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Jafari M, Kheiri H. Free terminal time optimal control of a fractional-order model for the HIV/AIDS epidemic. INT J BIOMATH 2021. [DOI: 10.1142/s179352452250022x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper, we present a fractional model for the HIV/AIDS epidemic and incorporate into the model control parameters of pre-exposure prophylaxis (PrEP), behavioral change and antiretroviral therapy (ART) aimed at controlling the spread of diseases. We prove the local and global asymptotic stability of disease-free and endemic equilibria of the model. We present a general fractional optimal control problem (FOCP) with free terminal time and develop the Adapted Forward-Backward Sweep method for numerical solving of the FOCP. Necessary conditions for a state/control/terminal time triplet to be optimal are obtained. The results show that the use of all controls increases the life expectancy of HIV-treated patients with ART and remarkably increases the number of people undergoing PrEP and changing their sexual habits. Also, when the derivative order [Formula: see text] ([Formula: see text]) limits to 1, the value of optimal terminal time increases while the value of objective functional decreases.
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Affiliation(s)
- Mohsen Jafari
- Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
| | - Hossein Kheiri
- Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
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J. Silva C, F. M. Torres D. Modeling and optimal control of HIV/AIDS prevention through PrEP. ACTA ACUST UNITED AC 2018. [DOI: 10.3934/dcdss.2018008] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
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Hayes R, Ayles H, Beyers N, Sabapathy K, Floyd S, Shanaube K, Bock P, Griffith S, Moore A, Watson-Jones D, Fraser C, Vermund SH, Fidler S. HPTN 071 (PopART): rationale and design of a cluster-randomised trial of the population impact of an HIV combination prevention intervention including universal testing and treatment - a study protocol for a cluster randomised trial. Trials 2014; 15:57. [PMID: 24524229 PMCID: PMC3929317 DOI: 10.1186/1745-6215-15-57] [Citation(s) in RCA: 175] [Impact Index Per Article: 17.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2013] [Accepted: 02/03/2014] [Indexed: 01/01/2023] Open
Abstract
BACKGROUND Effective interventions to reduce HIV incidence in sub-Saharan Africa are urgently needed. Mathematical modelling and the HIV Prevention Trials Network (HPTN) 052 trial results suggest that universal HIV testing combined with immediate antiretroviral treatment (ART) should substantially reduce incidence and may eliminate HIV as a public health problem. We describe the rationale and design of a trial to evaluate this hypothesis. METHODS/DESIGN A rigorously-designed trial of universal testing and treatment (UTT) interventions is needed because: i) it is unknown whether these interventions can be delivered to scale with adequate uptake; ii) there are many uncertainties in the models such that the population-level impact of these interventions is unknown; and ii) there are potential adverse effects including sexual risk disinhibition, HIV-related stigma, over-burdening of health systems, poor adherence, toxicity, and drug resistance.In the HPTN 071 (PopART) trial, 21 communities in Zambia and South Africa (total population 1.2 m) will be randomly allocated to three arms. Arm A will receive the full PopART combination HIV prevention package including annual home-based HIV testing, promotion of medical male circumcision for HIV-negative men, and offer of immediate ART for those testing HIV-positive; Arm B will receive the full package except that ART initiation will follow current national guidelines; Arm C will receive standard of care. A Population Cohort of 2,500 adults will be randomly selected in each community and followed for 3 years to measure the primary outcome of HIV incidence. Based on model projections, the trial will be well-powered to detect predicted effects on HIV incidence and secondary outcomes. DISCUSSION Trial results, combined with modelling and cost data, will provide short-term and long-term estimates of cost-effectiveness of UTT interventions. Importantly, the three-arm design will enable assessment of how much could be achieved by optimal delivery of current policies and the costs and benefits of extending this to UTT. TRIAL REGISTRATION ClinicalTrials.gov NCT01900977.
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Affiliation(s)
- Richard Hayes
- Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, UK
| | - Helen Ayles
- Department of Clinical Research, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, UK
- Zambia AIDS Related TB Project, University of Zambia, Rideway Campus, Nationalist Road, Lusaka, Zambia
| | - Nulda Beyers
- Desmond Tutu TB Centre, Stellenbosch University, Francie van Zijl Avenue, Clinical Building, K Floor, Romm 0065, Tygerberg Campus, Western Cape 7505, South Africa
| | - Kalpana Sabapathy
- Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, UK
| | - Sian Floyd
- Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, UK
| | - Kwame Shanaube
- Zambia AIDS Related TB Project, University of Zambia, Rideway Campus, Nationalist Road, Lusaka, Zambia
| | - Peter Bock
- Desmond Tutu TB Centre, Stellenbosch University, Francie van Zijl Avenue, Clinical Building, K Floor, Romm 0065, Tygerberg Campus, Western Cape 7505, South Africa
| | - Sam Griffith
- FHI360, Science Facilitation Department, 2224 E NC Hwy 54, Durham, NC 27713, USA
| | - Ayana Moore
- FHI360, Science Facilitation Department, 2224 E NC Hwy 54, Durham, NC 27713, USA
| | - Deborah Watson-Jones
- Department of Clinical Research, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, UK
| | - Christophe Fraser
- St Mary’s Campus, HIV Clinical Trials Unit, Winston Churchill Wing, London W2 1NY, UK
| | - Sten H Vermund
- Institute for Global Health and Department of Pediatrics, Vanderbilt University, Institute for Global Health, 2525 West End Avenue, Suite 750, Nashville, TN 32703, USA
| | - Sarah Fidler
- Department of Infectious Disease Epidemiology, Imperial College London, St Mary’s Campus, Norfolk Place, London W2 1PG, UK
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Cohen MS, Smith MK, Muessig KE, Hallett TB, Powers KA, Kashuba AD. Antiretroviral treatment of HIV-1 prevents transmission of HIV-1: where do we go from here? Lancet 2013; 382:1515-24. [PMID: 24152938 PMCID: PMC3880570 DOI: 10.1016/s0140-6736(13)61998-4] [Citation(s) in RCA: 154] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Antiretroviral drugs that inhibit viral replication were expected to reduce transmission of HIV by lowering the concentration of HIV in the genital tract. In 11 of 13 observational studies, antiretroviral therapy (ART) provided to an HIV-infected index case led to greatly reduced transmission of HIV to a sexual partner. In the HPTN 052 randomised controlled trial, ART used in combination with condoms and counselling reduced HIV transmission by 96·4%. Evidence is growing that wider, earlier initiation of ART could reduce population-level incidence of HIV. However, the full benefits of this strategy will probably need universal access to very early ART and excellent adherence to treatment. Challenges to this approach are substantial. First, not all HIV-infected individuals can be located, especially people with acute and early infection who are most contagious. Second, the ability of ART to prevent HIV transmission in men who have sex with men (MSM) and people who use intravenous drugs has not been shown. Indeed, the stable or increased incidence of HIV in MSM in some communities where widespread use of ART has been established emphasises the concern that not enough is known about treatment as prevention for this crucial population. Third, although US guidelines call for immediate use of ART, such guidelines have not been embraced worldwide. Some experts do not believe that immediate or early ART is justified by present evidence, or that health-care infrastructure for this approach is sufficient. These concerns are very difficult to resolve. Ongoing community-based prospective trials of early ART are likely to help to establish the population-level benefit of ART, and-if successful-to galvanise treatment as prevention.
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Affiliation(s)
- Myron S Cohen
- Department of Medicine, University of North Carolina, Chapel Hill, NC, USA; Department of Microbiology, University of North Carolina, Chapel Hill, NC, USA; Department of Epidemiology, University of North Carolina, Chapel Hill, NC, USA.
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Kumar P, Choonara YE, Toit LC, Pillay V. In silico elucidation of the inclusion phenomenon and permeation behavior of a zidovudine–cyclodextrin complex via static lattice atomistic simulation. J INCL PHENOM MACRO 2013. [DOI: 10.1007/s10847-013-0316-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Dutta MJ. Disseminating HIV pre-exposure prophylaxis information in underserved communities. Am J Prev Med 2013; 44:S133-6. [PMID: 23253754 DOI: 10.1016/j.amepre.2012.09.030] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/31/2012] [Revised: 09/04/2012] [Accepted: 09/19/2012] [Indexed: 11/29/2022]
Affiliation(s)
- Mohan J Dutta
- Center for Culture-Centered Approach to Research and Evaluation (CARE), National University of Singapore, Singapore.
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Groves AK, Maman S, Moodley D. HIV+ women's narratives of non-disclosure: resisting the label of immorality. Glob Public Health 2012; 7:799-811. [PMID: 22594880 DOI: 10.1080/17441692.2012.679742] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Abstract
Increasing partner disclosure rates among HIV+ individuals is widely seen as an important public health strategy to reduce HIV transmission. One approach for encouraging disclosure is to emphasise individuals' moral responsibility to disclose their status to their partners. We use South Africa as a case study to draw attention to two problems with labelling non-disclosure as immoral. First, we argue that because women are tested for HIV at much higher rates than men, any approach that involves blaming HIV+ individuals for not disclosing their status will disproportionately burden women. Second, through the narratives of six HIV+ women, we highlight how a focus on morality undervalues the complexity of sexual partnerships. Specifically, women describe how their perceived obligation to disclose their status is directly influenced by communication with their sexual partners. Women also discuss how the onset of different life events might alter the meaning of HIV and change obligations regarding disclosure within the partnership. The differences in testing rates across gender combined with the complexity of sexual partnerships leads us to suggest that labelling non-disclosure as immoral does little to advance HIV prevention. There is an urgent need to identify alternative interventions that support women through the disclosure process.
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Affiliation(s)
- Allison Kjellman Groves
- Health Behavior and Health Education, UNC Gillings School of Global Public Health, Chapel Hill, NC, USA.
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Smith MK, Powers KA, Muessig KE, Miller WC, Cohen MS. HIV treatment as prevention: the utility and limitations of ecological observation. PLoS Med 2012; 9:e1001260. [PMID: 22802740 PMCID: PMC3393666 DOI: 10.1371/journal.pmed.1001260] [Citation(s) in RCA: 53] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
Results from several observational studies of HIV-discordant couples and a randomized controlled trial (HIV Prevention Trials Network 052) show that antiretroviral therapy (ART) can greatly reduce heterosexual HIV transmission in stable HIV-discordant couples. However, such data do not prove that ART will reduce HIV incidence at the population level. Observational investigations using ecological measures have been used to support the implementation of HIV treatment for the specific purpose of preventing transmission at the population level. Many of these studies note ecological associations between measures of increased ART uptake and decreased HIV transmission. Given the urgency of implementing HIV prevention measures, ecological studies must de facto be used to inform current strategies. However, the hypothesis that widespread ART can eliminate HIV infection may have raised expectations beyond what we may be able to achieve. Here we review and discuss the construct of the exposure and outcome measures and analysis methods used in ecological studies. By examining the strengths and weaknesses of ecological analyses, we aim to aid understanding of the findings from these studies to inform future policy decisions regarding the use of ART for HIV prevention.
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Affiliation(s)
- M. Kumi Smith
- Department of Epidemiology, University of North Carolina, Chapel Hill, North Carolina, United States of America
| | - Kimberly A. Powers
- Department of Epidemiology, University of North Carolina, Chapel Hill, North Carolina, United States of America
- Department of Medicine, University of North Carolina, Chapel Hill, North Carolina, United States of America
| | - Kathryn E. Muessig
- Department of Medicine, University of North Carolina, Chapel Hill, North Carolina, United States of America
| | - William C. Miller
- Department of Epidemiology, University of North Carolina, Chapel Hill, North Carolina, United States of America
- Department of Medicine, University of North Carolina, Chapel Hill, North Carolina, United States of America
| | - Myron S. Cohen
- Department of Epidemiology, University of North Carolina, Chapel Hill, North Carolina, United States of America
- Department of Medicine, University of North Carolina, Chapel Hill, North Carolina, United States of America
- Department of Microbiology and Immunology, University of North Carolina, Chapel Hill, North Carolina, United States of America
- * E-mail:
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Abstract
In 2009, the United Nations Estimated that 33.2 Million People worldwide were living with human immunodeficiency virus type 1 (HIV-1) infection and that 2.6 million people had been newly infected. The need for effective HIV-1 prevention has never been greater. In this review, we address recent critical advances in our understanding of HIV-1 transmission and acute HIV-1 infection. Fourth-generation HIV-1 testing, now available worldwide,, will allow the diagnosis of infection in many patients and may lead to new treatments and opportunities for prevention.
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Affiliation(s)
- Myron S Cohen
- Institute of Global Health and Infectious Diseases, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA.
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Postexposure prophylaxis, preexposure prophylaxis or universal test and treat: the strategic use of antiretroviral drugs to prevent HIV acquisition and transmission. AIDS 2010; 24 Suppl 4:S27-39. [PMID: 21042050 DOI: 10.1097/01.aids.0000390705.73759.2c] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Abstract
This review considers the use of antiretroviral drugs specifically to prevent HIV transmission. Antiretroviral therapy (ART) can be implemented for the protection of uninfected individuals both before (preexposure prophylaxis) and after (postexposure prophylaxis) exposure to HIV infection. Preexposure prophylaxis may be used coitally dependently when individuals are intermittently exposed or by continuous daily dosing for those constantly exposed; postexposure prophylaxis is used in 28-day courses. Alternatively, ART can be used strategically to reduce the viral load and consequent infectiousness of an HIV-infected individual, thereby limiting the risk of onward viral transmission. A policy of universal HIV testing to enhance the identification of all HIV-positive individuals followed by immediate treatment of all HIV-positive individuals, irrespective of their CD4 cell counts (universal test and treat), has been postulated as a potential tool capable of reducing HIV incidence at a population level. This concept represents a paradigm shift in the use of ART, targeting infectious individuals for prevention rather than protecting uninfected exposed populations. This strategy could have the advantage of preventing transmission and reducing HIV incidence at a population level, as well as delivering universal access to therapy for all people living with HIV and AIDS, potentially eliminating mother-to-child HIV transmission and limiting concomitant diseases such as tuberculosis. This review critically examines the scientific basis of ART for HIV prevention, summarizing the risks and opportunities of the potential expansion of ART for prevention. Specifically, we consider the evidences for and against targeting HIV-uninfected individuals compared with enhanced HIV testing and treatment of HIV-infected individuals in terms of impact on viral transmission.
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Sexual transmission of HIV-1. Antiviral Res 2009; 85:276-85. [PMID: 19874852 DOI: 10.1016/j.antiviral.2009.10.012] [Citation(s) in RCA: 58] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2009] [Revised: 10/02/2009] [Accepted: 10/16/2009] [Indexed: 12/18/2022]
Abstract
HIV-1 transmission occurs in a limited number of ways all of which are preventable. Overall, the risk of HIV-1 transmission following a single sexual exposure is low especially in comparison with other sexually transmitted infections (STIs); with estimates of the average probability of male to female HIV-1 transmission only 0.0005-0.0026 per coital act. The risk of acquiring HIV-1 from a single contact varies enormously and is dependant upon the infectiousness of the HIV-1 positive individual and the susceptibility to HIV-1 of their sexual partner. An understanding of the determinants of HIV-1 transmission is important not only to assess the infection risk to an individual when exposed to the virus (e.g. to determine the provision of post exposure prophylaxis), but also to make accurate predictions on the potential spread of HIV-1 infection in a population and to direct appropriate targeted prevention strategies. In this review article we summarise the current literature on the major worldwide source of HIV-1 acquisition, sexual transmission. This article forms part of a special issue of Antiviral Research marking the 25th anniversary of antiretroviral drug discovery and development, Vol 85, issue 1, 2010.
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Abstract
Effective antiretroviral therapy (ART) may reduce HIV sexual transmission by lowering genital HIV levels. A prospective study of men starting ART (n = 25) demonstrated rapid, substantial reductions in semen HIV RNA. However, despite an undetectable blood viral load, isolated semen HIV shedding was detected at more than one visit in 12 of 25 (48%) participants, with semen HIV RNA levels exceeding 5000 copies/ml in four of 25 (16%). Isolates were drug-sensitive, and this phenomenon was not associated with semen drug levels or regimen.
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Efficacy evidences in prevention of HIV infection in developing countries. A critical appraisal from population-based studies. ACTA ACUST UNITED AC 2009. [DOI: 10.1007/s12682-009-0019-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Forrest JI, Kaida A, Dietrich J, Miller CL, Hogg RS, Gray G. Perceptions of HIV and fertility among adolescents in Soweto, South Africa: stigma and social barriers continue to hinder progress. AIDS Behav 2009; 13 Suppl 1:55-61. [PMID: 19343491 DOI: 10.1007/s10461-009-9552-z] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2009] [Accepted: 03/16/2009] [Indexed: 11/28/2022]
Abstract
The scale up of highly active antiretroviral therapy (HAART) for the treatment of HIV has raised new concerns relating to fertility desires and outcomes. Among these concerns is social stigma surrounding HIV and childbearing. High rates of infection and patterns of high fertility make adolescents a crucial demographic to qualify perceptions of HIV and fertility. We conducted two focus groups (n = 11 males, n = 8 females) with participants ascertained from an HIV adolescent community advisory board in Soweto, South Africa. Adolescents raised concern over re-infection by HIV positive couples attempting to conceive. They also used this concern to justify their attitudes that HIV positive couples should adopt when faced with the desire to have children. Lastly, participants spoke of a need to revise adolescent sexual and reproductive health services to make them more youth-friendly where users could avoid stigma generated by community healthcare workers. This study adds to the growing literature that calls for an evaluation of adolescent HIV educational programs and a healthcare worker intervention that specifically targets stigma surrounding HIV and childbearing.
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Affiliation(s)
- Jamie I Forrest
- Faculty of Health Sciences, Simon Fraser University, 8888 University Avenue, Burnaby, BC, Canada.
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Anema A, Lima VD, Johnston K, Levy A, Montaner JSG. Expanded Highly Active Antiretroviral Therapy Coverage - A Powerful Strategy to Curb Progression to AIDS, Death and New Infections. EUROPEAN INFECTIOUS DISEASE 2009; 3:41-43. [PMID: 21243116 PMCID: PMC3020076] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Sustained combination of HIV prevention strategies is essential to curb the spread of the HIV/AIDS epidemic. The use of highly active antiretroviral therapy (HAART) decreases morbidity and mortality, as well as HIV transmission, among treated individuals. The concept of 'treatment as prevention' is dependent on HAART's ability to sustain HIV-1 RNA virological suppression at the individual and population levels, and has been demonstrated in studies evaluating transmission in mother-to-child, sero-discordant couples and large treated populations. The worldwide expansion of maximally effective antiretroviral drug regimens has been coupled with concerns regarding the magnitude of the financial investment required. However, HAART's compounding effect on reduced morbidity, mortality and transmission makes the expansion of HAART coverage highly cost-averting. Building on a mathematical model that evaluated the impact of expanded HAART access on viral load in a Canadian setting, we demonstrate that an investment of CA$249 million over the lifetime of treated individuals would result in a net gain of CA$2.1 billion over 30 years. This provides a powerful economic incentive to rapidly scale up HAART access worldwide.
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Affiliation(s)
- Aranka Anema
- British Columbia Centre for Excellence in HIV/AIDS, St Paul’s Hospital
- Department of Medicine, University of British Columbia
| | - Viviane D Lima
- British Columbia Centre for Excellence in HIV/AIDS, St Paul’s Hospital
- Department of Medicine, University of British Columbia
| | - Karissa Johnston
- School of Population and Public Health, University of British Columbia
| | - Adrian Levy
- School of Population and Public Health, University of British Columbia
| | - Julio SG Montaner
- British Columbia Centre for Excellence in HIV/AIDS, St Paul’s Hospital
- Department of Medicine, University of British Columbia
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