ࡱ > P | bjbj 4 ' ' ' ' ' ; ; ; ; , g ; 2 0 K 0 {( {( {( {( V) V * d + 4 \2 ^2 ^2 ^2 ^2 ^2 ^2 3 6 B ^2 ' D+ V) V) D+ D+ ^2 ' ' {( {( s2 X, X, X, D+ j ' {( ' {( - X, D+ \2 X, X, X, {( z ; + F X, - 2 0 2 X, 6 + d 6 X, 6 ' X, l D+ D+ X, D+ D+ D+ D+ D+ ^2 ^2 X, D+ D+ D+ 2 D+ D+ D+ D+ 6 D+ D+ D+ D+ D+ D+ D+ D+ D+ : Hidden Drug Resistant HIV to Emerge in the Era of Universal Treatment Access in Southeast Asia
Supporting information: Mathematical details
MACROBUTTON MTEditEquationSection2 Equation Chapter 1 Section 1 SEQ MTEqn \r \h \* MERGEFORMAT SEQ MTSec \r 1 \h \* MERGEFORMAT SEQ MTChap \r 1 \h \* MERGEFORMAT Introduction:
The results presented in the main text are based on a mathematical model. Here we present a full description of the model and a listing of all parameters and assumptions used.
Model Equations
HIV disease and transmission dynamics are described with a system of 91 ordinary differential equations, one for each of the 13 structural compartments of our model (Fig. 1) multiplied by seven population subgroups (Fig. S1). These equations are as follows, where subscripts i, and j are used to denote the population subgroups, Table S1 outlines all parameter values used in the model:
EMBED Equation.DSMT4 MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTEqn \c \* Arabic \* MERGEFORMAT 1)
EMBED Equation.DSMT4 MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTEqn \c \* Arabic \* MERGEFORMAT 2)
EMBED Equation.DSMT4 MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTEqn \c \* Arabic \* MERGEFORMAT 3)
EMBED Equation.DSMT4 MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTEqn \c \* Arabic \* MERGEFORMAT 4)
EMBED Equation.DSMT4 MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTEqn \c \* Arabic \* MERGEFORMAT 5)
EMBED Equation.DSMT4 MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTEqn \c \* Arabic \* MERGEFORMAT 6)
EMBED Equation.DSMT4 MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTEqn \c \* Arabic \* MERGEFORMAT 7)
EMBED Equation.DSMT4 MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTEqn \c \* Arabic \* MERGEFORMAT 8)
EMBED Equation.DSMT4 MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTEqn \c \* Arabic \* MERGEFORMAT 9)
EMBED Equation.DSMT4 MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTEqn \c \* Arabic \* MERGEFORMAT 10)
EMBED Equation.DSMT4 MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTEqn \c \* Arabic \* MERGEFORMAT 11)
EMBED Equation.DSMT4 MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTEqn \c \* Arabic \* MERGEFORMAT 12)
EMBED Equation.DSMT4 . MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTEqn \c \* Arabic \* MERGEFORMAT 13)
Change in the number of uninfected (susceptible) individuals is governed by equation GOTOBUTTON ZEqnNum998005 \* MERGEFORMAT REF ZEqnNum998005 \* Charformat \! \* MERGEFORMAT (1); the force of infection terms, EMBED Equation.DSMT4 and EMBED Equation.DSMT4 (described below) for seroconverting with wild-type or drug-resistant virus respectively. Once infected, individuals progress into primary HIV infection, governed by equations GOTOBUTTON ZEqnNum556749 \* MERGEFORMAT REF ZEqnNum556749 \* Charformat \! \* MERGEFORMAT (2)- GOTOBUTTON ZEqnNum649931 \* MERGEFORMAT REF ZEqnNum649931 \* Charformat \! \* MERGEFORMAT (4). A proportion EMBED Equation.DSMT4 of individuals infected with a drug-resistant strain will have minority-resistant variants at the time of infection.
Equations GOTOBUTTON ZEqnNum815022 \* MERGEFORMAT REF ZEqnNum815022 \* Charformat \! \* MERGEFORMAT (5) - GOTOBUTTON ZEqnNum968891 \* MERGEFORMAT REF ZEqnNum968891 \* Charformat \! \* MERGEFORMAT (7) describe the change in the number of individuals in the chronic infection stage of HIV. After the chronic stage, HIV-infected individuals become treatment-eligible (governed by equations GOTOBUTTON ZEqnNum112836 \* MERGEFORMAT REF ZEqnNum112836 \* Charformat \! \* MERGEFORMAT (8)- GOTOBUTTON ZEqnNum677722 \* MERGEFORMAT REF ZEqnNum677722 \* Charformat \! \* MERGEFORMAT (10)), at which point they may receive ART at rate EMBED Equation.DSMT4 ; we assume that in the era of universal treatment access people will initiate ART within a period of 6 weeks to 1 year of becoming treatment-eligible (see Table S1), although IDUs may take longer to seek treatment because of legal and social barriers. Once on treatment (governed by equations GOTOBUTTON ZEqnNum462627 \* MERGEFORMAT REF ZEqnNum462627 \* Charformat \! \* MERGEFORMAT (11)- GOTOBUTTON ZEqnNum395058 \* MERGEFORMAT REF ZEqnNum395058 \* Charformat \! \* MERGEFORMAT (13)), we assume that patients will continue using their ART regime, even if treatment failure occurs.
We assume that individuals with majority-resistance strains can become minority-resistant at a rate EMBED Equation.DSMT4 . This represents wild-type strains becoming the dominant type of virus. We also assume that once on treatment, individuals with minority-resistant strains become majority-resistant under the selective pressure of ART at a rate of EMBED Equation.DSMT4 . Drug susceptible individuals can acquire resistance at a rate of EMBED Equation.DSMT4 .
In all equations, we assume that individuals can leave the sexually active population at a rate EMBED Equation.DSMT4 . Infected individuals can also leave the population due to death caused by HIV. This is represented by EMBED Equation.DSMT4 . We assume different rates for each disease stage, and also differing rates for those infected with drug resistant virus.
Probability of Transmission
The transmission probability is based on a number of factors. Disease stage alters the transmission probability according to viral load using the relation ADDIN EN.CITE Gray200199917Gray, Ronald H.Wawer, Maria J.Brookmeyer, RonSewankambo, Nelson K.Serwadda, DavidWabwire-Mangen, FredLutalo, TomLi, XianbinvanCott, ThomasQuinn, Thomas C.Probability of HIV-1 transmission per coital act in monogamous, heterosexual, HIV-1-discordant couples in Rakai, UgandaThe LancetThe Lancet1149-115335792632001http://www.sciencedirect.com/science/article/B6T1B-42VM8B6-8/2/7109559e8acd3ecd2da16a44cb89db8f [1]:
EMBED Equation.DSMT4 , MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTEqn \c \* Arabic \* MERGEFORMAT 14)
where w is the baseline viral load (in our case chronic infection), EMBED Equation.DSMT4 is the baseline transmission probability, and v is the new viral load. Condom use is also a factor affecting transmission. We incorporate condom use in the per partnership calculation based using a binomial calculation ADDIN EN.CITE Rottingen200214214214217Rottingen, J. A.Garnett, G. P.Department of Infectious Disease Epidemiology, Imperial College School of Medicine at St. Mary's, London, United Kingdom. j.a.rotingen@basalmed.uio.noThe epidemiological and control implications of HIV transmission probabilities within partnershipsSex Transm DisSex Transm DisSexually transmitted diseases818-2729122002/12/06*Disease Transmission, InfectiousHIV Infections/*transmissionHumans*Models, Theoretical*Sexual Partners2002Dec0148-5717 (Print)12466726http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=1246672600007435-200212000-00014 [pii]eng[2] in the following equations:
EMBED Equation.DSMT4 MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTEqn \c \* Arabic \* MERGEFORMAT 15)
EMBED Equation.DSMT4 MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTEqn \c \* Arabic \* MERGEFORMAT 16)
Here, EMBED Equation.DSMT4 is the number of acts, EMBED Equation.DSMT4 is the proportion of acts using condoms, EMBED Equation.DSMT4 is the efficacy of condoms, and EMBED Equation.DSMT4 is the multiplicative factor affecting drug resistant virus due to reduced fitness.
Force of Infection:
The force of infection is governs the rate of new infections based on the transmission probabilities, number of partners, and the number of infected. These are described in equations GOTOBUTTON ZEqnNum557659 \* MERGEFORMAT REF ZEqnNum557659 \* Charformat \! \* MERGEFORMAT (17) and GOTOBUTTON ZEqnNum537962 \* MERGEFORMAT REF ZEqnNum537962 \* Charformat \! \* MERGEFORMAT (18):
EMBED Equation.DSMT4 MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTEqn \c \* Arabic \* MERGEFORMAT 17)
EMBED Equation.DSMT4 MACROBUTTON MTPlaceRef \* MERGEFORMAT MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTEqn \c \* Arabic \* MERGEFORMAT 18)
Where EMBED Equation.DSMT4 represents the average number of contacts between population group i and group j, and EMBED Equation.DSMT4 , EMBED Equation.DSMT4 , and EMBED Equation.DSMT4 are described as follows:
EMBED Equation.DSMT4 MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTEqn \c \* Arabic \* MERGEFORMAT 19)
EMBED Equation.DSMT4 MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTEqn \c \* Arabic \* MERGEFORMAT 20)
EMBED Equation.DSMT4 MACROBUTTON MTPlaceRef \* MERGEFORMAT SEQ MTEqn \h \* MERGEFORMAT ( SEQ MTEqn \c \* Arabic \* MERGEFORMAT 21)
Here, EMBED Equation.DSMT4 , EMBED Equation.DSMT4 , and EMBED Equation.DSMT4 refers to the transmission probability associated with drug susceptible, detectible drug resistant, and undetectable drug resistant strains. The additional notations P, C, TE, and T in front of the viral class groups denote the disease stages, primary, chronic, treatment eligible and treated respectively. The number of infected individuals is denoted by EMBED Equation.DSMT4 , EMBED Equation.DSMT4 and EMBED Equation.DSMT4 , using the same convention as for the transmission probabilities. The total population is given by EMBED Equation.DSMT4 .
Sensitivity Analysis:
We performed a full uncertainty and sensitivity analysis using SaSAT ADDIN EN.CITE Hoare200895959517Hoare, A.Regan, D. G.Wilson, D. P.Sampling and sensitivity analyses tools (SaSAT) for computational modellingTheoretical Biology and Medical ModellingTheoretical Biology and Medical Modelling4512008[3]. We generated 10,000 individual parameter sets via Latin hypercube sampling for the parameters described in Table S1. The model was implemented with Matlab R2008b. Steady state levels were obtained in the absence of treatment and simulations leading to an overall HIV prevalence between 0.5% and 5% were retained, leaving 2,318 parameter sets. The model was then run to simulate 10 years of the HIV epidemic with full access to ART for treatment-eligible individuals. Partial rank correlation coefficients and factor prioritization by reduction of variance methods were carried out to identify dominant factors, from which response surfaces were generated using multivariate regression analyses.
Table S1: List of model parameters and their values
ParameterDescriptionValueRef EMBED Equation.DSMT4 Average progression time from primary to chronic infection for individuals infected with drug-sensitive HIV 2-6 months ADDIN EN.CITE ADDIN EN.CITE.DATA [4,5,6] EMBED Equation.DSMT4 Average progression time from primary to chronic infection for individuals infected with drug-resistant HIV EMBED Equation.DSMT4 . EMBED Equation.DSMT4 (min 2 months) ADDIN EN.CITE ADDIN EN.CITE.DATA [7] EMBED Equation.DSMT4 Average progression time from chronic infection to treatment-eligible or AIDS for individuals infected with drug-sensitive HIV 8 10 years ADDIN EN.CITE ADDIN EN.CITE.DATA [8,9,10] EMBED Equation.DSMT4 Multiplier for relative increase in average time for individual infected with drug resistant virus to progress from chronic infection to treatment eligibility, considering reduced viral fitness.0.75 1.5 EMBED Equation.DSMT4 Average progression time from chronic infection to treatment-eligible or AIDS for individuals infected with drug-resistant HIV EMBED Equation.DSMT4 IDU0Percentage of population who are injecting drug users (IDUs)% Total Pop0.05 0.5% ADDIN EN.CITE ADDIN EN.CITE.DATA [11,12,13]% of IDU that are Female10 20 %SW0Percentage of sexually active women that are sex workers (SWs) 0.5-1% ADDIN EN.CITE ADDIN EN.CITE.DATA [14,15]MC0Percentage of men who are clients of SWs5 10% ADDIN EN.CITE ADDIN EN.CITE.DATA [16,17,18]MSM0Percentage of men who are MSM1-5 % ADDIN EN.CITE ADDIN EN.CITE.DATA [18,19,20,21,22,23] EMBED Equation.DSMT4 Average rate of AIDS deaths for individuals in Primary Infection class ~0 EMBED Equation.DSMT4 Average rate of AIDS deaths for individuals Chronic Infection class~0 EMBED Equation.DSMT4 Average time to death for untreated individuals with drug-sensitive virus in the AIDS/treatment-eligible stage of infection 2 4 years ADDIN EN.CITE ADDIN EN.CITE.DATA [24,25,26] EMBED Equation.DSMT4 Proportion of drug-sensitive treated individuals that achieve viral suppression0.6 0.85 ADDIN EN.CITE Blower200529292917Blower, S.Bodine, E.Kahn, J.McFarland, W.The antiretroviral rollout and drug-resistant HIV in Africa: insights from empirical data and theoretical modelsAIDSAIDS (London, England)AidsAIDS (London, England)AidsAIDS (London, England)1-14191Africa/epidemiologyAnti-Retroviral Agents/*therapeutic useDisease OutbreaksDrug Resistance, ViralHIV/drug effectsHIV Infections/*drug therapy/epidemiology/transmissionHumansModels, BiologicalPrevalenceRisk-TakingSentinel Surveillance2005Jan 30269-9370 (Print)15627028http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=15627028 eng[27] EMBED Equation.DSMT4 Average time to death for untreated individuals with drug-resistant virus in the AIDS/treatment-eligible stage of infection EMBED Equation.DSMT4 years EMBED Equation.DSMT4 Average time to death for treated individuals with drug-sensitive virus in the AIDS/treatment-eligible stage of infection EMBED Equation.DSMT4 ADDIN EN.CITE ADDIN EN.CITE.DATA [24,28,29]a EMBED Equation.DSMT4 Average time to death for treated individuals with drug-resistant virus in the AIDS/treatment-eligible stage of infection EMBED Equation.DSMT4 ADDIN EN.CITE ADDIN EN.CITE.DATA [28,30]b EMBED Equation.DSMT4 Percentage of individuals on ART to acquire resistance (have treatment failure) each year3-5% ADDIN EN.CITE ADDIN EN.CITE.DATA [31,32] EMBED Equation.DSMT4 Average time for drug resistance to re-emerge upon treatment in individuals that have reservoirs of drug-resistant strains3 months - EMBED Equation.DSMT4 ADDIN EN.CITE ADDIN EN.CITE.DATA [33,34]c EMBED Equation.DSMT4 Average time for virus reversion to wild type0.25 5 years ADDIN EN.CITE ADDIN EN.CITE.DATA [35,36] EMBED Equation.DSMT4 Proportion of those infected with transmitted drug resistant virus in which resistant viral strain is detectable0-100% EMBED Equation.DSMT4 Average time for individuals to be in sexually active population30 35 years ADDIN EN.CITE ADDIN EN.CITE.DATA [28,37] EMBED Equation.DSMT4 Probability of transmission via needle sharing per single event, if initial user is HIV-positive0.005 0.01 ADDIN EN.CITE ADDIN EN.CITE.DATA [38,39] EMBED Equation.DSMT4 Reduction in fitness of drug resistant HIV, decreasing transmission probability of drug-resistant strains0.05 0.5 ADDIN EN.CITE ADDIN EN.CITE.DATA [27,40,41]wBaseline viral load taken at chronic infection104 105 copies/ml ADDIN EN.CITE ADDIN EN.CITE.DATA [42,43]vPIAverage viral load at primary infection stage105 108 copies/ml ADDIN EN.CITE ADDIN EN.CITE.DATA [5,42]vCIAverage viral load at chronic infection stage104 105 copies/ml ADDIN EN.CITE ADDIN EN.CITE.DATA [5,8,42,43]vTE Average viral load at treatment eligible stage105 106 copies/ml ADDIN EN.CITE ADDIN EN.CITE.DATA [10,42]vT Average viral load at Treated stage10 200 copies/ml ADDIN EN.CITE ADDIN EN.CITE.DATA [44,45,46] EMBED Equation.DSMT4 Baseline male-to-female transmission probability per actd0.0001 0.002 ADDIN EN.CITE ADDIN EN.CITE.DATA [1,47,48,49,50,51,52] EMBED Equation.DSMT4 Baseline female-to-male transmission probability per act0.0001 0.0015 ADDIN EN.CITE ADDIN EN.CITE.DATA [47,49,50,51,52,53] EMBED Equation.DSMT4 Baseline male-to-male transmission probability per act0.001 0.01 ADDIN EN.CITE ADDIN EN.CITE.DATA [49,52,54] EMBED Equation.DSMT4 Number of sexual partnerships per year of males (who are also clients of SWs)with SW2 5 ADDIN EN.CITE ADDIN EN.CITE.DATA [55,56]with GF0.5 1.5 EMBED Equation.DSMT4 Number of sexual partnerships per year of a male injecting drug userwith SW2 5 ADDIN EN.CITE ADDIN EN.CITE.DATA [55,56]with GF0.5 1.5 EMBED Equation.DSMT4 Number of partnerships per year of general males (who are not IDUs nor clients of SWs)0.75 1.5 ADDIN EN.CITE ADDIN EN.CITE.DATA [56] EMBED Equation.DSMT4 Number of partnerships per year of MSM2 - 6 ADDIN EN.CITE ADDIN EN.CITE.DATA [57,58,59,60] EMBED Equation.DSMT4 Proportion of acts in which condoms are used for non-SW females0 20% ADDIN EN.CITE ADDIN EN.CITE.DATA [56,61,62] EMBED Equation.DSMT4 Proportion of acts in which condoms are used by SWs10 - 50% ADDIN EN.CITE ADDIN EN.CITE.DATA [61,63] EMBED Equation.DSMT4 Proportion of acts in which condoms are used by MSM10 50% ADDIN EN.CITE ADDIN EN.CITE.DATA [57,64] EMBED Equation.DSMT4 Efficacy of condoms (per act)80-95% ADDIN EN.CITE ADDIN EN.CITE.DATA [54,65,66] EMBED Equation.DSMT4 Number of acts per partnership between SW and MC per year 1-6 ADDIN EN.CITE Buckingham200523232317Buckingham, R. W.Moraros, J.Bird, Y.Meister, E.Webb, N. C.Department of Health Science, New Mexico State University, Las Cruces, NM 88003, USA.Factors associated with condom use among brothel-based female sex workers in ThailandAIDS CareAIDS careAIDS CareAIDS careAIDS CareAIDS care640-7175AdultCondoms/*utilizationContraception BehaviorCross-Sectional StudiesFemale*Health Knowledge, Attitudes, PracticeHumansProstitution/ethnology/*statistics & numerical dataQuestionnairesSafe SexSexually Transmitted Diseases/*prevention & controlThailand2005Jul0954-0121 (Print)16036250http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=16036250 eng[63] EMBED Equation.DSMT4 Number of acts per partnership between GF and MC100 150 ADDIN EN.CITE ADDIN EN.CITE.DATA [67,68] EMBED Equation.DSMT4 Number of acts per partnership between GF and GM100 150 ADDIN EN.CITE ADDIN EN.CITE.DATA [67,68] EMBED Equation.DSMT4 Number of times injected drugs per year 300 1000 per year ADDIN EN.CITE ADDIN EN.CITE.DATA [69,70,71] EMBED Equation.DSMT4 Percentage of IDUs that share needles60 75% ADDIN EN.CITE Perngmark200348484817Perngmark, P.Celentano, D. D.Kawichai, S.Department of Health Policy, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD, USA.Needle sharing among southern Thai drug injectorsAddictionAddiction (Abingdon, England)AddictionAddiction (Abingdon, England)AddictionAddiction (Abingdon, England)1153-61988AdultCross-Sectional StudiesFemaleHIV Infections/transmissionHumansMaleNeedle Sharing/*psychologyPatient EducationRisk FactorsSubstance-Related Disorders/*psychologyThailand2003Aug0965-2140 (Print)12873250http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=12873250 eng[72] EMBED Equation.DSMT4 Proportion of injections in which sharing IDUs share needles0 1 EMBED Equation.DSMT4 Reduction factor in the rate at which IDUs seek treatment, since they are not as likely as other groups.0 - 1 Clinical experience EMBED Equation.DSMT4 Average time to receive treatment for SWs6 weeks 6 monthsEstimatee EMBED Equation.DSMT4 Average time to receive treatment for the non-SWs and non-IDUs6 weeks 12 monthsEstimatef EMBED Equation.DSMT4 Average time to receive treatment for IDUs EMBED Equation.DSMT4 Estimateg Experimental Parameter
We assume that HIV-infected individuals will not die from AIDS-related illnesses until they have progressed through primary and chronic infection, to the stage of infection of AIDS.
a The ranges is assumed for those who achieve viral suppression
b For this range, it is assumed that an individual with a drug resistant virus will survive longer that those without any treatment, but not as long as those with a drug susceptible virus
c Low range is based on time taken for resistance to re-emerge after structured treatment interruption, and high range based on time for resistance to normally develop
d Baseline taken at Chronic infection
e Estimate based on high organisation of this group, with several testing options and locations available
f Assumed that testing may not occur as regularly for these groups as with FSW
g We assume that IDUs are less likely to seek treatment immediately due to social and cultural factors
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