[1]

Available from: http://en.wikipedia.org/wiki/MichaelisMenten.

[2]

Avaliable from: http://www.iasociety.org/Whatwedo/TowardsanHIVCure/Activities/TheRomeStatement.

[3]

B. M. Adams, H. T. Banks, H. Kwon and H. T. Tran, Dynamic multidrug therapies for HIV: Optimal and STI control apporahces, Math. Biosci. Eng., 1 (2004), 223241.

[4]

B. Autran, B. Descours, V. AvettandFenoel and C. Rouzioux, Elite controllers as a model of functional cure, Curr. Opin. HIV AIDS, 6 (2011), 181187.

[5]

S. Bajariz, G. Webb and D. E. Kirschner, Predicting differential responses to structured treatment tnterruptions during HAART, Bull. Math. Biol., 66 (2004), 10931118.

[6]

K. J. Bar, C. Y. Tsao, S. S. Iyer, J. M. Decker, Y. Yang, M. Bonsignori, X. Chen, K. K. Hwang, D. C. Montefiori, H. X. Liao, P. Hraber, W. Fischer, H. Li, S. Wang, S. Sterrett, B. F. Keele, V. V. Ganusov, A. S. Perelson, B. T. Korber, I. Georgiev, J. S. McLellan, J. W. Pavlicek, F. Gao, B. F. Haynes, B. H. Hahn, P. D. Kwong and G. M. Shaw, Early lowtiter neutralizing antibodies impede HIV1 replication and select for virus escape, PLoS Pathog., 8 (2012), e1002721.

[7]

S. Bonhoeffer, R. M. May, G. M. Shaw and M. A. Nowak, Virus dynamics and drug therapy, Proc. Natl. Acad. Sci. U.S.A., 94 (1997), 69716976.

[8]

S. Bonhoeffer and M. A. Nowak, Preexistence and emergence of drug resistance in HIV1 infection, Proc. Biol. Sci., 264 (1997), 631637.

[9]

S. Bonhoeffer, M. Rembiszewski, G. M. Ortiz and D. F. Nixon, Risks and benefits of structured antiretroviral drug therapy interruptions in HIV1 infection, AIDS, 14 (2000), 23132322.

[10]

G. Carcelain and B. Autran, Immune interventions in HIV infection, Immunological Reviews, 254 (2013), 355371.

[11]

J. M. Coffin, HIV population dynamics in vivo: Implications for genetic variation, pathogenesis, and therapy, Science, 267 (1995), 483489.

[12]

H. Dahari, E. Shudo, R. M. Ribeiro and A. S. Perelson, Modeling complex decay profiles of hepatitis B virus during antiviral therapy, Hepatology, 49 (2009), 3238.

[13]

S. Eikenberry, S. Hews, J. D. Nagy and Y. Kuang, The dynamics of a delay model of hepatitis B virus infection with logistic hepatocyte growth, Mathematical Biosciences and Engineering, 6 (2009), 283299.

[14]

European AIDS Clinical Society (EACS), EACS Guidelines, 2013. Available from: http://www.eacsociety.org/guidelines/eacsguidelines/eacsguidelines.html.

[15]

Global Fact Sheet, UNAIDS. org, 2013. Available from: http://files.unaids.org/en/media/unaids/contentassets/documents/epidemiology/2013/gr2013/20130923_FactSheet_Global_en.pdf.

[16]

W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, SpringerVerlag, New York, 1975.

[17]

M. Gopal, Control Systems: Principles and Design, Tata McGrawHill Education, New Delhi, 2002.

[18]

A. V. Herz, S. Bonhoeffer, R. M. Anderson, R. M. May and M. A. Nowak, Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay, Proc. Natl. Acad. Sci. U.S.A, 93 (1996), 72477251.

[19]

S. Hews, S. Eikenberry, J. D. Nagy and Y. Kuang, Rich dynamics of a hepatitis B viral infection model with logistic hepatocyte growth, J. Math. Biol., 60 (2010), 573590.

[20]

D. D. Ho, A. U. Neuman, A. S. Perelson, W. Chen, J. M. Leonard and M. Markowitz, Rapid turnover of plasma virions and CD4 lymphocytes in HIV1 infection, Nature, 373 (1995), 123126.

[21]

L. Hocqueloux, T. Prazuck, V. AvettandFenoel, A. Lafeuillade, B. Cardon, J. P. Viard and C. Rouzioux, Longterm immunovirologic control following antiretroviral therapy interruption in patients treated at the time of primary HIV1 infection, AIDS, 24 (2010), 15981601.

[22]

H. Korthals Altes, R. M. Ribeiro and R. J. de Boer, The race between initial Thelper expansion and virus growth upon HIV infection influences polyclonality of the response and viral setpoint, Proc. Biol. Sci., 270 (2003), 13491358.

[23]

S. R. Lewin, R. M. Ribeiro, T. Walters, G. K. Lau, S. Bowden, S. Locarnini and A. S. Perelson, Analysis of hepatitis B viral load decline under potent therapy: complex decay profiles observed, Hepatology, 34 (2001), 10121020.

[24]

Y. F. Liaw and C. M. Chu, Hepatitis B virus infection, The Lancet, 373 (2009), 582592.

[25]

Y. F. Liaw, J. H. Kao and T. Piratvisuth, et al., AsianPacific consensus statement on the management of chronic hepatitis B: A 2012 update, Heptaol. Int., 6 (2012), 531561.

[26]

J. D. Lifson, J. L. Rossio, R. Arnaout, L. Li, T. L. Parks, S. K. Schneider, R. F. Kiser, V. J. Coalter, G. Walsh, R. J. Imming, B. Fisher, B. M. Flynn, N. Bischofberger, M. Jr. Piatak, V. M. Hirsch, M. A. Nowak and D. Wodarz, Containment of simian immunodeficiency virus infection: Cellular immune responses and protection from rechallenge following transient postinoculation antiretroviral treatment, J. Virol., 74 (2000), 25842593.

[27]

J. D. Lifson, J. L. Rossio, M. Piatak, T. Parks, L. Li, R. Kiser, V. Coalter, B. Fisher, B. M. Flynn, S. Czajak, V. M. Hirsch, K. A. Reimann, J. E. Schmitz, J. Ghrayeb, N. Bischofberger, M. A. Nowak, R. C. Desrosiers and D. Wodarz, Role of CD8(+) lymphocytes in control of simian immunodeficiency virus infection and resistance to rechallenge after transient early antiretroviral treatment, J. Virol., 75 (2001), 1018710199.

[28]

J. Lisziewicz and F. Lori, Structured treatment interruptions in HIV/AIDS therapy, Microbes and Infection, 4 (2002), 207214.

[29]

J. Lisziewicz, E. Rosenberg, J. Lieberman et al., Control of HIV despite the discontinuation of antiretroviral therapy, N. Engl. J. Med., 340 (1999), 16831684.

[30]

S. J. Little, A. R. McLean, C. A. Spina, D. D. Richman and D. V. Havlir, Viral dynamics of acute HIV1 infection, J. Exp. Med., 190 (1999), 841850.

[31]

S. Lodi, L. Meyer, A. D. Kelleher, M. Rosinska, J. Ghosn, M. Sannes and K. Porter, Immunovirologic control 24 months after interruption of antiretroviral therapy initiated close to hiv seroconversion, Arch. Intern. Med., 172 (2012), 12521255.

[32]

M. Markowitz, M. Louie, A. Hurley, E. Sun, M. Di. Mascio, A. S. Perelson and D. D. Ho, A novel antiviral intervention results in more accurate assessment of human immunodeficiency virus type 1 replication dynamics and Tcell decay in vivo, J. Virol., 77 (2003), 50375038.

[33]

L. Michaelis and M. L. Menten, Die Kinetik der Invertinwirkung, Biochem. Z., 49 (1913), 333369.

[34]

H. Mohri, S. Bonhoeffer, S. Monard, A. S. Perelson and D. D. Ho, Rapid turnover of T lymphocytes in SIVinfected rhesus macaques, Science, 279 (1998), 12231227.

[35]

M. A. Nowak, S. Bonhoeffer, G. M. Shaw and R. M. May, Antiviral drug treatment: Dynamics of resistance in free virus and infected cell populations, J. Theor. Biol, 184 (1997), 203217.

[36]

M. A. Nowak and R. M. May, Virus Dynamics, Oxford University Press, New York, 2000.

[37]

G. M. Ortiz, D. F. Nixon, A. Trkola, et al., HIV1specific immune responses in subjects who temporarily contain antiretroviral therapy, J. Clin. Invest., 104 (1999), R13R18.

[38]

A. S. Perelson, Modeling the withinhost dynamics of HIV infection, BMC Biology, 11 (2013), 96105.

[39]

A. S. Perelson, P. Essunger, Y. Cao, M. Vesanen, A. Hurley, K. Saksela, M. Markowitz and D. D. Ho, Decay characteristics of HIV1infected compartments during combination therapy, Nature, 387 (1997), 188191.

[40]

A. S. Perelson, A. U. Neumann, M. Markowitz, J. M. Leonard and D. D. Ho, HIV1 dynamics in vivo: Virion clearance rate, infected cell lifespan, and viral generation time, Science, 271 (1996), 15821586.

[41]

A. N. Phillips, Reduction of HIV concentration during acute infection: independence from a specific immune response, Science, 271 (1996), 497499.

[42]

L. S. Pontryagin, V. G. Boltyanski, R. V. Gamkrelidze and E. F. Mischenko, Mathematical Theory of Optimal Processes, Wiley, New York, 1964.

[43]

R. M. Ribeiro, S. Bonhoeffer and M. A. Nowak, The frequency of resistant mutant virus before antiviral therapy, AIDS, 12 (1998), 461465.

[44]

R. M. Ribeiro and S. Bonhoeffer, Production of resistant HIV mutants during antiretroviral therapy, Proc. Natl. Acad. Sci. U.S.A., 97 (2000), 76817686.

[45]

R. M. Ribeiro, A. Lo and A. S. Perelson, Dynamics of hepatitis B virus infection, Microbes Infect., 4 (2002), 829835.

[46]

R. M. Ribeiro, L. Qin, L. L. Chavez, D. Li, S. G. Self and A. S. Perelson, Estimation of the initial viral growth rate and basic reproductive number during acute HIV1 infection, J. Virol., 84 (2010), 60966102.

[47]

L. Rong and A. S. Perelson, Modeling HIV persistence, the latent reservoir, and viral blips, J. Theor. Biol., 260 (2009), 308331.

[48]

L. Rong and A. S. Perelson, Modeling latently infected cell activation: Viral and latent reservoir persistence, and viral blips in HIVinfected patients on potent therapy, PLoS Comput. Biol., 5 (2009), e1000533, 18pp.

[49]

D. I. Rosenbloom, A. L. Hill, S. A. Rabi, R. F. Siliciano and M. A. Nowak, Antiretroviral dynamics determines HIV evolution and predicts therapy outcome, Nat. Med., 18 (2012), 13781385.

[50]

S. K. Sarin, B. S. Sandhu, B. C. Sharma, M. Jain, J. Singh and V. Malhotra, Beneficial effects of 'lamivudine pulse' therapy in HBeAgpositive patients with normal ALT, J. Viral. hpat., 11 (2004), 552558.

[51]

M. A. Stafford, L. Corey, Y. Cao, E. S. Daar, D. D. Ho and A. S. Perelson, Modeling plasma virus concentration during primary HIV infection, J. Theor. Biol., 203 (2000), 285301.

[52]

N. I. Stilianakis, C. A. Boucher, M. D. De Jong, R. Van Leeuwen, R. Schuurman and R. J. De Boer, Clinical data sets of human immunodeficiency virus type 1 reverse transcriptaseresistant mutants explained by a mathematical model, J. Virol., 71 (1997), 161168.

[53]

The Strategies for Management of Antiretroviral Therapy (SMART) Study Group, CD4+ CountGuided Interruption of Antiretroviral Treatment, N. Engl. J. Med., 355 (2006), 22832296.

[54]

M. A. Thompson, J. A. Aberg, J. F. Hoy, A. Telenti, C. Benson, P. Cahn, J. J. Eron, H. F. Gunthard, S. M. Hammer, P. Reiss, D. D. Richman, G. Rizzardini, D. L. Thomas, D. M. Jacobsen and P. A. Volberding, Antiretroviral treatment of adult HIV infection: 2012 recommendations of the International Antiviral SocietyUSA panel, JAMA, 308 (2012), 387402.

[55]

G. D. Tomaras, N. L. Yates, P. Liu, L. Qin, G. G. Fouda, L. L. Chavez, A. C. Decamp, R. J. Parks, V. C. Ashley, J. T. Lucas, M. Cohen, J. Eron, C. B. Hicks, H. X. Liao, S. G. Self, G. Landucci, D. N. Forthal, K. J. Weinhold, B. F. Keele, B. H. Hahn, M. L. Greenberg, L. Morris, S. S. Karim, W. A. Blattner, D. C. Montefiori, G. M. Shaw, A. S. Perelson and B. F. Haynes, Initial Bcell responses to transmitted human immunodeficiency virus type 1: Virionbinding immunoglobulin M (IgM) and IgG antibodies followed by plasma antigp41 antibodies with ineffective control of initial viremia, J. Virol., 82 (2008), 1244912463.

[56]

E. Van Gulck, L. Bracke, L. Heyndrickx, S. Coppens, D. Atkinson, C. Merlin, A. Pasternak, E. Florence and G. Vanham, Immune and viral correlates of "secondary viral control" after treatment interruption in chronically HIV1 infected patients, PLoS One, 7 (2012), e37792.

[57]

E. Van Gulck, L. Heyndrickx, L. Bracke, S. Coppens, E. Florence, A. Buve, P. Lewi and G. Vanham, Control of viral replication after cessation of HAART, AIDS Res. Ther., 8 (2011), 6pp.

[58]

G. Vanham and E. Van Gulck, Can immunotherapy be useful as a "functional cure" for infection with Human Immunodeficiency Virus1? Retrovirology, 9 (2012), 121.

[59]

X. Wei, S. K. Ghosh, M. E. Taylor, J. A. Johnson, E. A. Emini, P. Deutsch, J. D. Lifson, S. Bonhoeffer, N. A. Nowak and B. H. Hahn, et al., Viral dynamics in human immunodeficiency virus type 1 infection, Nature, 373 (1995), 117122.

[60]

D. Wodarz, Killer Cell Dynamics: Mathematical and Computational Approaches to Immunology, Springer, New York, 2007.

[61]

D. Wodarz, R. A. Arnaout, M. A. Nowak and J. D. Lifson, Transient antiretroviral treatment during acute simian immunodeficiency virus infection facilitates longterm control of the virus, Philos. Trans. R. Soc. Lond. B. Biol. Sci., 355 (2000), 10211029.
