A. Jarne, D. Commenges, and L. Villain, Modeling CD4 + T cells dynamics in HIV-infected patients receiving repeated cycles of exogenous Interleukin 7, The Annals of Applied Statistics, vol.11, issue.3, pp.1593-1616, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01579008

A. T. Haase, Population biology of HIV-1 infection: viral and CD4+ T cell demographics and dynamics in lymphatic tissues, Annual Review of Immunology, vol.17, issue.1, pp.625-656, 1999.

S. M. Hammer, K. E. Squires, and M. D. Hughes, A controlled trial of two nucleoside analogues plus indinavir in persons with human immunodeficiency virus infection and CD4 cell counts of 200 per cubic millimeter or less, New England Journal of Medicine, vol.337, issue.11, pp.725-733, 1997.

S. Grabar, L. Moing, V. Goujard, and C. , Clinical outcome of patients with HIV-1 infection according to Immunologic and virologic response after 6 months of highly active antiretroviral therapy, Annals of Internal Medicine, vol.133, issue.6, pp.401-410, 2000.

, Life expectancy of individuals on combination antiretroviral therapy in high-income countries: a collaborative analysis of 14 cohort studies, Lancet, vol.372, issue.9635, p.293, 2008.

, Collaboration Cascade, others. Effective therapy has altered the spectrum of cause-specific mortality following HIV seroconversion, AIDS, vol.20, issue.5, pp.741-749, 2006.

S. Beq, J. Delfraissy, and J. Theze, Interleukin-7 (IL-7): immune function, involvement in the pathogenesis of HIV infection and therapeutic potential, European Cytokine Network, vol.15, issue.4, pp.279-289, 2004.

L. Vassena, M. Proschan, A. S. Fauci, and P. Lusso, Interleukin 7 reduces the levels of spontaneous apoptosis in CD4+ and CD8+ T cells from HIV-1-infected individuals, Proceedings of the National Academy of Sciences, vol.104, issue.7, pp.2355-2360, 2007.

Y. Levy, C. Lacabaratz, and L. Weiss, Enhanced T cell recovery in HIV-1-infected adults through IL-7 treatment, The Journal of Clinical Investigation, vol.119, issue.4, pp.997-1007, 2009.
URL : https://hal.archives-ouvertes.fr/inserm-00484803

Y. Levy, I. Sereti, and G. Tambussi, Effects of recombinant human interleukin 7 on T-cell recovery and thymic output in HIV-infected patients receiving antiretroviral therapy: results of a phase I/IIa randomized, placebo-controlled, multicenter study, Clinical Infectious Diseases, vol.55, issue.2, pp.291-300, 2012.

I. Sereti, R. M. Dunham, and J. Spritzler, IL-7 administration drives T cell-cycle entry and expansion in HIV-1 infection, Blood, vol.113, issue.25, pp.6304-6314, 2009.

C. Lewden, G. Chêne, and P. Morlat, HIV-infected adults with a CD4 cell count greater than 500 cells/mm3 on long-term combination antiretroviral therapy reach same mortality rates as the general population, JAIDS Journal of Acquired Immune Deficiency Syndromes, vol.46, issue.1, pp.72-77, 2007.
URL : https://hal.archives-ouvertes.fr/inserm-00170726

R. Thiébaut, A. Jarne, and J. Routy, Repeated cycles of recombinant human interleukin 7 in HIV-infected patients with low CD4 T-cell reconstitution on antiretroviral therapy: results of 2 phase II multicenter studies, Clinical Infectious Diseases, vol.62, issue.9, pp.1178-1185, 2016.

A. S. Perelson and R. M. Ribeiro, Modeling the within-host dynamics of HIV infection, BMC biology, vol.11, issue.1, p.96, 2013.

D. Boer, R. J. Perelson, and A. S. , Quantifying T lymphocyte turnover, Journal of Theoretical Biology, vol.327, pp.45-87, 2013.

M. Lavielle, A. Samson, K. Fermin, A. Mentré, and F. , Maximum Likelihood Estimation of Long-Term HIV Dynamic Models and Antiviral Response, Biometrics, vol.67, issue.1, pp.250-259, 2011.
URL : https://hal.archives-ouvertes.fr/inserm-00486937

J. Guedj, L. Rong, H. Dahari, and A. S. Perelson, A perspective on modelling hepatitis C virus infection, Journal of Viral Hepatitis, vol.17, issue.12, pp.825-833, 2010.

R. Ke, C. Loverdo, H. Qi, R. Sun, and J. O. Lloyd-smith, Rational design and adaptive management of combination therapies for Hepatitis C virus infection, PLoS computational biology, vol.11, issue.6, p.1004040, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01224118

G. M. Kepler, H. T. Banks, M. Davidian, and E. S. Rosenberg, A model for HCMV infection in immunosuppressed patients, Mathematical and Computer Modelling, vol.49, issue.7-8, pp.1653-1663, 2009.

F. Crauste, L. Pujo-menjouet, S. Génieys, C. Molina, and O. Gandrillon, Adding self-renewal in committed erythroid progenitors improves the biological relevance of a mathematical model of erythropoiesis, Journal of Theoretical Biology, vol.250, issue.2, pp.322-338, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00194422

R. Thiébaut, J. Drylewicz, and M. Prague, Quantifying and Predicting the Effect of Exogenous Interleukin-7 on CD4+ T Cells in HIV-1 Infection, PLoS Computational Biology, vol.10, issue.5, p.1003630, 2014.

S. A. Murphy, Optimal dynamic treatment regimes, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.65, issue.2, pp.331-355, 2003.

J. M. Robins, Optimal structural nested models for optimal sequential decisions, pp.189-326, 2004.

X. Huang, J. Ning, and A. S. Wahed, Optimization of individualized dynamic treatment regimes for recurrent diseases, Statistics in Medicine, vol.33, issue.14, pp.2363-2378, 2014.

M. S. Lynch, K. G. Oslin, D. Mckay, J. R. Tenhave, and T. , Developing adaptive treatment strategies in substance abuse research. Drug and Alcohol Dependence, vol.88, pp.24-30, 2007.

M. L. Petersen, D. S. Laan, and M. J. , Individualized treatment rules: Generating candidate clinical trials, Statistics in Medicine, vol.26, issue.25, pp.4578-4601, 2007.

M. E. Em, T. S. Richardson, and D. A. Stephens, Demystifying optimal dynamic treatment regimes, Biometrics, vol.63, issue.2, pp.447-455, 2007.

B. Rich, M. E. Em, and D. A. Stephens, Optimal individualized dosing strategies: A pharmacologic approach to developing dynamic treatment regimens for continuous-valued treatments, Biometrical Journal, vol.58, issue.3, pp.502-517, 2016.

M. Prague, D. Commenges, and J. M. Gran, Dynamic models for estimating the effect of HAART on CD4 in observational studies: Application to the Aquitaine Cohort and the Swiss HIV Cohort Study, Biometrics, vol.73, issue.1, pp.294-304, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01406614

S. Rosenberg-eric, D. Marie, H. Banks, and . Thomas, Using mathematical modeling and control to develop structured treatment interruption strategies for HIV infection, Drug & Alcohol Dependence, vol.88, pp.41-51, 2007.

G. Toffoli, G. Corona, B. Basso, and M. Boiocchi, Pharmacokinetic optimisation of treatment with oral etoposide, Clinical Pharmacokinetics, vol.43, issue.7, pp.441-466, 2004.

F. Castiglione and B. Piccoli, Optimal control in a model of dendritic cell transfection cancer immunotherapy, Bulletin of Mathematical Biology, vol.68, issue.2, pp.255-274, 2006.

H. T. Banks and J. Taesoo, Kwon Hee-Dae. Feedback control of HIV antiviral therapy with long measurement time, Int. J. Pure Appl. Math, vol.66, issue.4, pp.461-485, 2011.

A. Croicu and L. Short, Optimal Control of a Mathematical Model for HIV Infection of CD4 + T Cells, Bulletin of Mathematical Biology, vol.77, issue.11, pp.2035-2071, 2015.

B. Chakraborty and S. A. Murphy, Dynamic treatment regimes. Annual review of statistics and its application, vol.1, pp.447-464, 2014.

M. Prague, D. Commenges, J. Drylewicz, and R. Thiébaut, Treatment Monitoring of HIV-Infected Patients based on Mechanistic Models, Biometrics, vol.68, issue.3, pp.902-911, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01579531

D. Commenges, P. Joly, A. Gégout-petit, and B. Liquet, Choice between Semi-parametric Estimators of Markov and Non-Markov Multi-state Models from Coarsened Observations, Scandinavian Journal of Statistics, vol.34, issue.1, pp.33-52, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00194275

M. Prague, D. Commenges, J. Guedj, J. Drylewicz, and R. Thiébaut, NIMROD: a program for inference via a normal approximation of the posterior in models with random effects based on ordinary differential equations, Computer Methods and Programs in Biomedicine, vol.111, issue.2, pp.447-458, 2013.
URL : https://hal.archives-ouvertes.fr/inserm-00939447

D. Commenges, H. Jacqmin-gadda, C. Proust, and J. Guedj, A newton-like algorithm for likelihood maximization: The robustvariance scoring algorithm. arXiv preprint math/0610402, 2006.

A. W. Vaart, Asymptotic statistics, 2000.

W. R. Gilks, N. G. Best, and K. Tan, Adaptive rejection Metropolis sampling within Gibbs sampling, Applied Statistics, pp.455-472, 1995.

J. Guedj, R. Thiébaut, and D. Commenges, Maximum likelihood estimation in dynamical models of HIV, Biometrics, vol.63, issue.4, pp.1198-1206, 2007.
URL : https://hal.archives-ouvertes.fr/inserm-00204269

K. Soetaert, T. Petzoldt, and R. W. Setzer, Solving differential equations in R: package deSolve, Journal of Statistical Software, p.33, 2010.

A. C. Hindmarsh, Ordinary differential equation system solver, 1992.

C. Pasin, F. Dufour, L. Villain, H. Zhang, and R. Thiébaut, Controlling IL-7 injections in HIV-infected patients, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01933170