Abstract
Viral latency is a major barrier to curing HIV infection with antiretroviral therapy, and consequently, for eliminating the disease globally. The establishment, maintenance, and potential clearance of latent infection are complex dynamic processes and can be best understood and described with the help of mathematical models. Here we review the use of viral dynamics models for HIV, with a focus on applications to the latent reservoir. Such models have been used to explain the multiphasic decay of viral load during antiretroviral therapy, the early seeding of the latent reservoir during acute infection and the limited inflow during treatment, the dynamics of viral blips, and the phenomenon of posttreatment control. In addition, mathematical models have been used to predict the efficacy of potential HIV cure strategies, such as latency-reversing agents, early treatment initiation, or gene therapies, and to provide guidance for designing trials of these novel interventions.
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References
Alizon S, Fraser C (2013) Within-host and between-host evolutionary rates across the HIV-1 genome. Retrovirology 10:49. doi:10.1186/1742-4690-10-49, URL:https://doi.org/10.1186/1742-4690-10-49
Ananworanich J, Mellors JW (2015) A cure for HIV: what will it take? Curr Opin HIV AIDS 10(1):1–3. doi:10.1097/COH.0000000000000125
Ananworanich J, Dubé K, Chomont N (2015) How does the timing of antiretroviral therapy initiation in acute infection affect HIV reservoirs? Curr Opin HIV AIDS 10(1):18–28. doi:10.1097/COH.0000000000000122, URL:http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4271317/
Anderson RM, May RM (1991) Infectious diseases of humans: dynamics and control. Oxford University Press, USA
Anderson RW, Ascher MS, Sheppard HW (1998) Direct HIV cytopathicity cannot account for CD4 decline in AIDS in the presence of homeostasis: a worst-case dynamic analysis. J Acquir Immune Defic Syndr 17(3):245–252. URL:http://www.ncbi.nlm.nih.gov/pubmed/9495225
Andrade A, Rosenkranz SL, Cillo AR, Lu D, Daar ES, Jacobson JM, Lederman M, Acosta EP, Campbell T, Feinberg J, Flexner C, Mellors JW, Kuritzkes DR, Team ftACTGA (2013) Three distinct phases of HIV-1 RNA decay in treatment-naive patients receiving raltegravir-based antiretroviral therapy: ACTG A5248. J Infect Dis 208(6):884–891. doi:10.1093/infdis/jit272, URL:http://jid.oxfordjournals.org/content/208/6/884
Archin NM, Vaidya NK, Kuruc JD, Liberty AL, Wiegand A, Kearney MF, Cohen MS, Coffin JM, Bosch RJ, Gay CL, Eron JJ, Margolis DM, Perelson AS (2012) Immediate antiviral therapy appears to restrict resting CD4+ cell HIV-1 infection without accelerating the decay of latent infection. Proc Natl Acad Sci USA 109(24):9523–9528. doi:10.1073/pnas.1120248109
Arnaout RA, Nowak MA, Wodarz D (2000) HIV-1 dynamics revisited: biphasic decay by cytotoxic T lymphocyte killing? Proc Roy Soc B Biol Sci 267(1450):1347–1354. URL:http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1690670/
Blankson JN, Finzi D, Pierson TC, Sabundayo BP, Chadwick K, Margolick JB, Quinn TC, Siliciano RF (2000) Biphasic decay of latently infected CD4+ T cells in acute human immunodeficiency virus type 1 infection. J Infect Dis 182(6):1636–1642. URL:http://jid.oxfordjournals.org/content/182/6/1636.short
Blankson J, Persaud D, Siliciano R (2002) The challenge of viral reservoirs in HIV-1 infection. Annu Rev Med 53(1):557–593
Bonhoeffer S, Nowak MA (1997) Pre-existence and emergence of drug resistance in HIV-1 infection. Proc Roy Soc B Biol Sci 264(1382):631–637
Bonhoeffer S, May RM, Shaw GM, Nowak MA (1997) Virus dynamics and drug therapy. Proc Natl Acad Sci USA 94:6971–6976
Borducchi EN, Cabral C, Stephenson KE, Liu J, Abbink P, Ng’ang’a D, Nkolola JP, Brinkman AL, Peter L, Lee BC, Jimenez J, Jetton D, Mondesir J, Mojta S, Chandrashekar A, Molloy K, Alter G, Gerold JM, Hill AL, Lewis MG, Pau MG, Schuitemaker H, Hesselgesser J, Geleziunas R, Kim JH, Robb ML, Michael NL, Barouch DH (2016) Ad26/MVA therapeutic vaccination with TLR7 stimulation in SIV-infected rhesus monkeys. Nature 540(7632):284–287. doi:10.1038/nature20583, URL:http://www.nature.com.ezp-prod1.hul.harvard.edu/nature/journal/v540/n7632/full/nature20583.html
Brauer F (2009) Mathematical epidemiology is not an oxymoron. BMC Publ Health 9(Suppl 1):S2. doi:10.1186/1471-2458-9-S1-S2, URL:http://www.biomedcentral.com/1471-2458/9/S1/S2/abstract
Bui JK, Mellors JW, Cillo AR (2015) HIV-1 virion production from single inducible proviruses following T-cell activation ex vivo. J Virol. doi:10.1128/JVI.02520-15, URL:http://jvi.asm.org.ezp-prod1.hul.harvard.edu/content/early/2015/11/05/JVI.02520-15
Bullen CK, Laird GM, Durand CM, Siliciano JD, Siliciano RF (2014) New ex vivo approaches distinguish effective and ineffective single agents for reversing HIV-1 latency in vivo. Nat Med 20(4):425–429. doi:10.1038/nm.3489, URL:http://www.nature.com/nm/journal/v20/n4/abs/nm.3489.html
Burg D, Rong L, Neumann AU, Dahari H (2009) Mathematical modeling of viral kinetics under immune control during primary HIV-1 infection. J Theor Biol 259(4):751–759. doi:10.1016/j.jtbi.2009.04.010, URL:http://www.sciencedirect.com/science/article/pii/S0022519309001702
Buzon MM, Massanella M, Llibre JM, Esteve A, Dahl V, Puertas MC, Gatell JM, Domingo P, Paredes R, Sharkey M, Palmer S, Stevenson M, Clotet B, Blanco J, Martinez-Picado J (2010) HIV-1 replication and immune dynamics are affected by raltegravir intensification of HAART-suppressed subjects. Nat Med 16(4):460–465. doi:10.1038/nm.2111, URL:http://dx.doi.org/10.1038/nm.2111
Byrareddy SN, Arthos J, Cicala C, Villinger F, Ortiz KT, Little D, Sidell N, Kane MA, Yu J, Jones JW, Santangelo PJ, Zurla C, McKinnon LR, Arnold KB, Woody CE, Walter L, Roos C, Noll A, Ryk DV, Jelicic K, Cimbro R, Gumber S, Reid MD, Adsay V, Amancha PK, Mayne AE, Parslow TG, Fauci AS, Ansari AA (2016) Sustained virologic control in SIV+ macaques after antiretroviral and 47 antibody therapy. Science 354(6309):197–202. doi:10.1126/science.aag1276, URL:http://science.sciencemag.org/content/354/6309/197
Chatterjee A, Guedj J, Perelson AS (2012) Mathematical modelling of HCV infection: what can it teach us in the era of direct-acting antiviral agents? Antiviral Ther 17(6 Pt B):1171–1182. doi:10.3851/IMP2428, URL:http://europepmc.org/articles/PMC3641583
Chomont N, El-Far M, Ancuta P, Trautmann L, Procopio FA, Yassine-Diab B, Boucher G, Boulassel MR, Ghattas G, Brenchley JM, Schacker TW, Hill BJ, Douek DC, Routy JP, Haddad EK, Sekaly RP (2009) HIV reservoir size and persistence are driven by T cell survival and homeostatic proliferation. Nat Med 15(8):893–900. doi:10.1038/nm.1972, URL:http://dx.doi.org/10.1038/nm.1972
Chomont N, DaFonseca S, Vandergeeten C, Ancuta P, Sékaly RP (2011) Maintenance of CD4+ T-cell memory and HIV persistence: keeping memory, keeping HIV. Curr Opin in HIV and AIDS 6(1):30–36. doi:10.1097/COH.0b013e3283413775
Chret A, Bacchus-Souffan C, Avettand-Fenol V, Mlard A, Nembot G, Blanc C, Samri A, Sez-Cirin A, Hocqueloux L, Lascoux-Combe C, Allavena C, Goujard C, Valantin MA, Leplatois A, Meyer L, Rouzioux C, Autran B, OPTIPRIM ANRS-147 Study Group (2015) Combined ART started during acute HIV infection protects central memory CD4+ T cells and can induce remission. The Journal of Antimicrobial Chemotherapy 70(7):2108–2120. doi:10.1093/jac/dkv084
Chun TW, Finzi D, Margolick J, Chadwick K, Schwartz D, Siliciano RF (1995) In vivo fate of HIV-1-infected T cells: quantitative analysis of the transition to stable latency. Nat Med 1(12):1284–1290
Chun TW, Carruth L, Finzi D, Shen X, DiGiuseppe JA, Taylor H, Hermankova M, Chadwick K, Margolick J, Quinn TC et al (1997) Quantification of latent tissue reservoirs and total body viral load in HIV-1 infection. Nature 387(6629):183–188
Chun TW, Justement JS, Murray D, Hallahan CW, Maenza J, Collier AC, Sheth PM, Kaul R, Ostrowski M, Moir S, Kovacs C, Fauci AS (2010) Rebound of plasma viremia following cessation of antiretroviral therapy despite profoundly low levels of HIV reservoir: implications for eradication. AIDS 24(18):2803–2808. doi:10.1097/QAD.0b013e328340a239, URL:http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3154092/
Clapham HE, Tricou V, Van Vinh Chau N, Simmons CP, Ferguson NM (2014) Within-host viral dynamics of dengue serotype 1 infection. J Roy Soc Interface 11(96). doi:10.1098/rsif.2014.0094, URL:http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4032531/
Cohn LB, Silva IT, Oliveira TY, Rosales RA, Parrish EH, Learn GH, Hahn BH, Czartoski JL, McElrath MJ, Lehmann C, Klein F, Caskey M, Walker BD, Siliciano JD, Siliciano RF, Jankovic M, Nussenzweig MC (2015) HIV-1 integration landscape during latent and active infection. Cell 160(3):420–432. doi:10.1016/j.cell.2015.01.020
Colgrove R, Japour A (1999) A combinatorial ledge: reverse transcriptase fidelity, total body viral burden, and the implications of multiple-drug HIV therapy for the evolution of antiviral resistance. Antiviral Res 41(1):45–56. doi:10.1016/S0166-3542(98)00062-X, URL:http://www.sciencedirect.com/science/article/pii/S016635429800062X
Conway JM, Coombs D (2011) A stochastic model of latently infected cell reactivation and viral blip generation in treated HIV patients. PLoS Comput Biol 7(4):e1002033. doi:10.1371/journal.pcbi.1002033, URL:http://dx.doi.org/10.1371/journal.pcbi.1002033
Conway JM, Perelson AS (2015) Post-treatment control of HIV infection. Proc Nat Acad Sci 112(17):5467–5472. doi:10.1073/pnas.1419162112, URL:http://www.pnas.org/content/112/17/5467
Conway JM, Perelson AS (2016) Residual viremia in treated HIV+ individuals. PLoS Comput Biol 12(1):e1004677. doi:10.1371/journal.pcbi.1004677
Cory TJ, Schacker TW, Stevenson M, Fletcher CV (2013) Overcoming pharmacologic sanctuaries. Current Opin HIV AIDS 8(3):190–195
Crooks AM, Bateson R, Cope AB, Dahl NP, Griggs MK, Kuruc JD, Gay CL, Eron JJ, Margolis DM, Bosch RJ, Archin NM (2015) Precise quantitation of the latent HIV-1 reservoir: implications for eradication strategies. J Infect Dis. doi:10.1093/infdis/jiv218, URL:http://jid.oxfordjournals.org/content/early/2015/04/15/infdis.jiv218
Dahari H, Shudo E, Ribeiro RM, Perelson AS (2009) Modeling complex decay profiles of hepatitis B virus during antiviral therapy. Hepatology 49(1):32–38. doi:10.1002/hep.22586, URL:http://onlinelibrary.wiley.com/doi/10.1002/hep.22586/abstract
Davey RT Jr, Bhat N, Yoder C, Chun TW, Metcalf JA, Dewar R, Natarajan V, Lempicki RA, Adelsberger JW, Miller KD, Kovacs JA, Polis MA, Walker RE, Falloon J, Masur H, Gee D, Baseler M, Dimitrov DS, Fauci AS, Lane HC (1999) HIV-1 and T cell dynamics after interruption of highly active antiretroviral therapy (HAART) in patients with a history of sustained viral suppression. Proc Natl Acad Sci USA 96(26):15109–15114
Diekmann O, Heesterbeek JaP, Metz JaJ (1990) On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. J Math Biol 28(4):365–382. doi:10.1007/BF00178324, URL:https://link-springer-com.ezp-prod1.hul.harvard.edu/article/10.1007/BF00178324
Dinoso JB, Kim SY, Wiegand AM, Palmer SE, Gange SJ, Cranmer L, O’Shea A, Callender M, Spivak A, Brennan T et al (2009) Treatment intensification does not reduce residual HIV-1 viremia in patients on highly active antiretroviral therapy. Proc Natl Acad Sci 106(23):9403
Doekes HM, Fraser C, Lythgoe KA (2017) Effect of the latent reservoir on the evolution of HIV at the within- and between-host levels. PLOS Comput Biol 13(1):e1005228. doi:10.1371/journal.pcbi.1005228, URL:http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1005228
Elliott JH, Wightman F, Solomon A, Ghneim K, Ahlers J, Cameron MJ, Smith MZ, Spelman T, McMahon J, Velayudham P, Brown G, Roney J, Watson J, Prince MH, Hoy JF, Chomont N, Fromentin R, Procopio FA, Zeidan J, Palmer S, Odevall L, Johnstone RW, Martin BP, Sinclair E, Deeks SG, Hazuda DJ, Cameron PU, Sékaly RP, Lewin SR (2014) Activation of HIV Transcription with short-course vorinostat in HIV-infected patients on suppressive antiretroviral therapy. PLoS Pathog 10(11):e1004473. doi:10.1371/journal.ppat.1004473, URL:http://dx.doi.org/10.1371/journal.ppat.1004473
Elliott JH, McMahon JH, Chang CC, Lee SA, Hartogensis W, Bumpus N, Savic R, Roney J, Hoh R, Solomon A, Piatak M, Gorelick RJ, Lifson J, Bacchetti P, Deeks SG, Lewin SR (2015) Short-term administration of disulfiram for reversal of latent HIV infection: a phase 2 dose-escalation study. The Lancet HIV 2(12):e520–e529. doi:10.1016/S2352-3018(15)00226-X, URL:http://www.sciencedirect.com/science/article/pii/S235230181500226X
Eriksson S, Graf EH, Dahl V, Strain MC, Yukl SA, Lysenko ES, Bosch RJ, Lai J, Chioma S, Emad F, Abdel-Mohsen M, Hoh R, Hecht F, Hunt P, Somsouk M, Wong J, Johnston R, Siliciano RF, Richman DD, O’Doherty U, Palmer S, Deeks SG, Siliciano JD (2013) Comparative analysis of measures of viral reservoirs in HIV-1 eradication studies. PLoS Pathog 9(2):e1003174. doi:10.1371/journal.ppat.1003174, URL:http://dx.doi.org/10.1371/journal.ppat.1003174
Etemad B, Sun X, Lederman MM, Gottlieb R, Aga E, Bosch RJ, Jacobson JM, Gandhi RT, Yu X, Li JZ (2016) Viral and immune characteristics of HIV post-treatment controllers in ACTG studies. In: CROI, Boston. URL:http://www.croiconference.org/sessions/viral-and-immune-characteristics-hiv-post-treatment-controllers-actg-studies
Fine P, Eames K, Heymann DL (2011) “Herd immunity”: a rough guide. Clinical infectious diseases: an official publication of the infectious diseases society of America 52(7):911–916. doi:10.1093/cid/cir007
Finzi D, Hermankova M, Pierson T, Carruth LM, Buck C, Chaisson RE, Quinn TC, Chadwick K, Margolick J, Brookmeyer R, Gallant J, Markowitz M, Ho DD, Richman DD, Siliciano RF (1997) Identification of a reservoir for HIV-1 in patients on highly active antiretroviral therapy. Science 278(5341):1295–1300. doi:10.1126/science.278.5341.1295, URL:http://www.sciencemag.org/content/278/5341/1295.abstract
Finzi D, Blankson J, Siliciano JD, Margolick JB, Chadwick K, Pierson T, Smith K, Lisziewicz J, Lori F, Flexner C, Quinn TC, Chaisson RE, Rosenberg E, Walker B, Gange S, Gallant J, Siliciano RF (1999) Latent infection of CD4+ T cells provides a mechanism for lifelong persistence of HIV-1, even in patients on effective combination therapy. Nat Med 5(5):512–517. doi:10.1038/8394
Frost SD, McLean AR (1994) Quasispecies dynamics and the emergence of drug resistance during zidovudine therapy of HIV infection. Aids 8(3):323–332
Gandhi RT, Zheng L, Bosch RJ, Chan ES, Margolis DM, Read S, Kallungal B, Palmer S, Medvik K, Lederman MM, Alatrakchi N, Jacobson JM, Wiegand A, Kearney M, Coffin JM, Mellors JW, Eron JJ, on behalf of the AIDS Clinical Trials Group A5244 team (2010) The effect of raltegravir intensification on low-level residual viremia in HIV-infected patients on antiretroviral therapy: a randomized controlled trial. PLoS Med 7(8):e1000321. doi:10.1371/journal.pmed.1000321, URL:http://dx.doi.org/10.1371/journal.pmed.1000321
Goujard C, Girault I, Rouzioux C, Lécuroux C, Deveau C, Chaix ML, Jacomet C, Talamali A, Delfraissy JF, Venet A, Meyer L, Sinet M, ANRS CO6 PRIMO Study Group (2012) HIV-1 control after transient antiretroviral treatment initiated in primary infection: role of patient characteristics and effect of therapy. Antiviral Ther 17(6):1001–1009. doi:10.3851/IMP2273
Hatano H, Strain MC, Scherzer R, Bacchetti P, Wentworth D, Hoh RA, Martin JN, McCune JM, Neaton J, Tracy R, Richman DD, Deeks SG (2013) Increase in 2-LTR circles and decrease in D-dimer after raltegravir intensification in treated HIV-infected patients: a randomized, placebo-controlled trial. J Infect Dis 208(9):1436–1442
Henrich TJ, Hanhauser E, Marty FM, Sirignano MN, Keating S, Lee TH, Robles YP, Davis BT, Li JZ, Heisey A, Hill AL, Busch MP, Armand P, Soiffer RJ, Altfeld M, Kuritzkes DR (2014) Antiretroviral-free HIV-1 remission and viral rebound after allogeneic stem cell transplantation: report of 2 cases. Ann Intern Med 161(5):319–327. doi:10.7326/M14-1027, URL:http://dx.doi.org/10.7326/M14-1027
Hill AL, Rosenbloom DIS, Fu F, Nowak MA, Siliciano RF (2014) Predicting the outcomes of treatment to eradicate the latent reservoir for HIV-1. Proc Nat Acad Sci 111(37):13475–13480. doi:10.1073/pnas.1406663111, URL:http://www.pnas.org/content/111/37/13475
Hill AL, Rosenbloom DIS, Goldstein E, Hanhauser E, Kuritzkes DR, Siliciano RF, Henrich TJ (2016a) Real-time predictions of reservoir size and rebound time during antiretroviral therapy interruption trials for HIV. PLOS Pathog 12(4):e1005535. doi:10.1371/journal.ppat.1005535, URL:http://journals.plos.org/plospathogens/article?id=10.1371/journal.ppat.1005535
Hill AL, Rosenbloom DIS, Siliciano JD, Siliciano RF (2016b) Insufficient evidence for rare activation of latent HIV in the absence of reservoir-reducing interventions. PLOS Pathog 12(8):e1005679. doi:10.1371/journal.ppat.1005679, URL:http://journals.plos.org/plospathogens/article?id=10.1371/journal.ppat.1005679
Hill AL, Rosenbloom DIS, Siliciano R (2017) Estimating the efficacy of HIV latency reversing agents from residual viremia measurements. In preparation
Ho DD, Neumann AU, Perelson AS, Chen W, Leonard JM, Markowitz M et al (1995) Rapid turnover of plasma virions and CD4 lymphocytes in HIV-1 infection. Nature 373(6510):123–126
Hosmane NN, Kwon KJ, Bruner KM, Capoferri AA, Beg S, Rosenbloom DIS, Keele BF, Ho YC, Siliciano JD, Siliciano RF (2017) Proliferation of latently infected CD4(+) T cells carrying replication-competent HIV-1: potential role in latent reservoir dynamics. J Exp Med 214(4):959–972. doi:10.1084/jem.20170193
Immonen TT, Conway JM, Romero-Severson EO, Perelson AS, Leitner T (2015) Recombination enhances HIV-1 envelope diversity by facilitating the survival of latent genomic fragments in the plasma virus population. PLOS Comput Biol 11(12):e1004625. doi:10.1371/journal.pcbi.1004625, URL:http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1004625
Jilek BL, Zarr M, Sampah ME, Rabi SA, Bullen CK, Lai J, Shen L, Siliciano RF (2012) A quantitative basis for antiretroviral therapy for HIV-1 infection. Nat Med 18(3):446–451. doi:10.1038/nm.2649, URL:http://www.nature.com/nm/journal/v18/n3/full/nm.2649.html
Jones LE, Perelson AS (2007) Transient viremia, plasma viral load, and reservoir replenishment in HIV-infected patients on antiretroviral therapy. J Acquir Immune Defic Syndr (1999) 45(5):483–493. doi:10.1097/QAI.0b013e3180654836, URL:http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2584971/
Joos B, Fischer M, Kuster H, Pillai SK, Wong JK, Böni J, Hirschel B, Weber R, Trkola A, Günthard HF, Swiss HIV Cohort Study (2008) HIV rebounds from latently infected cells, rather than from continuing low-level replication. Proc Nat Acad Sci U S A 105(43):16725–16730. doi:10.1073/pnas.0804192105
Kaufmann DE, Lichterfeld M, Altfeld M, Addo MM, Johnston MN, Lee PK, Wagner BS, Kalife ET, Strick D, Rosenberg ES, Walker BD (2004) Limited durability of viral control following treated acute HIV infection. PLOS Med 1(2):e36. doi:10.1371/journal.pmed.0010036, URL:http://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.0010036
Kelly JK (1996) Replication rate and evolution in the human immunodeficiency virus. J Theor Biol 180(4):359–364. doi:10.1006/jtbi.1996.0108, URL:http://www.sciencedirect.com/science/article/pii/S0022519396901083
Kermack WO, McKendrick AG (1927) A contribution to the mathematical theory of epidemics. Proc Roy Soc Lond A Math Phys Eng Sci 115(772):700–721. doi:10.1098/rspa.1927.0118, URL:http://rspa.royalsocietypublishing.org/content/115/772/700
Kieffer TL, Finucane MM, Nettles RE, Quinn TC, Broman KW, Ray SC, Persaud D, Siliciano RF (2004) Genotypic analysis of HIV-1 drug resistance at the limit of detection: virus production without evolution in treated adults with undetectable HIV loads. J Infect Dis 189(8):1452–1465. doi:10.1086/382488
Kim H, Perelson AS (2006) Viral and latent reservoir persistence in HIV-1-infected patients on therapy. PLoS Comput Biol 2(10):e135. doi:10.1371/journal.pcbi.0020135, URL:http://dx.plos.org/10.1371/journal.pcbi.0020135
Lifson JD, Rossio JL, Arnaout R, Li L, Parks TL, Schneider DK, Kiser RF, Coalter VJ, Walsh G, Imming RJ (2000) Containment of simian immunodeficiency virus infection: cellular immune responses and protection from rechallenge following transient postinoculation antiretroviral treatment. J Virol 74(6):2584–2593
Lifson JD, Rossio JL, Piatak M, Parks T, Li L, Kiser R, Coalter V, Fisher B, Flynn BM, Czajak S (2001) Role of CD8+ lymphocytes in control of simian immunodeficiency virus infection and resistance to rechallenge after transient early antiretroviral treatment. J Virol 75(21):10187–10199
Lim SY, Osuna CE, Hesselgesser J, Hill AL, Miller MD, Geleziunas R, Lee W, Whitney JB (2017) TLR7 agonist treatment of SIV+ monkeys on ART can lead to complete viral remission. URL:http://www.croiconference.org/sessions/tlr7-agonist-treatment-siv-monkeys-art-can-lead-complete-viral-remission, #338LB
Lodi S, Meyer L, Kelleher AD, Rosinska M, Ghosn J, Sannes M, Porter K (2012) Immunovirologic control 24 months after interruption of antiretroviral therapy initiated close to HIV seroconversion. Arch Intern Med 172(16):1252–1255. doi:10.1001/archinternmed.2012.2719
Luo R, Piovoso MJ, Martinez-Picado J, Zurakowski R (2012) HIV model parameter estimates from interruption trial data including drug efficacy and reservoir dynamics. PLoS One 7(7):e40198. doi:10.1371/journal.pone.0040198, URL:http://dx.doi.org/10.1371/journal.pone.0040198
Luo R, Cardozo EF, Piovoso MJ, Wu H, Buzon MJ, Martinez-Picado J, Zurakowski R (2013) Modelling HIV-1 2-LTR dynamics following raltegravir intensification. J Roy Soc Interface 10(84). doi:10.1098/rsif.2013.0186, URL:http://rsif.royalsocietypublishing.org/content/10/84/20130186
Luzuriaga K, Gay H, Ziemniak C, Sanborn KB, Somasundaran M, Rainwater-Lovett K, Mellors JW, Rosenbloom D, Persaud D (2015) Viremic relapse after HIV-1 remission in a perinatally infected child. New Engl J Med 372(8):786–788. doi:10.1056/NEJMc1413931
Lythgoe KA, Fraser C (2012) New insights into the evolutionary rate of HIV-1 at the within-host and epidemiological levels. Proc Roy Soc B Biol Sci. doi:10.1098/rspb.2012.0595, URL:http://www.ncbi.nlm.nih.gov/pubmed/22593106
Maenza J, Tapia K, Holte S, Stekler JD, Stevens CE, Mullins JI, Collier AC (2015) How often does treatment of primary HIV lead to post-treatment control? Antiviral Ther. doi:10.3851/IMP2963
Maldarelli F, Wu X, Su L, Simonetti FR, Shao W, Hill S, Spindler J, Ferris AL, Mellors JW, Kearney MF, Coffin JM, Hughes SH (2014) Specific HIV integration sites are linked to clonal expansion and persistence of infected cells. Science 345(6193):179–183. doi:10.1126/science.1254194, URL:http://www.sciencemag.org/content/345/6193/179
Markowitz M, Louie M, Hurley A, Sun E, Di Mascio M, Perelson AS, Ho DD (2003) A novel antiviral intervention results in more accurate assessment of human immunodeficiency virus type 1 replication dynamics and T-cell decay in vivo. J Virol 77(8):5037–5038. doi:10.1128/JVI.77.8.5037-5038.2003
Martinez-Picado J, Deeks SG (2016) Persistent HIV-1 replication during antiretroviral therapy. Curr Opin HIV AIDS 11(4):417–423. doi:10.1097/COH.0000000000000287
McLean AR, Nowak MA (1992) Competition between zidovudine-sensitive and zidovudine-resistant strains of HIV. AIDS 6(1):71
Murillo LN, Murillo MS, Perelson AS (2013) Towards multiscale modeling of influenza infection. J Theor Biol 332:267–290. doi:10.1016/j.jtbi.2013.03.024, URL:http://www.sciencedirect.com/science/article/pii/S0022519313001501
Murray AJ, Kwon KJ, Farber DL, Siliciano RF (2016) The latent reservoir for HIV-1: how immunologic memory and clonal expansion contribute to HIV-1 persistence. J Immun 197(2):407–417. doi:10.4049/jimmunol.1600343, URL:http://www.jimmunol.org.ezp-prod1.hul.harvard.edu/content/197/2/407
Neumann AU, Lam NP, Dahari H, Gretch DR, Wiley TE, Layden TJ, Perelson AS (1998) Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon- therapy. Science 282(5386):103–107. doi:10.1126/science.282.5386.103, URL:http://www.sciencemag.org/content/282/5386/103
No A, Plum J, Verhofstede C (2005) The latent HIV-1 reservoir in patients undergoing HAART: an archive of pre-HAART drug resistance. J Antimicrob Chemother 55(4):410–412. doi:10.1093/jac/dki038, URL:http://jac.oxfordjournals.org/content/55/4/410.abstract
Nowak MA, May RMC (2000) Virus dynamics: mathematical principles of immunology and virology. Oxford University Press, USA
Nowak MA, Anderson RM, McLean AR, Wolfs TF, Goudsmit J, May RM (1991) Antigenic diversity thresholds and the development of AIDS. Science 254(5034):963–969
Nowak MA, Bonhoeffer S, Hill AM, Boehme R, Thomas HC, McDade H (1996) Viral dynamics in hepatitis B virus infection. Proc Natl Acad Sci 93:4398–4402
Nuraini N, Tasman H, Soewono E, Sidarto KA (2009) A with-in host dengue infection model with immune response. Math Comput Model 49(56):1148–1155. doi:10.1016/j.mcm.2008.06.016, URL:http://www.sciencedirect.com/science/article/pii/S0895717708002732
Palmer S, Maldarelli F, Wiegand A, Bernstein B, Hanna GJ, Brun SC, Kempf DJ, Mellors JW, Coffin JM, King MS (2008) Low-level viremia persists for at least 7 years in patients on suppressive antiretroviral therapy. Proc Nat Acad Sci U S A 105(10):3879–3884. doi:10.1073/pnas.0800050105, URL:http://www.ncbi.nlm.nih.gov/pubmed/18332425
Pennings PS (2012) Standing genetic variation and the evolution of drug resistance in HIV. PLoS Comput Biol 8(6):e1002527. doi:10.1371/journal.pcbi.1002527, URL:http://dx.doi.org/10.1371/journal.pcbi.1002527
Pennings PS, Kryazhimskiy S, Wakeley J (2014) Loss and recovery of genetic diversity in adapting populations of HIV. PLoS Genet 10(1):e1004000. doi:10.1371/journal.pgen.1004000, URL:http://dx.doi.org/10.1371/journal.pgen.1004000
Perelson AS, Ribeiro RM (2004) Hepatitis B virus kinetics and mathematical modeling. Semin Liver Dis 24(S 1):11–16. doi:10.1055/s-2004-828673, URL:https://www.thieme-connect.com/products/ejournals/html/10.1055/s-2004-828673
Perelson AS, Neumann AU, Markowitz M, Leonard JM, Ho DD (1996) HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time. Science 271(5255):1582–1586. URL:http://www.ncbi.nlm.nih.gov/pubmed/8599114
Perelson AS, Essunger P, Cao Y, Vesanen M, Hurley A, Saksela K, Markowitz M, Ho DD (1997) Decay characteristics of HIV-1-infected compartments during combination therapy. Nature 387(6629):188–191. doi:10.1038/387188a0, URL:http://dx.doi.org/10.1038/387188a0
Persaud D, Pierson T, Ruff C, Finzi D, Chadwick KR, Margolick JB, Ruff A, Hutton N, Ray S, Siliciano RF (2000) A stable latent reservoir for HIV-1 in resting CD4+ T lymphocytes in infected children. J Clin Invest 105(7):995–1003. URL:http://www.ncbi.nlm.nih.gov/pmc/articles/PMC377486/
Petravic J, Martyushev A, Reece JC, Kent SJ, Davenport MP (2014) Modeling the timing of antilatency drug administration during HIV treatment. J Virol 88(24):14050–14056. doi:10.1128/JVI.01701-14
Petravic J, Rasmussen TA, Lewin SR, Kent SJ, Davenport MP (2017) Relationship between measures of HIV reactivation and the decline of latent reservoir under latency-reversing agents. J Virol. doi:10.1128/JVI.02092-16
Phillips AN (1996) Reduction of HIV concentration during acute infection: independence from a specific immune response. Science 271(5248):497
Pinkevych M, Cromer D, Tolstrup M, Grimm AJ, Cooper DA, Lewin SR, Søgaard OS, Rasmussen TA, Kent SJ, Kelleher AD, Davenport MP (2015) HIV reactivation from latency after treatment interruption occurs on average every 5–8 days—implications for HIV remission. PLoS Pathog 11(7):e1005000. doi:10.1371/journal.ppat.1005000, URL:http://dx.doi.org/10.1371/journal.ppat.1005000
Ramratnam B, Bonhoeffer S, Binley J, Hurley A, Zhang L, Mittler JE, Markowitz M, Moore JP, Perelson AS, Ho DD (1999) Rapid production and clearance of HIV-1 and hepatitis C virus assessed by large volume plasma apheresis. Lancet 354(9192):1782–1785. doi:10.1016/S0140-6736(99)02035-8, URL:http://www.sciencedirect.com/science/article/pii/S0140673699020358
Rasmussen TA, Tolstrup M, Brinkmann CR, Olesen R, Erikstrup C, Solomon A, Winckelmann A, Palmer S, Dinarello C, Buzon M, others (2014) Panobinostat, a histone deacetylase inhibitor, for latent-virus reactivation in HIV-infected patients on suppressive antiretroviral therapy: a phase 1/2, single group, clinical trial. Lancet HIV 1(1):e13–e21. URL:http://www.sciencedirect.com/science/article/pii/S2352301814700141
Razooky BS, Pai A, Aull K, Rouzine IM, Weinberger LS (2015) A hardwired HIV latency program. Cell 160(5):990–1001. doi:10.1016/j.cell.2015.02.009, URL:http://www.cell.com.ezp-prod1.hul.harvard.edu/article/S0092867415001749/abstract
Regoes RR, Wodarz D, Nowak MA (1998) Virus dynamics: the effect of target cell limitation and immune responses on virus evolution. J Theor Biol 191(4):451–462
Ribeiro RM (2002) In vivo dynamics of T cell activation, proliferation, and death in HIV-1 infection: why are CD4+ but not CD8+ T cells depleted? Proc Nat Acad Sci 99(24):15572–15577. doi:10.1073/pnas.242358099, URL:http://www.ncbi.nlm.nih.gov.ezp-prod1.hul.harvard.edu/pmc/articles/PMC137758/
Ribeiro RM, Bonhoeffer S, Nowak MA (1998) The frequency of resistant mutant virus before antiviral therapy. AIDS 12(5):461
Ribeiro RM, Qin L, Chavez LL, Li D, Self SG, Perelson AS (2010) Estimation of the initial viral growth rate and basic reproductive number during acute HIV-1 infection. J Virol 84(12):6096–6102. doi:10.1128/JVI.00127-10, URL:http://jvi.asm.org/content/84/12/6096.abstract
Rong L, Perelson AS (2009a) Asymmetric division of activated latently infected cells may explain the decay kinetics of the HIV-1 latent reservoir and intermittent viral blips. Math Biosci 217(1):77–87. doi:10.1016/j.mbs.2008.10.006
Rong L, Perelson AS (2009b) Modeling latently infected cell activation: viral and latent reservoir persistence, and viral blips in HIV-infected patients on potent therapy. PLoS Comput Biol 5(10):e1000533. doi:10.1371/journal.pcbi.1000533, URL:http://dx.doi.org/10.1371/journal.pcbi.1000533
Rosenberg ES, Altfeld M, Poon SH, Phillips MN, Wilkes BM, Eldridge RL, Robbins GK, D’Aquila RT, Goulder PJR, Walker BD (2000) Immune control of HIV-1 after early treatment of acute infection. Nature 407(6803):523–526. doi:10.1038/35035103, URL:http://dx.doi.org/10.1038/35035103
Rosenbloom DIS, Hill AL, Rabi SA, Siliciano RF, Nowak MA (2012) Antiretroviral dynamics determines HIV evolution and predicts therapy outcome. Nat Med 18(9):1378–1385. doi:10.1038/nm.2892, URL:http://www.nature.com.ezp-prod1.hul.harvard.edu/nm/journal/v18/n9/full/nm.2892.html
Rouzine I, Coffin J (1999) Linkage disequilibrium test implies a large effective population number for HIV in vivo. Proc Nat Acad Sci 96(19):10758
Rouzine IM, Razooky BS, Weinberger LS (2014) Stochastic variability in HIV affects viral eradication. Proc Nat Acad Sci 111(37):13251–13252. doi:10.1073/pnas.1413362111, URL:http://www.pnas.org/content/111/37/13251
Rouzine I, Weinberger A, Weinberger L (2015) An evolutionary role for HIV latency in enhancing viral transmission. Cell 160(5):1002–1012. doi:10.1016/j.cell.2015.02.017, URL:http://www.sciencedirect.com/science/article/pii/S009286741500183X
Ruff CT, Ray SC, Kwon P, Zinn R, Pendleton A, Hutton N, Ashworth R, Gange S, Quinn TC, Siliciano RF, Persaud D (2002) Persistence of wild-type virus and lack of temporal structure in the latent reservoir for human immunodeficiency virus type 1 in pediatric patients with extensive antiretroviral exposure. J Virol 76(18):9481–9492. doi:10.1128/JVI.76.18.9481-9492.2002, URL:http://jvi.asm.org/content/76/18/9481
Ruiz L, Martinez-Picado J, Romeu J, Paredes R, Zayat MK, Marfil S, Negredo E, Sirera G, Tural C, Clotet B (2000) Structured treatment interruption in chronically HIV-1 infected patients after long-term viral suppression. AIDS 14(4):397
Saez-Cirion A, Jacquelin B, Barré-Sinoussi F, Müller-Trutwin M (2014) Immune responses during spontaneous control of HIV and AIDS: what is the hope for a cure? Philos Trans Roy Soc Lond Series B Biol Sci 369(1645):20130436. doi:10.1098/rstb.2013.0436
Schiffer JT, Swan DA, Magaret A, Corey L, Wald A, Ossig J, Ruebsamen-Schaeff H, Stoelben S, Timmler B, Zimmermann H, Melhem MR, Van Wart SA, Rubino CM, Birkmann A (2016) Mathematical modeling of herpes simplex virus-2 suppression with pritelivir predicts trial outcomes. Sci Transl Med 8(324):324ra15, DOI 10.1126/scitranslmed.aad6654
Sedaghat AR, Siliciano JD, Brennan TP, Wilke CO, Siliciano RF (2007) Limits on replenishment of the resting CD4+ T cell reservoir for HIV in patients on HAART. PLoS Pathog 3(8):e122. doi:10.1371/journal.ppat.0030122, URL:http://dx.plos.org/10.1371/journal.ppat.0030122
Sedaghat A, Siliciano R, Wilke C (2008) Low-level HIV-1 replication and the dynamics of the resting CD4+ T cell reservoir for HIV-1 in the setting of HAART. BMC Infect Dis 8(1):2. doi:10.1186/1471-2334-8-2, URL:http://www.biomedcentral.com/1471-2334/8/2
Sez-Cirin A, Bacchus C, Hocqueloux L, Avettand-Fenoel V, Girault I, Lecuroux C, Potard V, Versmisse P, Melard A, Prazuck T, Descours B, Guergnon J, Viard JP, Boufassa F, Lambotte O, Goujard C, Meyer L, Costagliola D, Venet A, Pancino G, Autran B, Rouzioux C (2013) Post-treatment HIV-1 controllers with a long-term virological remission after the interruption of early initiated antiretroviral therapy ANRS VISCONTI study. PLoS Pathog 9(3):e1003211. doi:10.1371/journal.ppat.1003211
Sgaard OS, Graversen ME, Leth S, Olesen R, Brinkmann CR, Nissen SK, Kjaer AS, Schleimann MH, Denton PW, Hey-Cunningham WJ, Koelsch KK, Pantaleo G, Krogsgaard K, Sommerfelt M, Fromentin R, Chomont N, Rasmussen TA, Østergaard L, Tolstrup M (2015) The depsipeptide romidepsin reverses HIV-1 latency in vivo. PLoS Pathog 11(9):e1005142. doi:10.1371/journal.ppat.1005142, URL:http://dx.doi.org/10.1371/journal.ppat.1005142
Shen L, Peterson S, Sedaghat AR, McMahon MA, Callender M, Zhang H, Zhou Y, Pitt E, Anderson KS, Acosta EP et al (2008) Dose-response curve slope sets class-specific limits on inhibitory potential of anti-HIV drugs. Nat Med 14(7):762–766
Siliciano JD, Kajdas J, Finzi D, Quinn TC, Chadwick K, Margolick JB, Kovacs C, Gange SJ, Siliciano RF (2003) Long-term follow-up studies confirm the stability of the latent reservoir for HIV-1 in resting CD4+ T cells. Nat Med 9(6):727–728. doi:10.1038/nm880, URL:http://dx.doi.org/10.1038/nm880
Simonetti FR, Sobolewski MD, Fyne E, Shao W, Spindler J, Hattori J, Anderson EM, Watters SA, Hill S, Wu X, Wells D, Su L, Luke BT, Halvas EK, Besson G, Penrose KJ, Yang Z, Kwan RW, Waes CV, Uldrick T, Citrin DE, Kovacs J, Polis MA, Rehm CA, Gorelick R, Piatak M, Keele BF, Kearney MF, Coffin JM, Hughes SH, Mellors JW, Maldarelli F (2016) Clonally expanded CD4+ T cells can produce infectious HIV-1 in vivo. Proc Nat Acad Sci 113(7):1883–1888. doi:10.1073/pnas.1522675113, URL:http://www.pnas.org/content/113/7/1883
Singh A, Razooky B, Cox CD, Simpson ML, Weinberger LS (2010) Transcriptional bursting from the HIV-1 promoter is a significant source of stochastic noise in HIV-1 gene expression. Biophys J 98(8):L32–L34. doi:10.1016/j.bpj.2010.03.001
Spivak A, Rabi A, McMahon MA, Shan L, Sedaghat AR, Wilke CO, Siliciano R (2010) Dynamic constraints on the second phase compartment of HIV-infected cells. AIDS Res Hum Retroviruses. doi:10.1089/AID.2010.0199, URL:http://www.ncbi.nlm.nih.gov/pubmed/21105850
Stafford MA, Corey L, Cao Y, Daar ES, Ho DD, Perelson AS (2000) Modeling plasma virus concentration during primary HIV infection. J Theor Biol 203(3):285–301. doi:10.1006/jtbi.2000.1076, URL:http://www.sciencedirect.com/science/article/pii/S0022519300910762
Wei X, Ghosh SK, Taylor ME, Johnson VA, Emini EA, Deutsch P, Lifson JD, Bonhoeffer S, Nowak MA, Hahn BH (1995) Viral dynamics in human immunodeficiency virus type 1 infection. Nature 373(6510):117–122
Weinberger LS, Burnett JC, Toettcher JE, Arkin AP, Schaffer DV (2005) Stochastic gene expression in a lentiviral positive-feedback loop: HIV-1 Tat fluctuations drive phenotypic diversity. Cell 122(2):169–182. doi:10.1016/j.cell.2005.06.006, URL:http://www.sciencedirect.com/science/article/B6WSN-4GRH1R2-7/2/856752b80260bf0e4ebecec7af038327
Whitney JB, Hill AL, Sanisetty S, Penaloza-MacMaster P, Liu J, Shetty M, Parenteau L, Cabral C, Shields J, Blackmore S, Smith JY, Brinkman AL, Peter LE, Mathew SI, Smith KM, Borducchi EN, Rosenbloom DIS, Lewis MG, Hattersley J, Li B, Hesselgesser J, Geleziunas R, Robb ML, Kim JH, Michael NL, Barouch DH (2014) Rapid seeding of the viral reservoir prior to SIV viraemia in rhesus monkeys. Nature 512(7512):74–77. doi:10.1038/nature13594, URL:http://www.nature.com/nature/journal/vaop/ncurrent/full/nature13594.html
Wind-Rotolo M, Durand C, Cranmer L, Reid A, Martinson N, Doherty M, Jilek BL, Kagaayi J, Kizza A, Pillay V, Laeyendecker O, Reynolds SJ, Eshleman SH, Lau B, Ray SC, Siliciano JD, Quinn TC, Siliciano RF (2009) Identification of nevirapine-resistant HIV-1 in the latent reservoir after single-dose nevirapine to prevent mother-to-child transmission of HIV-1. J Infect Dis 199(9):1301. doi:10.1086/597759, URL: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2703715/report=abstract
Wodarz D, Arnaout RA, Nowak MA, Lifson JD (2000a) Transient antiretroviral treatment during acute simian immunodeficiency virus infection facilitates long-term control of the virus. Philos Trans Roy Soc B Biol Sci 355(1400):1021–1029. URL:http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1692816/
Wodarz D, Page KM, Arnaout RA, Thomsen AR, Lifson JD, Nowak MA (2000b) A new theory of cytotoxic T-lymphocyte memory: implications for HIV treatment. Philos Trans Roy Soc B Biol Sci 355(1395):329–343
Yates A, Stark J, Klein N, Antia R, Callard R (2007) Understanding the slow depletion of memory CD4+ T cells in HIV infection. PLoS Med 4(5):e177. doi:10.1371/journal.pmed.0040177, URL:http://dx.doi.org/10.1371/journal.pmed.0040177
Zhang J, Perelson AS (2013) Contribution of follicular dendritic cells to persistent HIV viremia. J Virol 87(14):7893–7901. doi:10.1128/JVI.00556-13
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Hill, A.L. (2017). Mathematical Models of HIV Latency. In: Silvestri, G., Lichterfeld, M. (eds) HIV-1 Latency. Current Topics in Microbiology and Immunology, vol 417. Springer, Cham. https://doi.org/10.1007/82_2017_77
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