with others prior to initiating into injection drug use [51].
In APK, PWID can leave the simulation due to either cessation of injection drug use
(parameter prob_cessation), or continue injection drug use until death or incarceration. Those
who achieve cessation are assigned a career duration from a normal distribution (parameter
mean_career_duration) of approximately 30 years based on published empirical studies and a
standard deviation of 12 years [48].
The annual probability of death increases with age while incarceration decreases with age
[48]. Because the effects compensate each other, we characterized the combined attrition due
to death and incarceration using an exponential attrition rate (parameter attrition_rate).
When the simulation is initiated, there is a tendency for the prevalence of HCV to fluctuate
due to the formation of many discordant relationships (not shown). To prevent this from bias-
ing the results, we used a burn-in procedure that continues for 365 simulated days (parameter
burn_in_days). During the burn-in PWID neither enter nor leave the simula tion, nor do they
grow older, but have ongoing HCV transmission and network dynamics. We initiate data col-
lection after the burn-in period and denoted this time point as January 1
st
, 2010.
Initial HCV infection state
We applied a logistic regression classification approach (Eq 1) to assign HCV status in each
individual in CNEP+.
LðXÞ¼
expð
P
i
b
i
X
i
Þ
1 þ expð
P
i
b
i
X
i
Þ
ð1Þ
Where X is demographic information about the PWID in CNEP+ and L is the logistic link
function. To train the classifier, the following information is read from NHBS 2009: age, age of
Table 2. Parameters for the generation of the synthetic population.
Parameter Value Range Notes
ab_prob_acute
a
0.02 0.01–0.03 set to 2% based on relative durations of acute phase and injection career
ab_prob_chronic
a
0.67 0.49–0.74 [42,47]
attrition_rate 0.024 per year 0.01–0.08 [48]
burn_in_days 365 - Calibrated by observing the time necessary for the HCV incidence to stabilize.
initial_PWID_count 32,000 30,000–34,000 [49]
mean_career_duration (years) 30.3 10–35 [48]
prob_cessation 0.232 0.13–0.33 [48]
prob_infected_when_arrive
(acute HCV infection)
0.05 0.01–0.09 0.9% prevalence among newer PWID, and 9% among other* PWID [50]
PWID_maturity_threshold (years) 5 3–7 Set by trading off sample size (larger value) and accuracy (smaller value).
a
, 1-(ab_prob_acute+ab_prob_chronic) represents the probability of HCV antibody positive PWID who is not viremic (i.e., recovered).
*, PWID who acquired HCV prior to initiating into injection drug use through other modes (e.g. sharing non-injection drug paraphernalia such as snorting
straws.
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first injecting drug use, size of drug in-network, gender, race, ZIP code of residence, frequency
of injections per day, probability of receptive sharing, and the HCV antibody status. In 10-fold
cross validation (i.e., when 1/10 of the data is left out of the calibration and instead used for
testing), the classifier achieved an average receiver operating characteristic (ROC) score of 0.68
(maximum is 1.0). All imputations were performed using the Weka machine learning toolkit
version 3.6.11 [52].
When presented with a profile from CNEP+, the classifier produces a probability that the
person is in a particular HCV AB status (AB+ or AB-). If an individual is AB+ th ree HCV
infection states are possible: acute, chronic (i.e., viremic), or recovered (no virus). These infec-
tion states are assigned based on the probabilities in Table 2. We calculated that approximately
2% of the CNEP+ population are acutely-infected (parameter ab_prob_acute ), 67% are chron-
ically infected (parameter ab_prob_chronic) and the remainder are recovered (31%). The
parameter ab_prob_acute is calculated from the observation that the duration of the acute
phase is approximately 100 days and represents less than 2% of the duration of a 10-year
PWID career and less than 1% of a 20-year PWID career.
Attributes
Each PWID in the simulation has attributes, i.e. quantities that vary from individual to individ-
ual such as location of residence, race/ethnicity, gender, frequency of drug injection, and HCV
infection status. These attributes are shown in Table 3 with representative statistics for the start
of the simulation in 2010. For PWID in 2010 (the initial population), the elapsed years of injec-
tion drug use represents the amount of time a subject has been injecting drugs at this time
point in the simulation. Thus, the average elapsed time for injecting drug use for PWID within
APK is 11.4 years in 2010. This is distinct fro m the mean career duration of 30 years used to
generate the synthetic population (Table 2), which represents the total length of time for an
Table 3. Attributes of PWID and representative data.
Attribute Statistics for 2010
Demographic attributes
Location (by ZIP code) City: 46%; Suburbs: 54%
Race/ethnicity Hispanic: 18% NH Black: 21% NH White: 58%
NH Other: 3%
Gender Female: 30%; Male: 70%
Age Mean: 35.3 years. IQR: 26.1–43.0 Over 30:
59% Under 30: 41%
Elapsed years of injection drug use Mean: 11.4 years. IQR: 3.3–16.0
Enrollment in any HR program HR: 48%; non-HR: 52%.
HCV infection state Infected (acute or chronic): 30% Recovered
(antibody +): 13%
Behavioral attributes
Daily drug injections Mean: 2.5; IQR: 0.89–3.26
Probability of receptive sharing Ranges from 0 (never)
to 1 (every injection)
Mean: 19%*. IQR: 0.0%-37%
Network attributes
In Degree (receptive network size) 56%- 0 (no network), 32%- 1, 12%- 2
Out Degree (giving network size) 65%- 0 (no network), 25%- 1, 10%- 2
NH = Non-Hispanic. IQR = interquartile range. HR = harm reduction program.
*i.e. sharing or equipment reuse in 19% of injections while 81% of injections involve sterile equipment.
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individual to reach cessation of drug use, i.e. the total length of an individual’s injecting career.
The simulation also maintains information about the network of relationships among PWID,
which we refer to as the social drug risk network. The network is directed in that each relation-
ship has the attributes from-PWID and to-PWID. The from-PWID (or giver) shares drugs,
injection equipment with the to-PWID (the recipient). The PWID’s in-degree and out-degree
attributes (Table 3) specify the number of receiving and giving relationships, respectively. New
infections with HCV may occur among PWID with in-degree 1 who are exposed to contami-
nated equipment (i.e., blood transmission from viremic PWID).
Each in silico PWID performs a finite number of drug injections every day, which is repre-
sented by a Poisson distribution around an individual mean value (Table 3). The probability of
receptive needle sharing is an attribute of the individual, and varies across the population
(Table 3). To represent these sharing events, the simulation selects at random a person from
the PWID’s in-network partners for sharing. The probability that a naive PWID would be
infected is represented by the parameter transmissibility (Table 1).
The CNEP dataset indicates that drug behavior remains stable over the PWID injection
career (e.g.<1% relative change per year of career in number of partners, number of daily injec-
tions or probability of sharing). As such, we assume in APK that once an in silico individual is
assigned a drug behavior it remains as is during her/his injecting career.
Network Formation
A central calculation for network formation is to determine the probability that two persons
are likely to encounter each other and form a relationship that promotes HCV transmission.
APK allows for three kinds of encounters (1) in the neighborhood close to the place of resi-
dence; (2) at a drug purchase market, and (3) other encounters, which includes co-workers or
any stranger in the city. The methods used to calculate network encounter rates, establishment
processes, and removal of networks are detailed in S1 Text (Supplemental Methods).
The network in the simulation is the sole route of transmission for HCV. Some individuals who
enter the simulation and who are assigned a network rapidly create a number of injecting-related
contacts (or “ties”). In these subjects, the network is dynamic, and during the course of their career,
some ties may be lost, while new ones form but result in an approximately constant network size.
We used the CNEP+ and NHBS 2009 data to determine the initial size of injection network for
each PWID in the synthetic population based on the premise that sharing of drugs, needles or par-
aphernalia transmits HCV [26,30]. The CNEP data also suggests that PWID may have two distinct
groups of partners, and the sizes of the two groups may be very different [36]: the in-network
(termed in-degree, Table 3) partners are people giving drugs or equipment to the PWID, while the
out-network (termed out-degree, Table 3) are those receiving drugs or equipment from the PWID.
Forthisreason,eachPWIDinAPKmaintainsboth kinds of partnerships, with some overlap.
The network construction is informed by the geography (based on ZIP codes) and th e
homophily for the person’s race/ethnicity and age (Table 4). The network changes over the
course of the simulation to represent the turnover in the PWID population, that is, the creation
and dissolution of social relationships. We assigned each PWID to a region defined by a single
postal ZIP code, which represents the PWID’s place of residence or the place of sojourn for
homeless individuals. We used each PWID’s ZIP code to determine his or her probability of
traveling to a given drug market and other parts of the metropolis. In turn, such travel may
lead to encounters with other PWID, and the establishment of drug injection networks. There
are several drug markets in well-defined geographic areas within metropolitan Chicago (Fig 2)
[39]. When two PWID access the same market, they are relatively more likely to establish a
connection as compared to PWIDs who do not (See S1 Text, Eq 1).
Agent-Based Model for Hepatitis C in People Who Inject Drugs
PLOS ONE | DOI:10.1371/journal.pone.0137993 September 30, 2015 9/23
Summary of simulated processes
The simulation uses the discrete event simulation (DES) methodology [53], wher eby the simu-
lation steps from event to event. Many types of events take place on a regular daily basis, partic-
ularly drug injection, sharing, and HCV transmission. PWID attrition, cessation or dissolution
of relationships occur infrequently based on a stochastic schedule.
We applied the following steps to introduce PWID into the simulation:
1. An individual X is drawn at random from the CNEP+ database. X already contains most of the
attributes (Table 3) of a PWID: race, gender, age, network size, HCV antibody test result, etc.
2. All of the attributes of X are copied to the synthetic PWID Y, including specific ID number,
race, gender, location (Table 3).
3. The HCV infection status of Y (acute/chronic/recovered) is assigned stochastically based on
the HCV antibody test result attribute assigned within the CNEP+ database (see Table 2).
4. Y is added to th e PWID population and begins his/her drug career. Network connections
are established as described above.
Table 4. Detailed statistics of the PWID population in APK. The initial 2010 PWID population is gradually removed through attrition, and is replaced by
the population of newly-initiating PWID. Values for the newly-initiating population reflect attributes at the time of joining the PWID population. Ages and drug-
related risk behaviors reported are mean values. All values for newly-initiating PWID are significantly more likely to be young and NH White.
PWID Jan.
2010
PWID newly
initiating-2010–
2020†
PWID Dec.
2020
Combined PWID population: Initial (2010) and newly-initiating (2010–
2020)
North
Side
South
Side
Suburban Under
30
Over
30
HR Non-
HR
Total 32000
(±1080)
8499 32000
(±1090)
4032 6134 23103 19178 21334 19603 20909
Female (%) 30 (±4) 36 32(±9) 27 34 32 35 28 31 31
Male (%) 70(±4) 64 68(±9) 73 66 68 65 72 69 69
NH Black (%) 21(±1) 11 17(±6) 11 68 3.6 3.0 32 24 13
Hispanic (%) 19(±6) 18 19(±6) 22 12 11 15 22 22 15
NH White (%) 57(±2) 67 60(±2) 60 19 81 78 43 51 68
Age (years) 35(±0.6) 26 40(±2) 34 42 29 24 42 34 33
Elapsed years of
injection drug use
11(±1) 0.1 16(±2) 10 17 6.0 3.2 14 9.4 8.6
Daily injections 2.5(±0.04) 2.4 2.5(±0.04) 2.4 2.7 2.3 2.4 2.5 2.7 2.2
Fraction receptive
sharing**
0.19(±0.03) 0.20 0.19(±0.03) 0.12 0.14 0.25 0.21 0.19 0.024 0.36
In degree* 0.51(±0.03) 0.59 0.53(±0.03) 0.43 0.42 0.57 0.60 0.43 0.37 0.64
Out degree* 0.45(±0.03) 0.48 0.46(±0.03) 0.40 0.40 0.50 0.54 0.38 0.33 0.57
HR (%) 49(±3) 49 50(±4) 68 66 34 48 49 100 0.0
Non-HR (%) 51(±3) 51 50(±4) 32 34 66 52 51 0.0 100
HCV RNA+ (%) 29(±3) 5.1 26(±4) 22 42 20 14 35 23 26
HCV antibody + but
not infected (%)
14(±3) 0.0 10(±2) 8.2 17 7.9 5.0 15 10 10
* The “in-degree” is the number of the in-network relationships, i.e. the number of persons from whom the PWID receives drugs or other risks, while the
“out-degree” is the number of connections to which the PWID gives drugs or other risks.
**Fraction of injections involving receiving drugs or injection equipment from another person in the network.
†
Variability data is not available. HR = PWID in Harm Reduction programs (e.g. needle exchange programs). nonHR = PWID not in harm reduction
programs
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Agent-Based Model for Hepatitis C in People Who Inject Drugs
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During the course of the simulation, each PWID performs the following actions:
1. Daily drug injection and possibly needle receiving/giving (with frequency specific to the
individual, including potential HCV infection).
2. Update of HCV infection stage for PWID going through 1
st
acute phase or acute phase
upon re-infection.
3. Update of both the IDU biological age and his/her injection drug career age.
In addition, APK carries out the following processes:
1. Formation of relationships between two PWID (only for PWID who maintain a network
and have recently lost a relationship).
2. Removal of PWID from the population, due to mortality, incarceration or cessation of drug use.
At the beginning of every simulated day, the simulation calculates the number of injections
each PWID would perform, which may be zero, one, two and so forth. PWID are then selected
stochastically to perform the injections. If a PWID has a non-zero probability p of receptive
sharing, then an average fraction p of the injections would involve selecting a partner from the
PWID’s in-network.
Software modeling platform and tools
We developed APK based on the Repast Symphony 2.1 open source platform, which was cre-
ated by Argonne National Laboratory (Argonne, IL) [53,54]. We built APK in the Java 7 pro-
gramming language that allows for simulation of hundreds of thousands of individuals and we
optimized and streamlined it to accommodate large geographic al areas and populations. Each
simulation uses a single computer core, and runs for 11 simulated years including 1 year of
burn-in, except for one simulation noted below which used 21 years including 1 year of burn-
in. We wrote all data analysis tools using the open source Python 2.7 programming language.
Statistical and sensitivity analysis procedures
We performed sensitivity analysis procedures where the values of the parameters were changed
and the simulation repeated 300 times. We performed simulations using the Stampede super-
computer at the University of Texas at Austin and the Elastic Compute Cloud from Amazon
Web Services. Because of the high computational cost of each simulation (~1 hr), our sensitiv-
ity analysis procedure used Latin Hypercube Procedure to maximize coverage of the parameter
space [55] and to accelerate the data collection substantially. Parameter values were drawn
from a normal distribution with the indicated mean value and truncated at the indicated value.
For each setting of the parameter values, we initialized the PWID population and simulated the
population and recorded the HCV epidemic. Incidence rates were calculated by counting acute
HCV infections, and for each PWID who became infected, tracking the time from entering the
simulation to the time of infection.
Results
Validation of APK
Software Verification. To augment the accuracy of the APK program, two programmers
(A.G. and A.H) performed a verification procedure [56] that includes code walkthroughs, pro-
filing and parameter testing to ensure the model was working as intended. These tests reduced
Agent-Based Model for Hepatitis C in People Who Inject Drugs
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the risk of error in the programming of the model. The verification procedure was comple-
mented by validation of the model with empirical data.
Validation of HCV prevalence predictions. We validated APK using the 2012 NHBS sur-
vey, the most recent representative data available on PWID for metropolitan Chicago. We uti-
lized the 2012 NHBS survey to construct a synthetic “validation” population for 2012. To do this,
we applied the same imputation procedure as APK (i.e. both based on CNEP+) to generate the
population characteristics, then applied the 2012 NHBS HCV prevalence. The resulting valida-
tion population was then compared to the HCV prevalence predicted from the APK simulation
initiated in 2010. The validation results show high concordance, i.e., the predicted and actual val-
ues match within 2% overall and one standard error in 11 out of 11 subpopulations (Fig 4).
Network structure validation. We used raw data obtained from a social network study
among young PWID (from the Young Social Network Study) to calibrate and validate the net-
work formation process by comparing the distances between pairs of PWID that exchange
drugs (Fig 5). The simulated and actual networks match closely with an average error of 1.3%.
For example, in about 30% of the pairs, the two PWID are geographically located within 2 km
of each other for both the empirical data and APK networks. The likelihood drops significantly
within the empirical data beyond 2 km, but has a second peak at 8–16 km; this drop beyond 2
km and the second peak are reproduced in APK.
Fig 4. Comparison of APK predictions for 2012 with the NHBS empirical survey data from 2012. APK correctly forecasts the prevalence overall and in
11 of 11 subgroups with substantially different prevalence values (average error in estimate: 2.0%). Error bars represent one standard deviation.
NHWhite = Non-Hispanic White; HR = Individuals in Harm Reduction Programs; nonHR = Individuals not in Harm Reduction Programs; LEQ30 = PWID aged
30 or younger; Over30 = PWID over 30 years of age; City = PWID within the City of Chicago; Suburban = PWID living in Chicago suburbs.
doi:10.1371/journal.pone.0137993.g004
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Composition of the PWID population is expected to change through
2020
The composition of the population was studied over the period from January 1, 2010 through
December 31
st
2020. The simulation indicates some significant changes in the Chicago PWID
population by 2020. First, the proportion of the PWID population from suburban compared to
urban Chicago areas is forecast to remain unchanged (or slightly increase) from 54% (SD: 3%)
in 2010 to 58% (SD: ±3%) in 2020 (Fig 6A). Second, due to the aging of existing PWID and rel-
atively low rates of attrition and long injection drug use careers (i.e. low cessation), the propor-
tion of PWID >30 years old is predicted to increase substantially over time with a
corresponding decrease in the proportion of those <30 years old (Fig 6A), resulting in an aver-
age age increase from 35 yr in 2010 to 40 (±1.8) yr in 2020 (data not shown). Specifically,
young PWID aged 21–30 are predicted to decline as a fraction of the population from 38% in
2010 to 22% (±6%) in 2020 while the fraction of PWID in their 30s, 40s and 50s would increase
(Fig 6B), with the greatest increase occurring in the 31–40 age group. Third, the PWID popula-
tion is projected to become increasingly non-Hispanic (NH) White (increasing by 3% to 60
±2%) and less NH Black (decreasing by 3% to 17±2%) (Fig 6C). However, the proportion of
PWID engaging in harm reduction (HR) practices is expected to remain steady, changing from
49% (SD: ±3%) in 2010 to 50% (SD: ±4%) in 2020 (Fig 6C).
As expected, there is significant regional variatio n in racial/ethnic composition and HCV
prevalence between 2010 and 2020 with the South Side of Chicago being predominantly NH
Fig 5. Distances in the drug-sharing network of among young PWID (age 30 or younger). The data shows the results for APK compared to empirical
data from the Young Social Network (YSN) dataset. Error bars represent one standard deviation.
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PLOS ONE | DOI:10.1371/journal.pone.0137993 September 30, 2015 13 / 23
Black (68%) with high anti-HCV prevalence (17%), while the suburban areas are predomi-
nantly NH White (81%) with lower anti-HCV prevalence (8%) (Table 4). Compared to the ini-
tial 2010 PWID population, newly-initiating PWID (2010–2020) were more likely to be NH
White (67% vs. 57% in the initia l 2010 population) and less likely to be chronically infected
(i.e., HCV RNA positive) (5% vs. 30% in the initial 2010 population) (Table 4).
Network structure of the PWID population
The network structure of the PWID population at the beginning of the simulation (2010) is
characterized by the presence of many isolated individuals, with the 32,000 PWID connected
by just 14,300 directed connections. These connections establish approximately 1300 strongly
connected components of more than one person, i.e. sub-networks with reciprocal exchange of
drugs, the largest of which has size 45 (for terminology see [57]). In 2010, a majority of PWID
(68%) do not receive drugs or equipment at all (in degree parameter, Table 4), and conse-
quently are not at risk for injection-related HCV infection.
Networks in APK reflect community areas with high homophily on select demographic
characteristics (e.g. race/ethnicity). For example, NH Whites in select urban and most subur-
ban areas are more likely to live near other NH Whites, which is expected to result in an
increased probability of encounter and formation of drug partnerships among NH Whites in
the APK model. In addition, racial/ethnic network homophily among PWID is documented in
epidemiological studies [1,39]. This pattern is realized in APK, which showed more racially
homophilic connections than would be expected if the mixing were random, i.e. the majority of
NH Blacks and NH Whites are connected to others of the same race in the APK model
(Table 5). Consistent with a recent study on young Chicago PWID (Boodram personal com-
munication), NH Whites showed higher racial/ethnic homophily with their injection network
members compared to Hispanics (all races) (80% vs 41%).
Prevalence of HCV will decline by 2020
The APK forecast for HCV prevalence, as measured by HCV antibody positivity, in metropolitan
Chicago is reported in Fig 7 and is expected to decline overall at a rate of 0.4% per year from 43%
in 2010 to 39% in 2020 (Fig 7A). However, the rate of decline from 2010–2020 differs by age,
Fig 6. Age and Composition of the PWID population from 2010–2020. (A) Composition of PWID from 2010–2020 based on location, Suburban and City,
and age, persons over and under 30 years of age. (B) Detailed distribution of PWID over time within different age groups <20; 21–30; 31–40; 41–50 and 51–
60 years of age, (C) Composition of PWID population within racial groups (NH Black, Hispanic and NH White) and within HR and non-HR groups, In all
figures trends show average of 300 simulations and errors represent one standard deviation between simulations. HR = PWID in harm reduction programs,
non-HR = PWID not enrolled in harm reduction programs.
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racial/ethnicity, and harm reduction group designation. For instance, HCV prevalence among
PWID 30 years old is forecast to decline more precipitously (27% to 13%) compared to those
>30 years of age (56% to 41%) (Fig 7A). By race/ethnicity, HCV prevalence decline is expected
to be greater among Hispanics (all races) (from 44% to 35%, ±5%) and among NH Blacks (from
57% to 48%, ±5%) compared to NH Whites (from 39% to 33%, ±4%) (Fig 7B). As expected,
those enrolled in needle exchange/harm reduction programs would experience a steeper decline
in HCV prevalence (from 42% to 30%, ±5%) compared to those who are not (from 46% to 41%,
±5%) (Fig 7B). By gender, HCV prevalence decline is forecast to occur at similar rates among
females (from 43% to 36%, ±5%) and males (from 44% to 36%, ±5%) (Fig 7C).
Although long term projection is associated with more uncertainty, an extended simulation
for years 2020–2030 showed that anti-HCV prevalence would continue to decline from 39% to
33% between 2020 and 2030 (data not shown). However, due to expected higher incidence
among the younger population over time (Fig 7), we project that HCV prevalence among the
younger population will not decline as steeply and will plateau around 13% in 2030 (data not
shown).
Incidence of HCV varies by sub-group
Fig 8A shows the HCV incidence per 100 person-years (PY) among PWID from 2010–2020.
HCV incidence overall is estimated at 0.51 per 100 PY, with significant differences between
Table 5. Statistics of actual network connections in APK by race/ethnicity. NH Whites and NH Blacks have high racial/ethnic homophily with injection
networks; therefore, HCV incidence in NH Blacks and NH Whites is driven by background prevalence in respective ethnic/racial groups.
To: NHWhite Hispanic NHBlack Other *Total
From: NHWhite 80% 12% 5% 3% 58%
Hispanic 43% 41% 12% 4% 18%
NHBlack 28% 21% 50% 2% 21%
Other 66% 18% 7% 9% 3%
*Total gives the fraction of the PWID population in that demographic group in 2010, and is the expected number of relationships under random
relationship formation.
doi:10.1371/journal.pone.0137993.t005
Fig 7. Forecast of HCV antibody prevalence in Chicago over a 10-year span, 2010–2020. (A) HCV antibody prevalence based on location, Suburban
and City, and age, persons over and under 30 years of age. (B) Prevalence within the total population, individual racial groups (NH White; NH Black and
Hispanic) and HR and non-HR groups. (C) Prevalence within the total population and based on gender. Trends show average of 300 simulations and error
bars represent one standard deviation. HR = PWID in harm reduction programs, non-HR = PWID not enrolled in harm reduction programs.
doi:10.1371/journal.pone.0137993.g007
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sub-populations. The primary sub-groups driving incidence are those with an injection net-
work, those arriving into the population after 2010, and suburban PWID. NH Whites are more
likely to be members of all three of these sub-groups between 2010–2020, which would account
for a three-fold higher incidence in this group compared to NH Blacks and Hispanics (0.66 vs.
0.17 and 0.41 per 100 PY, respectively). The HCV incidence among all PWID with at least one
in-network injection partner is 1.2 per 100 PY, with an even higher incidence among this
group if they are also young and newly arriving into the population (3.3 per 100 PY) (data not
shown). Compared to their respective counterparts, those enrolled in harm-reduction pro-
grams, older PWID >30 years, and male PWID have lower HCV incidence (Fig 8A). Analysis
of the incidence over time for all populations (Fig 8B) shows that incidence declines from
approximately 250 cases per year in 2010 to under 100 by 2019. This is consistent with a rap-
idly declining prevalence we reported in Fig 7.
Rapid HCV Acquisition within the first years of injection career
We tracked the injection career length for all PWID in the simulation, which we then used to
estimate the timing of new HCV infections. An estimated 29% of HCV infections are expected
to occur during the first year of injecting drug use and another 18% during the following year
(Fig 9). The probability of HCV acquisition slowly declines during subsequent years due to
infection saturation of the population. This pattern is also reflected in the higher incidence
found among new initiates into injection drug use (i.e. arriving sub-group in Fig 8A), which
ultimately also results in a sharp increase in anti-HCV prevalence among this group by the end
of the first year of injection drug use that stabilizes over the subsequent years (Fig 10A).
Among newly-arriving PWID during 2010–2020, it is notable that NH Blacks are expected to
experience lower HCV prevalence over time as compared to NH Whites. This may refle ct both
changes in high risk behaviors and network composition over time. We observed a sharper
increase in HCV prevalence in females initiating into drug use than males (Fig 10B), while the
lowest increase in prevalence over the first year is seen in newly initiating PWID enrolled in
harm reduction programs (Fig 10B).
Discussion
Our study describes a novel agent-based model (termed APK) for the PWID population in
metropolitan Chicago and applied this to study and predict changes in HCV prevalence in this
population. A barrier to developing realistic prediction models for PWID is a lack of empirical-
grounded data that includes biological, behavioral, network and geographical parameters. We
addressed this shortcoming with APK by combining multiple diverse large-scale datasets (Fig
1) derived from empirical studies on metropolitan Chicago PWID to develop a representative
PWID population. In APK, each individual PWID is based on a profile developed from these
empirical data that includes demographic characteristics, risk behaviors, HCV infection status,
place of residence, and injection network size. The metropolitan Chicago geography is repre-
sented in APK by zones based on the 2010 US Census ZIP code level data. Geographical dis-
tance between the zones is considered in the probability of network connections among PWID
and is also criti cal for forecasting HCV at the neighborhood level and among the suburban
PWID. In addition to these internal features, APK includes sensitivity analysis capabilities and
an advanced graphical user interface that enables exploration of a running simulation and visu-
alization of the geographic and demographic distribution of the disease.
Using APK, we investigated the long-term trends for the PWID population in metropolitan
Chicago and HCV infections among PWID. Overall, the model predicts that the PWID popu-
lation would increase in mean age substantially by 2020 (Fig 6), while the overall prevalence of
Agent-Based Model for Hepatitis C in People Who Inject Drugs
PLOS ONE | DOI:10.1371/journal.pone.0137993 September 30, 2015 16 / 23
HCV would decline (Fig 7). As expected, PWID enrolled in harm reduction programs (HR)
are forecast to experience a sharper decline in prevalence (1.1% per year) compared to those
not enrolled in harm reduction programs (nonHR) (0.5% per year) (Fig 7B). This finding may
reflect the underlying effectiveness of harm reduction programs in preventing HCV infection,
as well as the overall smaller networks and lower frequency of needle sharing in this population
compared to non-harm reduction PWID. Among racial/ethnic groups, we project that NH
Blacks will experience a relatively rapid decline in HCV prevalence (Fig 7B), but still continue
to have the highest prevalence overall. This pattern is similar to the harm reduction group; as
such, compared to NH Whites; NH Blacks have smaller injection networks (average in-degree
0.61 vs. 0.41, respectively) and lower frequency of needle sharing (0.14 vs. 0.22 per injection
episode). These differences in network size and frequency of needle sharing in the NH White
population could account for the lower rate of prevalence decline in this subgroup (Fig 7B).
We project the overall HCV incidence rate to be 0.51 per 100 PY, which is low in compari-
son to empirical studies from large cities such as Baltimore and Seattle (47 and 9.8 per 100 PY,
respectively) [58]. However, Chicago is notable for relatively low incidence; the most recent
estimate of HCV incidence among Chicago PWID comes from the CIDUS III study (2002–
2004) [24,59], which reported incidence of 6.0 per 100 person-years and is based on only a
6-month follow-up of 18–30 year olds with relatively short median injection career length
[24,59,60]. In contrast, APK encompasses wider geographic and racial/ethnic diversity among
the population in APK. Nonetheless, this decline in incidence has been observed in other cities
(e.g. Vancouver, Canada [61]) and might be found elsewhere but be underre ported because
some subgroups show relatively stable trends, as shown in Fig 7. HCV incidence is heightened
among the newly-initiating sub-population of PWID (Fig 8A) who are also more likely to be
younger (<30 years) and suburban rather than longer-term, older PWID (Table 4). For exam-
ple, young newly-initiating PWID with at least one network relationship have an HCV inci-
dence in APK of 3.3 per 100 PY, while all PWID over 30 years report an HCV incidence of 0.3
per 100 PY (Fig 8A). For these reasons, we expect that by 2020 the epidemic will be increasingly
found among suburban NH White PWID who are not enrolled in harm reduction programs.
Fig 8. Incidence of HCV among PWID in metropolitan Chicago. (A) Incidence density by group and geographic area summed over 2010–2019. (B) Total
incidence of HCV by year. Values are expressed as HCV incidence per 100 PY and have an estimated uncertainty of ±20%. HR = Individuals in Harm
Reduction Programs; nonHR = Individuals not in Harm Reduction Programs. Network = Individuals having at least one incoming connections in the PWID
network.
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These predictions from the APK model are consistent with previous studies showing an ongo-
ing shift in the racial composition of PWID populations throughout the United States [8–
10,62,63]. Previous studies also showed that the majority of new HCV infections occur during
the first or second year of injection drug use [25,64] and the incidence is heightened among
females as compared to males [65], which agrees with our findings (Figs 9 and 10B).
Populations at high risk for acquiring HCV may be suitable candidates for future vaccine
clinical trials. Although a number of promising vaccines are being developed [66,67], testing of
those vaccines is complicated because of the complexity of the PWID population [68]. We
expect that populations in which we predict elevated incidence of HCV would be the best can-
didates for testing possible vaccines. Based on our findings, such studies might preferentially
recruit from PWID <30 years old not enrolled in harm reduction programs. Although this
may be a challenging group to target our findings indicate that the development of novel
recruitment methods that are designed for this population, such as mobile apps, should be vig-
orously explored and would be highly beneficial in the long-term.
Fig 9. Timing of HCV infections over the duration of the injection career, among PWID who become infected. The horizontal axis indicates months
from the beginning of injecting drug use. Each bar represents a 4 month period.
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We found that the overall prevalence of HCV is expected to decline, which is consistent
with the attrition process in the PWID population, and is not unexpected when viewed in a his-
torical context. The APK-predicted rate of overall decline (8% over 10 years) is within historical
trends for HCV among Chicago area PWID. For example, according to the three CIDUS stud-
ies that recruited both harm reduction and non-harm reduction PWID, the prevalence among
Chicago PWID 18–40 years old declined from 70% (CIDUS I, 1994–96) to 27% (CIDUS II,
1997–99), and then to 14% (CIDUS III 2002–04) [16 ]. Our long term forecast for 2020 –2030 is
for prevalence to continue to decline but at a slower pace.
A number of limitations and simplifications inherent to APK must be considered when
interpreting our findings. First, to generate the synthetic population, APK relies on data from
the COIP Needle Exchange Program and, although some corrections were applied, our repre-
sentation is less accurate of PWID who are not enrolled in the needle exchange program (non-
harm reduction) or who may live too far to acces s COIP’s services. Second, our network con-
struction parameters are fitted to young social networks data that includes only PWID 30 years
old or younger, but older PWID might have different network structures. A better understand-
ing of the non-harm reduction and older populations would increase the accuracy of the simu-
lations and this component of APK will be refined in future when these data become available.
Third, while APK considers aging and the duration of the drug career, it does not model how
age affects drug behaviors and risk awareness. We examined this assumption using cross-sec-
tional data from the CIDUS III study [59] and confirmed that injection behaviors, including
network size, number of daily injections and frequency of sharing show no consistent associa-
tion for about ten years of drug use. Indeed, we saw that APK can accurately forecast HCV
prevalence three years into the future, suggesting that behavioral chan ges by individual PWID
do not play a significant role in the spread of HCV in th e population as a whole. Fourth, APK
simplifies the interrelated processes of attrition and cessation of injection drug use. In particu-
lar, APK uses an exponential model of incarceration and mortality, and extrapolates the dura-
tion of injection drug careers based on data from the Los Angeles, CA area [48]. Only long-
term follow up studies (>30 years) of PWI D in the Chicago are a would provide the necessary
data to validate this aspect of the simulation. Fifth, APK accounts for place of residence and the
drug markets but does not directly model daily mobility of the PWID. Places of work,
Fig 10. The prevalence of HCV over the injecting career among PWID who initiate into injection drug
use. (A) Prevalence within the total population and within individual racial/ethnic groups, NH White, Hispanic,
NH Black. (B) Prevalence within the total population and divided for gender and harm reduction (HR)
enrollment. Time is counted from the beginning of an individual’s initiation into stable injection drug use (and
APK), and assumes 5% incidence due to experimental use of Heroin before transition to stable injection use.
The curves represent the combined injection careers of all PWID who initiated over 2010–2020. Data is
shown as the mean of 300 simulations and the error bars represent one standard deviation.
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pharmacies, hospitals, and other sites could be also important for the transmission of HCV,
however their epidemiological role, unlike airborne pathogens [ 69] is expected to be secondary
to the place of residence and the drug markets for HCV spread. Similarly, although APK con-
siders the formation of relationships through encounters, other processes might play a contrib-
uting role in relationship formation, such as introduction via mutual friends.
Despite those concerns, we suggest that our findings are robust to these uncertainties, as
demonstrated by validation with empirical data (Figs 4 and 5). The majority of the uncertainty
is accounted for by the sensitivity analysis procedure and shown in Figs 6 and 7. Additionally,
based on our validation studies, we believe that the simulation can provide accurate forecasting
for three years and as such the best application for our simulations would be to evaluate scenar-
ios such as public health interventions. The forecasting range APK provides is comparable to
the duration of medium-term epidemiological studies, such as those that conside r syringe
exchanges, behavioral and medical interventions.
Overall, APK is the first detailed and data-rich agent-based mode l available for the PWID
population in metropolitan Chicago and may be the most detailed model worldwide [17]. It
could be adapted to other cities in the US and world wide based on a comprehensive survey of
the PWID population including their geographic locations, network connectivity and HCV
infection status. APK could also consider infections (including co-infections) with hepatitis B
or HIV and to evaluate intervention strategies such as anti-HCV antiviral treatment scale up
and HCV vaccine trial design and evaluation.
Supporting Information
S1 Text. Supplemental Methods.
(DOCX)
Acknowledgments
The authors would like to thank Lawrence Ouellet and Susan Mniszewski for critical reading of
the manuscript.
Author Contributions
Conceived and designed the experiments: AG BB HD MM. Performed the experiments: AG
BB. Analyzed the data: AG BB NP AH HD MM. Contributed reagents/materials/analysis tools:
AG BB NP. Wrote the paper: AG BB NP AH HD MM. Designed software: AG BB HD.
References
1. WHO. World Health Organization. Hepatitis C Fact Sheet No 164. 2015 Available: http://www.who.int/
mediacentre/factsheets/fs164/en/.
2. CDC. Centers for Disease Control and Prevention. HCV statistics. 2014 Available: http://www.cdc.gov/
hepatitis/HCV/StatisticsHCV.htm.
3. El-Serag HB. Epidemiology of viral hepatitis and hepatocellular carcinoma. Gastroenterology. 2012;
142(6): 1264–73e1. doi: 10.1053/j.gastro.2011.12.061 PMID: 22537432.
4. Ly KN, Xing J, Klevens RM, Jiles RB, Ward JW, Holmberg SD. The increasing burden of mortality from
viral hepatitis in the United States between 1999 and 2007. Annals of Internal Medicine. 2012; 156(4):
271–8. doi: 10.7326/0003-4819-156-4-201202210-00004 PMID: 22351712.
5. Kane A, Lloyd J, Zaffran M, Simonsen L, Kane M. Transmission of hepatitis B, hepatitis C and human
immunodeficiency viruses through unsafe injections in the developing world: model-based regional
estimates. Bulletin of the World Health Organization. 1999; 77(10): 801–7. PMID: 10593027.
6. Alter MJ. Epidemiology of hepatitis C virus infection. World Journal of Gastroenterology. 2007; 13(17):
2436. PMID: 17552026
Agent-Based Model for Hepatitis C in People Who Inject Drugs
PLOS ONE | DOI:10.1371/journal.pone.0137993 September 30, 2015 20 / 23
7. CDC. Centers for Disease Control and Prevention. Viral hepatitis and drug users. 2012. Available:
http://www.cdc.gov/hepatitis/Statistics/2012Surveillance/index.htm.
8. Armstrong GL. Injection drug users in the United States, 1979–2002: an aging population. Archives of
Internal Medicine. 2007; 167(2): 166–73. doi: 10.1001/archinte.167.2.166 PMID: 17242318.
9. Broz D, Ouellet LJ. Racial and ethnic changes in heroin injection in the United States: implications for
the HIV/AIDS epidemic. Drug and alcohol dependence. 2008; 94(1–3): 221–33. doi: 10.1016/j.
drugalcdep.2007.11.020 PMID: 18242879.
10. Neaigus A, Gyarmathy VA, Miller M, Frajzyngier VM, Friedman SR, Des Jarlais DC. Transitions to
injecting drug use among noninjecting heroin users: social network influence and individual susceptibil-
ity. J Acquir Immune Defic Syndr. 2006; 41(4): 493–503. PMID: 16652059.
11. Page K, Hahn JA, Evans J, Shiboski S, Lum P, Delwart E, et al. Acute hepatitis C virus infection in
young adult injection drug users: a prospective study of incident infection, resolution, and reinfection.
Journal of Infectious Diseases. 2009; 200(8):1216–26. doi: 10.1086/605947 PMID: 19764883.
12. CDC. Notes from the field: risk for hepatitis C virus infections among young adults-Massachusetts,
2010 (Reprinted from MMWR, vol 60, pg 1457–1458, 2011). JAMA: Journal of the American Medical
Association. 2011; 306: 2448.
13. CDC. Use of enhanced surveillance for hepatitis C virus infection to detect a cluster among young injec-
tion-drug users—New York, November 2004-April 2007 (Reprinted from MMWR, vol 57, pg 517–521,
2008). JAMA: Journal of the American Medical Association. 2008; 300:34–6.
14. CDC. Hepatitis C virus Infection among adolescents and young adults-Massachusetts, 2002–2009
(Reprinted from MMWR, vol 60, pg 537–541, 2011). JAMA: Journal of the American Medical Associa-
tion. 2011; 305:2511–3.
15. Broz D, Pham H, Spiller M, Wejnert C, Le B, Neaigus A, et al. Prevalence of HIV infection and risk
behaviors among younger and older injecting drug users in the United States, 2009. AIDS and Behav-
ior. 2013; 18: 284–296. doi: 10.1007/s10461-013-0660-4 PMID: 24242754.
16. Amon JJ, Garfein RS, Ahdieh-Grant L, Armstrong GL, Ouellet LJ, Latka MH, et al. Prevalence of hepati-
tis C virus infection among injection drug users in the United States, 1994–2004. Clinical Infectious Dis-
eases 2008; 46: 1852–8. doi: 10.1086/588297 PMID: 18462109.
17. Cousien A, Tran V, Deuffic‐Burban S, Jauffret‐Roustide M, Dhersin JS, Yazdanpanah Y. Dynamic
modelling of hepatitis C virus transmission among people who inject drugs: a methodological review.
Journal of Viral Hepatitis. 2014. doi: 10.1111/jvh.12337
PMID: 25270261
18. Martin NK, Vickerman P, Grebely J, Hellard M, Hutchinson SJ, Lima VD, et al. Hepatitis C virus treat-
ment for prevention among people who inject drugs: Modeling treatment scale-up in the age of direct-
acting antivirals. Hepatology. 2013; 58: 1598–1609 doi: 10.1002/hep.26431 PMID: 23553643.
19. Anderson RM, May RM. Infectious diseases of humans: dynamics and control. Oxford: Oxford Univer-
sity Press; 1991.
20. Bonabeau E. Agent-based modeling: Methods and techniques for simulating human systems. Pro-
ceedings of the National Academy of Sciences of the United States of America. 2002; 99: 7280–7.
PMID: 12011407
21. Brewer DD, Hagan H, Sullivan DG, Muth SQ, Hough ES, Feuerborn NA, et al. Social structural and
behavioral underpinnings of hyperendemic hepatitis C virus transmission in drug injectors. Journal of
Infectious Diseases. 2006; 194: 764–72. doi: 10.1086/505585 PMID: 16941342.
22. Wylie JL, Shah L, Jolly AM. Demographic, risk behaviour and personal network variables associated
with prevalent hepatitis C, hepatitis B, and HIV infection in injection drug users in Winnipeg, Canada.
BMC Public Health. 2006; 6: 229. doi: 10.1186/1471-2458-6-229 PMID: 16970811.
23. Hickman M, Carnwath Z, Madden P, Farrell M, Rooney C, Ashcroft R, et al. Drug-related mortality and
fatal overdose risk: pilot cohort study of heroin users recruited from specialist drug treatment sites in
London. Journal of Urban Health 2003; 80: 274–87. doi: 10.1093/jurban/jtg030 PMID: 12791803.
24. Boodram B, Golub ET, Ouellet LJ. Socio-behavioral and geographic correlates of prevalent hepatitis C
virus infection among young injection drug users in metropolitan Baltimore and Chicago. Drug and
Alcohol Dependence. 2010; 111: 136–45. doi: 10.1016/j.drugalcdep.2010.04.003 PMID: 20472373.
25. Garfein RS, Vlahov D, Galai N, Doherty MC, Nelson KE. Viral infections in short-term injection drug
users: the prevalence of the hepatitis C, hepatitis B, human immunodeficiency, and human T-lympho-
tropic viruses. American Journal of Public Health. 1996; 86: 655–61. PMID: 8629715.
26. van den Hoek JA, van Haastrecht HJ, Goudsmit J, de Wolf F, Coutinho RA. Prevalence, incidence, and
risk factors of hepatitis C virus infection among drug users in Amsterdam. Journal of Infectious Dis-
eases. 1990; 162: 823–6. PMID: 2119400.
Agent-Based Model for Hepatitis C in People Who Inject Drugs
PLOS ONE | DOI:10.1371/journal.pone.0137993 September 30, 2015 21 / 23
27. Thorpe LE, Bailey SL, Huo D, Monterroso ER, Ouellet LJ. Injection-related risk behaviors in young
urban and suburban injection drug users in Chicago (1997–1999). J Acquir Immune Defic Syndr. 2001;
27: 71–8. PMID: 11404523.
28. Hutchinson S, Bird S, Taylor A, Goldberg D. Modelling the spread of hepatitis C virus infection among
injecting drug users in Glasgow: Implications for prevention. International Journal of Drug Policy. 2006;
17(3):211–21. doi: 10.1016/j.drugpo.2006.02.008
29. Mather D, Crofts N. A computer model of the spread of hepatitis C virus among injecting drug users.
European Journal of Epidemiology. 1999; 15(1):5–10. PMID: 10098989.
30. Rolls DA, Daraganova G, Sacks-Davis R, Hellard M, Jenkinson R, McBryde E, et al. Modelling hepatitis
C transmission over a social network of injecting drug users. Journal of Theoretical Biology. 2012; 297
(0):73–87. http://dx.doi.org/10.1016/j.jtbi.2011.12.008.
31. Hahn JA, Wylie D, Dill J, Sanchez MS, Lloyd-Smith JO, Page-Shafer K, et al. Potential impact of vacci-
nation on the hepatitis C virus epidemic in injection drug users. Epidemics. 2009; 1(1):47–57. doi: 10.
1016/j.epidem.2008.10.002 PMID: 20445816.
32. Germann TC, Kadau K, Longini IM, Macken CA. Mitigation strategies for pandemic influenza in the
United States. Proceedings of the National Academy of Sciences. 2006; 103(15):5935–40.
33. Del Valle S, Mniszewski S, Hyman JM. Modeling the Impact of Behavior Changes on the Spread of
Pandemic Influenza. Modeling the Interplay Between Human Behavior and Spread of Infectious Dis-
eases: Springer-Verlang; 2013.
34. Del Valle SY, Hyman JM, Hethcote HW, Eubank SG. Mixing patterns between age groups in social net-
works. Soc Networks. 2007; 29(4):539–54. doi: 10.1016/j.socnet.2007.04.005
35. Tempalski B, Pouget ER, Cleland CM, Brady JE, Cooper HL, Hall HI, et al. Trends in the population
prevalence of people who inject drugs in US metropolitan areas 1992–2007. PloS One. 2013; 8:
e64789. doi: 10.1371/journal.pone.0064789 PMID: 23755143.
36. Huo D, Ouellet LJ. Needle exchange and injection-related risk behaviors in Chicago: a longitudinal
study. J Acquir Immune Defic Syndr. 2007; 45: 108–14. PMID: 17460474.
37. Lansky A, Abdul-Quader AS, Cribbin M, Hall T, Finlayson TJ, Garfein RS, et al. Developing an HIV
behavioral surveillance system for injecting drug users: the National HIV Behavioral Surveillance Sys-
tem. Public Health Rep. 2007; 122 Suppl 1: 48–55. PMID: 17354527.
38. Heckathorn D. Respondent-driven sampling: a new approach to the study of hidden populations. Social
Problems. 1997; 44: 174–99.
39. National Institute of Drug Abuse. Epidemiologic Trends in Substance Abuse: Proceedings of the Com-
munity Epidemiology Work Group, Volume II. 2010. Available: http://www.drugabuse.gov/about-nida/
organization/workgroups-interest-groups-consortia/community-epidemiology-work-group-cewg/
meeting-reports
40. Thorpe LE, Ouellet LJ, Hershow R, Bailey SL, Williams IT, Williamson J, et al. Risk of hepatitis C virus
infection among young adult injection drug users who share injection equipment. American Journal of
Epidemiology. 2002; 155: 645–53. PMID: 11914192.
41. Youm Y, Mackesy-Amiti ME, Williams CT, Ouellet LJ. Identifying hidden sexual bridging communities in
Chicago. Journal of Urban Health 2009; 86:107
–20. doi: 10.1007/s11524-009-9371-6 PMID: 19543836.
42. Dahari H, Feinstone SM, Major ME. Meta-analysis of hepatitis C virus vaccine efficacy in chimpanzees
indicates an importance for structural proteins. Gastroenterology. 2010; 139: 965–74. doi: 10.1053/j.
gastro.2010.05.077 PMID: 20621699.
43. Osburn WO, Fisher BE, Dowd KA, Urban G, Liu L, Ray SC, et al. Spontaneous control of primary hepa-
titis C virus infection and immunity against persistent reinfection. Gastroenterology. 2010; 138:315–24.
doi: 10.1053/j.gastro.2009.09.017 PMID: 19782080.
44. Dahari H, Major M, Zhang X, Mihalik K, Rice CM, Perelson AS, et al. Mathematical modeling of primary
hepatitis C infection: noncytolytic clearance and early blockage of virion production. Gastroenterology.
2005; 128(4):1056–66. PMID: 15825086.
45. Micallef J, Kaldor J, Dore G. Spontaneous viral clearance following acute hepatitis C infection: a sys-
tematic review of longitudinal studies. Journal of Viral Hepatitis. 2006; 13: 34–41. PMID: 16364080
46. Vickerman P, Hickman M, Judd A. Modelling the impact on hepatitis C transmission of reducing syringe
sharing: London case study. International Journal of Epidemiology. 2007; 36: 396–405. doi: 10.1093/
ije/dyl276 PMID: 17218325.
47. Boodram B, Hershow RC, Cotler SJ, Ouellet LJ. Chronic hepatitis C virus infection and increases in
viral load in a prospective cohort of young, HIV-uninfected injection drug users. Drug and Alcohol
Dependence. 2011; 119: 166–71. doi: 10.1016/j.drugalcdep.2011.06.005 PMID: 21724339.
48. Hser YI, Hoffman V, Grella CE, Anglin MD. A 33-year follow-up of narcotics addicts. Archives of Gen-
eral Psychiatry. 2001; 58: 503–8. PMID: 11343531
Agent-Based Model for Hepatitis C in People Who Inject Drugs
PLOS ONE | DOI:10.1371/journal.pone.0137993 September 30, 2015 22 / 23
49. Tempalski B, Pouget ER, Cleland CM, Brady JE, Cooper HL, Hall HI, et al. Trends in the population
prevalence of people who inject drugs in US metropolitan areas 1992–2007. PloS One. 2013; 8(6):
e64789. doi: 10.1371/journal.pone.0064789 PMID: 23755143
50. Mackesy-Amiti ME, Boodram B, Williams C, Ouellet LJ, Broz D. Sexual risk behavior associated with
transition to injection among young non-injecting heroin users. AIDS and Behavior. 2013; 17: 2459–66.
doi: 10.1007/s10461-012-0335-6 PMID: 23065126.
51. Neaigus A, Gyarmathy VA, Zhao M, Miller M, Friedman SR, Des Jarlais DC. Sexual and other noninjec-
tion risks for HBV and HCV seroconversions among noninjecting heroin users. Journal of Infectious
Diseases. 2007; 195(7):1052–61. PMID: 17330797
52. Hall M, Frank E, Holmes G, Pfahringer B, Reutemann P, Witten IH. The WEKA Data Mining Software:
An Update. SIGKDD Explorations. 2009; 11(1): 10–18.
53. North MJ, Collier NT, Ozik J, Tatara ER, Macal CM, Bragen M, et al. Complex adaptive systems modeling
with repast simphony. Complex Adaptive Systems Modeling. 2013; 1: 1–26. doi: 10.1186/2194-3206-1-3
54. North MJ, Collier NT, Vos JR. Experiences creating three implementations of the repast agent modeling
toolkit. ACM Transactions on Modeling and Computer Simulation (TOMACS). 2006; 16: 1–25.
55. Iman RL. Latin hypercube sampling. In: Melnick EL, Everitt BS, editors. Encyclopedia of Quantitative
Risk Analysis and Assessment. 3: Wiley; 2008. p. 969–72.
56. North MJ, Macal CM. Managing business complexity: discovering strategic solutions with agent-based
modeling and simulation: Oxford University Press; 2007.
57. Wasserman S. Social network analysis: Methods and applications. Cambridge, UK: Cambridge Uni-
versity Press; 1994.
58. Hagan H, Des Jarlais DC, Stern R, Lelutiu-Weinberger C, Scheinmann R, Strauss S, et al. HCV synthe-
sis project: preliminary analyses of HCV prevalence in relation to age and duration of injection. Interna-
tional Journal of Drug Policy. 2007; 18: 341–51. PMID: 17854721
59. Garfein RS, Swartzendruber A, Ouellet LJ, Kapadia F, Hudson SM, Thiede H, et al. Methods to recruit
and retain a cohort of young-adult injection drug users for the Third Collaborative Injection Drug Users
Study/Drug Users Intervention Trial (CIDUS III/DUIT). Drug and Alcohol Dependence. 2007; 91 Suppl
1:S4–17. doi: 10.1016/j.drugalcdep.2007.05.007 PMID: 17582705.
60. Tsui JI, Evans JL, Lum PJ, Hahn JA, Page K. Association of opioid agonist therapy with lower incidence
of hepatitis C virus infection in young adult injection drug users. JAMA Internal Medicine. 2014; 174:
1974–81. doi: 10.1001/jamainternmed.2014.5416 PMID: 25347412.
61. Grebely J, Lima VD, Marshall BDL, Milloy M-J, DeBeck K, Montaner J, et al. Declining Incidence of
Hepatitis C Virus Infection among People Who Inject Drugs in a Canadian Setting, 1996–2012. PLoS
ONE 2014; 9: e97726. doi: 10.1371/journal.pone.0097726 PMID: 24897109
62. Mathers BM, Degenhardt L, Bucello C, Lemon J, Wiessing L, Hickman M. Mortality among people who
inject drugs: a systematic review and meta-analysis. Bulletin of the World Health Organization. 2013;
91: 102–23. doi: 10.2471/BLT.12.108282 PMID: 23554523.
63.
National Institute of Drug Abuse. Epidemiologic Trends in Drug Abuse: Proceedings of the Community
Epidemiology Work Group. Vol II 2011. Available: http://www.drugabuse.gov/about-nida/organization/
workgroups-interest-groups-consortia/community-epidemiology-work-group-cewg/meeting-reports
64. Hagan H, Pouget ER, Des Jarlais DC, Lelutiu-Weinberger C. Meta-regression of hepatitis C virus infec-
tion in relation to time since onset of illicit drug injection: the influence of time and place. American Jour-
nal of Epidemiology. 2008; 168: 1099–109. doi: 10.1093/aje/kwn237 PMID: 18849303
65. Hagan H, Thiede H, Des Jarlais DC. Hepatitis C virus infection among injection drug users: survival
analysis of time to seroconversion. Epidemiology. 2004; 15: 543–9. PMID: 15308953
66. Strickland GT, El-Kamary SS, Klenerman P, Nicosia A. Hepatitis C vaccine: supply and demand. Lan-
cet Infectious Diseases. 2008; 8: 379–86. doi: 10.1016/S1473-3099(08)70126-9 PMID: 18501853.
67. Swadling L, Capone S, Antrobus RD, Brown A, Richardson R, Newell EW, et al. A human vaccine strat-
egy based on chimpanzee adenoviral and MVA vectors that primes, boosts, and sustains functional
HCV-specific T cell memory. Science Translational Medicine. 2014; 6: 261ra153. doi: 10.1126/
scitranslmed.3009185 PMID: 25378645.
68. Feinstone SM, Hu DJ, Major ME. Prospects for prophylactic and therapeutic vaccines against hepatitis C
virus. Clinical Infectious Diseases 2012; 55 Suppl 1: S25–32. doi: 10.1093/cid/cis362 PMID: 22715210.
69. Mniszewski S, Del Valle S, Priedhorsky R, Hyman JM, Hickman KS. Understanding the impact of face
mask usage through epidemic simulation of large social networks. Dabbaghian V and Mago V K (eds),
Theories and Simulations of Complex Social Systems, Intelligent Systems Reference Library 52,
Springer-Verlag Berlin Heidelberg. 2014:97–115.
Agent-Based Model for Hepatitis C in People Who Inject Drugs
PLOS ONE | DOI:10.1371/journal.pone.0137993 September 30, 2015 23 / 23
