A. Engelman and P. Cherepanov, The structural biology of HIV-1 : mechanistic and therapeutic insights, HIV during the incubation period of AIDS, vol.362, p.279, 2012.

. Enting, Antiretroviral drugs and the central nervous system, AIDS, vol.12, issue.15, pp.1941-1955, 1998.

[. Finzi, Latent infection of CD4+ T cells provides a mechanism for lifelong persistence of HIV-1, even in patients on effective combination therapy, Nature Medicine, vol.5, issue.5, p.512, 1999.

. Fischl, The efficacy of azidothymidine (AZT) in the treatment of patients with AIDS and AIDS-related complex, New England Journal of Medicine, vol.317, issue.4, pp.185-191, 1987.

[. Fister, Optimizing chemotherapy in an HIV model, Electronic Journal of Differential Equations, issue.32, pp.1-12, 1998.

R. Freitas, A. A. Freitas, and B. Rocha, Population biology of lymphocytes : the flight for survival, Annual Review of Immunology, vol.18, issue.1, pp.83-111, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00108283

. Friis-møller, Cardiovascular disease risk factors in HIV patients-association with antiretroviral therapy. results from the dad study, AIDS, vol.17, issue.8, pp.1179-1193, 2003.

[. Fry, IL7 therapy dramatically alters peripheral T-cell homeostasis in normal and SIV-infected nonhuman primates, Blood, vol.101, issue.6, pp.2294-2299, 2003.

. Gabrielsson, J. Weiner-;-gabrielsson, and D. Weiner, Pharmacokinetic and pharmacodynamic data analysis : concepts and applications, vol.2, 2001.

[. Gadina, Translational and clinical advances in JAK-STAT biology : The present and future of jakinibs, Journal of Leukocyte Biology, 2018.

[. Gallo, , 1983.

, Isolation of human T-cell leukemia virus in acquired immune deficiency syndrome (AIDS)

, Science, vol.220, issue.4599, pp.865-867

[. Galluzzi, Classification of current anticancer immunotherapies, Oncotarget, vol.5, issue.24, p.12472, 2014.
URL : https://hal.archives-ouvertes.fr/inserm-01142463

[. García, , 2004.

, T-cell response to highly active antiretroviral therapy according to baseline CD4+ T-cell count, JAIDS Journal of Acquired Immune Deficiency Syndromes, vol.36, issue.2, pp.702-713

[. Gavegnano, , 2017.

, Novel mechanisms to inhibit HIV reservoir seeding using Jak inhibitors, PLoS Pathogens, vol.13, issue.12, p.1006740

[. Gilks, Adaptive rejection Metropolis sampling within Gibbs sampling, Applied Statistics, pp.455-472, 1995.

W. ;. Ginsburg, G. S. Ginsburg, and H. F. Willard, Essentials of genomic and personalized medicine, 2009.

[. Girard, , 2011.

, Human immunodeficiency virus (HIV) immunopathogenesis and vaccine development : a review, Vaccine, vol.29, issue.37, pp.6191-6218

J. Glass, J. D. Johnson, and R. T. , Human immunodeficiency virus and the brain, Annual Review of Neuroscience, vol.19, issue.1, pp.1-26, 1996.

[. Gotwals, , 2017.

, Prospects for combining targeted and conventional cancer therapy with immunotherapy, Nature Reviews Cancer, vol.17, issue.5, p.286

[. Grabar, 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.

[. Guedj, A perspective on modelling hepatitis C virus infection, Journal of Viral Hepatitis, vol.17, issue.12, pp.825-833, 2010.

[. Levy, 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

[. Levy, 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.

[. Lewden, 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

. Lewis, A homeostatic model for CD4 count recovery in HIV-infected children. Population Approach Group in Europe, The Journal of Experimental Medicine, vol.190, issue.6, pp.841-850, 1999.

[. Logerot, HIV reservoir dynamics in HAART-treated poor immunological responder patients under IL-7 therapy, vol.32, pp.715-720, 2018.

M. Losso and D. Abrams, Effect of interleukin-2 on clinical outcomes in patients with a CD4+ cell count of 300/mm3 : primary results of the esprit study, 16th Conference on Retroviruses and Opportunistic Infections, pp.8-11, 2009.

A. J. Lotka and . Lundström, IL-7 in human health and disease, Seminars in Immunology, vol.24, pp.218-224, 1925.

. Lunn, , 2000.

, WinBUGS-a Bayesian modelling framework : concepts, structure, and extensibility. Statistics and Computing, vol.10, pp.325-337

[. Mackall, Harnessing the biology of IL-7 for therapeutic application, Nature Reviews Immunology, vol.11, issue.5, p.330, 2011.

. Mackay and C. Mackay, Migration pathways and immunologic memory among T lymphocytes, Seminars in Immunology, vol.4, pp.51-58, 1992.

[. Maldarelli, Specific HIV integration sites are linked to clonal expansion and persistence of infected cells, Science, vol.345, issue.6193, pp.179-183, 2014.

[. Malone, Sources of variability in repeated T-helper lymphocyte counts from human immunodeficiency virus type 1-infected patients : total lymphocyte count fluctuations and diurnal cycle are important, Journal of Acquired Immune Deficiency Syndromes, vol.3, issue.2, pp.144-151, 1990.

[. Mastroianni, Circulating levels of interleukin-7 in antiretroviral-naive and highly active antiretroviral therapy-treated HIV-infected patients, HIV clinical trials, vol.2, issue.2, pp.108-112, 2001.

[. Melchionda, Adjuvant IL-7 or IL-15 overcomes immunodominance and improves survival of the CD8+ memory cell pool, The Journal of Clinical Investigation, vol.115, issue.5, pp.1177-1187, 2005.

J. Miller and G. Mitchell, Thymus and antigen-reactive cells, Immunological Reviews, vol.1, issue.1, pp.3-42, 1969.

M. , Protection from thymic epithelial cell injury by keratinocyte growth factor : a new approach to improve thymic and peripheral T-cell reconstitution after bone marrow transplantation, Blood, vol.99, issue.12, pp.4592-4600, 2002.

[. Mitsuya, 3'-Azido3'-deoxythymidine (BW A509U) : an antiviral agent that inhibits the infectivity and, Nature, vol.333, issue.6173, p.571, 1985.

. Nowak, Virus dynamics : mathematical principles of immunology and virology, 2000.

[. O'brien, ;. Hendrickson, S. J. O'brien, and S. L. Hendrickson, Host genomic influences on HIV/AIDS, Genome Biology, vol.14, issue.1, p.201, 2013.

[. Okamoto, Effects of exogenous interleukin-7 on human thymus function, Blood, vol.99, issue.8, pp.2851-2858, 2002.

P. Okoye, A. A. Okoye, and L. J. Picker, CD4+ T-cell depletion in HIV infection : mechanisms of immunological failure, Immunological Reviews, vol.254, issue.1, pp.54-64, 2013.

W. H. Organization, Global health estimates 2016 : Deaths by cause, age, sex, by country and by region, 2000.

[. Palella, Declining morbidity and mortality among patients with advanced human immunodeficiency virus infection, New England Journal of Medicine, vol.338, issue.13, pp.853-860, 1998.

V. ;. Palmisano, L. Palmisano, and S. Vella, A brief history of antiretroviral therapy of HIV infection : success and challenges. Annali dell'Istituto superiore di sanitÃ, vol.47, pp.44-48, 2011.

[. Pantaleo, Major expansion of (208+ T cells with a predominant, Nature, vol.370, p.11, 1994.

F. Pantaleo, G. Pantaleo, and A. Fauci, Immunopathogenesis of HIV infection, Annual Reviews in Microbiology, vol.50, issue.1, pp.825-854, 1996.

[. Pappalardo, Vaccine protocols optimization : in silico experiences, Biotechnology Advances, vol.28, issue.1, pp.82-93, 2010.

D. M. Pardoll, The blockade of immune checkpoints in cancer immunotherapy, Nature Reviews Cancer, vol.12, issue.4, p.252, 2012.

. Pasin, , 2018.

, Controlling IL-7 injections in HIV-infected patients

. Seder, W. E. Paul, and R. A. Seder, Lymphocyte responses and cytokines, Cell, vol.76, issue.2, pp.241-251, 1994.

. Perelson, Dynamics of HIV-1 and CD4+ lymphocytes in vivo, AIDS, vol.11, pp.17-24, 1996.

A. S. Perelson, Modelling viral and immune system dynamics, Nature Reviews Immunology, vol.2, issue.1, pp.28-36, 2002.

. Perelson, Decay characteristics of HIV-1, 1997.

. Perelson, HIV-1 dynamics in vivo : virion clearance rate, infected cell life-span, and viral generation time, Science, vol.271, issue.5255, pp.1582-1586, 1996.

A. S. Perelson and R. M. Ribeiro, Modeling the withinhost dynamics of HIV infection, BMC Biology, vol.11, issue.1, p.96, 2013.

[. Petersen, Individualized treatment rules : Generating candidate clinical trials, Statistics in Medicine, vol.26, issue.25, pp.4578-4601, 2007.

[. Petersen, Assessing the effectiveness of antiretroviral adherence interventions : using marginal structural models to replicate the findings of randomized controlled trials, JAIDS Journal of Acquired Immune Deficiency Syndromes, vol.43, pp.96-103, 2006.

A. N. Phillips, Reduction of HIV concentration during acute infection : independence from a specific immune response, Science, vol.271, issue.5248, pp.497-499, 1996.

. Phillips, Use of CD4 lymphocyte count to predict long term survival free of AIDS after HIV infection, BMJ, vol.309, issue.6950, pp.309-313, 1994.

[. Piconi, Hydroxychloroquine drastically reduces immune activation in HIV-infected, ART-treated, immunological non-responders, Blood, p.2011, 2011.

[. Putter, A Bayesian approach to parameter estimation in HIV dynamical models, Statistics in Medicine, vol.21, issue.15, pp.2199-2214, 2002.

T. C. Quinn-;-quinn, Acute primary HIV infection, Jama, vol.278, issue.1, pp.58-62, 1997.

[. Ramratnam, Rapid production and clearance of HIV-1 and hepatitis C virus assessed by large volume plasma apheresis, The Lancet, vol.354, issue.9192, pp.1782-1785, 1999.

J. Ramsay-;-ramsay, Functional data analysis. Encyclopedia of Statistics in Behavioral Science, 2005.

. Redgrove, K. A. Mclaughlin-;-redgrove, and E. A. Mclaughlin, The role of the immune response in chlamydia trachomatis infection of the male genital tract : a double-edged sword, Frontiers in Immunology, vol.5, p.534, 2014.

R. , Determinants of paradoxical CD4 cell reconstitution after protease inhibitor-containing antiretroviral regimen, AIDS, vol.13, issue.6, pp.669-676, 1999.

[. Richman, The toxicity of azidothymidine (AZT) in the treatment of patients with AIDS and AIDS-related complex, New England Journal of Medicine, vol.317, issue.4, pp.192-197, 1987.

[. Richman, The challenge of finding a cure for HIV infection, Science, vol.323, issue.5919, pp.1304-1307, 2009.

. Riddell, Phase I study of cellular adoptive immunotherapy using genetically modified CD8+ HIV-specific T cells for HIV seropositive patients undergoing allogeneic bone marrow transplant, Human Gene Therapy, vol.3, issue.3, pp.319-338, 1992.

[. Riou, , 2007.

, Convergence of TCR and cytokine signaling leads to FOXO3a phosphorylation and drives the survival of CD4+ central memory T cells, The Journal of Experimental Medicine, vol.204, issue.1, pp.79-91

[. Schacker, , 2002.

, Persistent abnormalities in lymphoid tissues of human immunodeficiency virus-infected patients successfully treated with highly active antiretroviral therapy, The Journal of Infectious Diseases, vol.186, issue.8, pp.1092-1097

. Schleidgen, What is personalized medicine : sharpening a vague term based on a systematic literature review, BMC Medical Ethics, vol.14, issue.1, p.55, 2013.

N. J. Schork, Personalized medicine : time for one-person trials, Nature, vol.520, issue.7549, pp.609-611, 2015.

. Scott, Acquired immunodeficiency syndrome in infants, New England Journal of Medicine, vol.310, issue.2, pp.76-81, 1984.

. Scripture-adams, Interleukin-7 induces expression of latent human immunodeficiency virus type 1 with minimal effects on T-cell phenotype, Journal of Virology, vol.76, issue.24, pp.13077-13082, 2002.

[. Seddon, Interleukin 7 and T cell receptor signals regulate homeostasis of CD4 memory cells, Nature Immunology, vol.4, issue.7, pp.680-686, 2003.

[. Selik, HIV infection as leading cause of death among young adults in us cities and states, JAMA, vol.269, issue.23, pp.2991-2994, 1993.

[. Sereti, IL-7 administration drives T cell-cycle entry and expansion in HIV-1 infection, Blood, vol.113, issue.25, pp.6304-6314, 2009.

[. Sereti, Decreases in colonic and systemic inflammation in chronic HIV infection after IL-7 administration, PLoS Pathogens, vol.10, issue.1, p.1003890, 2014.

. Serrano-villar, , 2013.

M. Á. , The CD4/CD8 ratio in HIV-infected subjects is independently associated with T-cell activation despite long-term viral suppression, Journal of Infection, vol.66, issue.1, pp.57-66, 2013.

. Serrano-villar, , 2014.

, HIV-infected individuals with low CD4/CD8 ratio despite effective antiretroviral therapy exhibit altered T cell subsets, heightened CD8+ T cell activation, and increased risk of non-AIDS morbidity and mortality, PLoS Pathogens, vol.10, issue.5, p.1004078

[. Shive, Inflammatory cytokines drive CD4+ T-cell cycling and impaired responsiveness to interleukin 7 : implications for immune failure in HIV disease, The Journal of Infectious Diseases, vol.210, issue.4, pp.619-629, 2014.

. Siegal, Severe acquired immunodeficiency in male homosexuals, manifested by chronic perianal ulcerative herpes simplex lesions, New England Journal of Medicine, vol.305, issue.24, pp.1439-1444, 1981.

[. Siliciano, Long-term followup studies confirm the stability of the latent reservoir for HIV-1 in resting CD4+ T cells, Nature Medicine, vol.9, issue.6, pp.727-728, 2003.

R. F. Siliciano, Opening fronts in HIV vaccine development : Targeting reservoirs to clear and cure, Nature Medicine, vol.20, issue.5, pp.480-481, 2014.

I. Sim, S. C. Sim, and M. Ingelman-sundberg, Pharmacogenomic biomarkers : new tools in current and future drug therapy, Trends in Pharmacological Sciences, vol.32, issue.2, pp.72-81, 2011.

. Smithgall, IL-7 up-regulates HIV-1 replication in naturally infected peripheral blood mononuclear cells, The Journal of Immunology, vol.156, issue.6, pp.2324-2330, 1996.

. Soetaert, Solving differential equations in R : package desolve, Journal of Statistical Software, p.33, 2010.

A. M. Spivak and V. Planelles, HIV-1 eradication : early trials (and tribulations), and Planelles, vol.22, pp.10-27, 2016.

. Sportès, Phase I study of recombinant human interleukin-7 administration in subjects with refractory malignancy, Clinical Cancer Research, pp.1078-0432, 2010.

. Sportès, Administration of rhIL-7 in humans increases in vivo TCR repertoire diversity by preferential expansion of naive T cell subsets, The Journal of Experimental Medicine, vol.205, issue.7, pp.1701-1714, 2008.

[. Stahl, Immunologic abnormalities in homosexual men : relationship to kaposi's sarcoma, The American Journal of Medicine, vol.73, issue.2, pp.171-178, 1982.

[. Stellbrink, , 2002.

, Effects of interleukin-2 plus highly active antiretroviral therapy on HIV-1 replication and proviral DNA (COSMIC trial), AIDS, vol.16, issue.11, pp.1479-1487

R. F. Stengel, Mutation and control of the human immunodeficiency virus, Mathematical Biosciences, vol.213, issue.2, pp.93-102, 2008.

M. Stevenson-;-stevenson, Molecular mechanisms for the regulation of HIV replication, persistence and latency, AIDS, vol.11, p.25, 1997.

. Strain, Effect of treatment, during primary infection, on establishment and clearance of cellular reservoirs of HIV-1, The Journal of Infectious Diseases, vol.191, issue.9, pp.1410-1418, 2005.

[. Tan, IL-7 is critical for homeostatic proliferation and survival of naive T cells, Proceedings of the National Academy of Sciences, vol.98, issue.15, pp.8732-8737, 2001.

[. Tarwater, Increase and plateau of CD4 T-cell counts in the 3 (1/2) years after initiation of potent antiretroviral therapy, Journal of Acquired Immune Deficiency Syndromes, vol.27, issue.2, pp.168-175, 1999.

. Teixeira, , 2001.

, Poor CD4 T cell restoration after suppression of HIV-1 replication may reflect lower thymic function, AIDS, vol.15, issue.14, pp.1749-1756

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

[. Thiébaut, Quantifying and predicting the effect of exogenous interleukin-7 on CD4+ T cells in HIV-1 infection, vol.10, p.1003630, 2014.

[. Thiébaut, 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.

[. Thiébaut, Épidémiologie des dissociations viro-immunologiques chez les patients infectés par le VIH-1. Médecine et Maladies Infectieuses, pp.31-32, 2005.

K. Thomas, J. S. Thomas, and F. Kabbinavar, Metastatic clear cell renal cell carcinoma : A review of current therapies and novel immunotherapies, 2015.

, Critical Reviews in Oncology/Hematology, vol.96, issue.3, pp.527-533

[. Thompson, Antiretroviral treatment of adult HIV infection : 2010 recommendations of the international AIDS society-usa panel, JAMA, vol.304, issue.3, pp.321-333, 2010.

[. Toffoli, Pharmacokinetic optimisation of treatment with oral etoposide, Clinical Pharmacokinetics, vol.43, issue.7, pp.441-466, 2004.

[. Tomer, Personalized schedules for surveillance of low risk prostate cancer patients, 2017.

, Global AIDS update, Asymptotic statistics, vol.3, 2000.

. Grevenynghe, , 2008.

, Transcription factor FOXO3a controls the persistence of memory CD4+ T cells during HIV infection, Nature Medicine, vol.14, issue.3, pp.266-274

. Van-sighem, Life expectancy of recently diagnosed asymptomatic HIV-infected patients approaches that of uninfected individuals, AIDS, vol.24, issue.10, pp.1527-1535, 2010.

[. Vandergeeten, Interleukin-7 promotes HIV persistence during antiretroviral therapy, Blood, vol.121, issue.21, pp.4321-4329, 2013.

T. J. Vanderweele, Marginal structural models for the estimation of direct and indirect effects, Epidemiology, pp.18-26, 2009.

[. Vassena, Interleukin 7 reduces the levels of spontaneous apoptosis in CD4+ and CD8+ T cells from HIV-1infected individuals, Proceedings of the National Academy of Sciences, vol.104, issue.7, pp.2355-2360, 2007.

. Volberding, Zidovudine in asymptomatic human immunodeficiency virus infection : a controlled trial in persons with fewer than 500 CD4-positive cells per cubic millimeter, New England Journal of Medicine, vol.322, issue.14, pp.941-949, 1990.

V. Volterra, Fluctuations in the abundance of a species considered mathematically, Nature, vol.118, pp.558-560, 1926.

[. Wang, IL-7 is a potent and proviral strain-specific inducer of latent HIV-1 cellular reservoirs of infected individuals on virally suppressive HAART, The Journal of Clinical Investigation, vol.115, issue.1, pp.128-137, 2005.

[. Wang, Estimating mixed-effects differential equation models, Statistics and Computing, vol.24, issue.1, pp.111-121, 2014.

[. Wei, Viral dynamics in human immunodeficiency virus type 1 infection, Nature, vol.373, issue.6510, pp.117-122, 1995.

[. Weiss, In vivo expansion of naive and activated CD4+ CD25+ FOXP3+ regulatory T cell populations in interleukin-2-treated HIV patients, Proceedings of the National Academy of Sciences, vol.107, issue.23, pp.10632-10637, 2010.
URL : https://hal.archives-ouvertes.fr/inserm-00489719

R. A. Weiss-;-weiss, How does HIV cause AIDS ?, Science, vol.260, issue.5112, pp.1273-1279, 1993.

E. F. Wheelock, Interferon-like virus-inhibitor induced in human leukocytes by phytohemagglutinin, Science, vol.149, issue.3681, pp.310-311, 1965.

[. Wikby, Agerelated changes in immune parameters in a very old population of swedish people : a longitudinal study, Experimental Gerontology, vol.29, issue.5, pp.531-541, 1994.

[. Wittkop, , 2011.

, Effect of transmitted drug resistance on virological and immunological response to initial combination antiretroviral therapy for HIV (eurocoord-chain joint project) : a european multicohort study. The Lancet Infectious Diseases, vol.11, pp.363-371

[. Wu, Parameter identifiability and estimation of HIV/AIDS dynamic models, Bulletin of Mathematical Biology, vol.70, issue.3, pp.785-799, 2008.

K. Wu, L. Wu, and V. N. Kewalramani, Dendritic-cell interactions with HIV : infection and viral dissemination, Nature Reviews Immunology, vol.6, issue.11, p.859, 2006.

[. Yarchoan, In vivo activity against HIV and favorable toxicity profile of 2', 3'-dideoxyinosine, Science, vol.245, issue.4916, pp.412-415, 1989.

C. Yates, A. Yates, and R. Callard, Cell death and the maintenance of immunological memory, Discrete And Continuous Dynamical Systems Series B, vol.1, issue.1, pp.43-60, 2001.

. Yates, Understanding the slow depletion of memory CD4+ T cells in HIV infection, PLoS Medicine, vol.4, issue.5, p.177, 2007.

[. Yukl, A Newtonlike algorithm for likelihood maximization: The robust-variance scoring algorithm, Challenges in detecting HIV REFERENCES, 2006.

C. , D. , J. , P. Gégout-petit, A. et al., Choice between semiparametric estimators of Markov and non-Markov multi-state models from coarsened observations. Scand, J. Stat, vol.34, p.2325241, 2007.

C. , D. Sayyareh, A. Letenneur, L. Guedj, J. et al., Estimating a difference of Kullback-Leibler risks using a normalized difference of AIC, Ann. Appl. Stat, vol.2, pp.1123-1142, 2008.
URL : https://hal.archives-ouvertes.fr/inserm-00285864

A. Jarne and . Al,

C. , D. Proust-lima, C. Samieri, C. , L. et al., A universal approximate cross-validation criterion for regular risk functions, Int. J. Biostat, vol.11, p.3341512, 2015.
URL : https://hal.archives-ouvertes.fr/hal-02136065

D. , J. Commenges, D. , T. , and R. , Maximum a posteriori estimation in dynamical models of primary HIV infection, Stat. Commun. Infec, p.2945221, 2012.

F. , B. Woodcock, D. J. Komorowski, M. Harper, C. V. Davis et al., Quantifying intrinsic and extrinsic noise in gene transcription using the linear noise approximation: An application to single cell data, Ann. Appl. Stat, vol.7, 1960.

F. , T. J. , M. , and C. L. , Interleukin-7: From bench to clinic, Blood, vol.99, pp.3892-3904, 2002.

G. , A. , K. , and B. D. , Fully symmetric interpolatory rules for multiple integrals over infinite regions with Gaussian weight, J. Comput. Appl. Math, vol.71, pp.299-309, 1996.

G. , J. Thiébaut, R. , C. , and D. , Maximum likelihood estimation in dynamical models of HIV, Biometrics, vol.63, pp.1198-1206, 2007.

G. , J. Thiébaut, R. , C. , and D. , Practical identifiability of HIV dynamics models, Bull. Math. Biol, vol.69, p.2353843, 2007.

D. D. Ho, A. U. Neumann, A. S. Perelson, W. Chen, J. M. Leonard et al., Rapid turnover of plasma virions and CD4 lymphocytes in HIV-1 infection, Nature, vol.373, pp.123-126, 1995.

H. , Y. Liu, D. , W. U. , and H. , Hierarchical Bayesian methods for estimation of parameters in a longitudinal HIV dynamic system, Biometrics, vol.62, p.2227489, 2006.

K. , R. M. Harbertson, J. Tan, J. T. Mcbreen, M. E. Surh et al., Interleukin 7 regulates the survival and generation of memory CD4 cells, J. Exp. Med, vol.198, pp.1797-1806, 2003.

K. , S. , K. , and G. , Information Criteria and Statistical Modeling, 2008.

K. , E. , L. , and M. , Maximum likelihood estimation in nonlinear mixed effects models, Comput. Statist. Data Anal, vol.49, 2005.

L. , Y. Lacabaratz, C. Weiss, L. Viard, J. Goujard et al., Enhanced T cell recovery in HIV-1-infected adults through IL-7 treatment, J. Clin. Invest, vol.119, p.997, 2009.
URL : https://hal.archives-ouvertes.fr/inserm-00484803

L. , Y. Sereti, I. Tambussi, G. Routy, J. Lelievre et al., 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, Clin. Infect. Dis, vol.55, pp.291-300, 2012.

M. , C. L. Fry, T. J. , G. , and R. E. , Harnessing the biology of IL-7 for therapeutic application, Nat. Rev., Immunol, vol.11, pp.330-342, 2011.

M. , C. L. Fry, T. J. Bare, C. Morgan, P. Galbraith et al., , 2001.

, IL-7 increases both thymic-dependent and thymic-independent T-cell regeneration after bone marrow transplantation, Blood, vol.97, pp.1491-1497

N. , A. Schmierer, A. March, C. Overell, R. Park et al., B cell precursor growth-promoting activity. Purification and characterization of a growth factor active on lymphocyte precursors, J. Exp. Med, vol.167, pp.988-1002, 1988.

Y. Okamoto, D. C. Douek, R. D. Mcfarland, K. , and R. A. , Effects of exogenous interleukin-7 on human thymus function, Blood, vol.99, pp.2851-2858, 2002.

P. , A. S. Neumann, A. U. Markowitz, M. Leonard, J. M. et al., , 1996.

, HIV-1 dynamics in vivo: Virion clearance rate, infected cell life-span, and viral generation time, Science, vol.271, pp.1582-1586

P. , J. C. , B. , and D. M. , Mixed-Effects Models in S and S-PLUS, 2000.

R. Camargo, J. F. Kulkarni, H. Agan, B. K. Gaitan, A. A. Beachy et al., Responsiveness of T cells to interleukin-7 is associated with higher CD4 + T cell counts in HIV-1-positive individuals with highly active antiretroviral therapy-induced viral load suppression, J Infect Dis, vol.199, issue.12, pp.1872-1882, 2009.

C. Pasin,

A. Cappuccio, F. Castiglione, and B. Piccoli, Determination of the optimal therapeutic protocols in cancer immunotherapy, Math Biosci, vol.209, issue.1, pp.1-13, 2007.

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

F. Castiglione and B. Piccoli, Cancer immunotherapy, mathematical modeling and optimal control, J Theor Biol, vol.247, issue.4, pp.723-732, 2007.

O. Costa, F. Dufour, and A. Piunovskiy, Constrained and unconstrained optimal discounted control of piecewise deterministic markov processes, SIAM J Control Optim, vol.54, issue.3, pp.1444-1474, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01412604

M. H. Davis, Piecewise-deterministic markov processes: a general class of non-diffusion stochastic models, J R Stat Soc Ser B (Methodol), vol.46, pp.353-388, 1984.

F. Dufour, H. Zhang, R. Eftimie, J. J. Gillard, and D. A. Cantrell, Numerical methods for simulation and optimization of piecewise deterministic markov processes, Bull Math Biol, vol.78, issue.10, pp.2091-2134, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01249897

A. Jarne, D. Commenges, L. Villain, M. Prague, Y. Lévy et al., Modeling CD4 + T cells dynamics in HIV-infected patients receiving repeated cycles of exogenous interleukin 7, Ann Appl Stat, vol.11, issue.3, pp.1593-1616, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01579008

C. G. Lange and M. M. Lederman, Immune reconstitution with antiretroviral therapies in chronic HIV-1 infection, J Antimicrob Chemother, vol.51, issue.1, pp.1-4, 2003.

M. Lavielle and F. Mentré, Estimation of population pharmacokinetic parameters of saquinavir in HIV patients with the monolix software, J Pharmacokinet Pharmacodyn, vol.34, issue.2, pp.229-249, 2007.
URL : https://hal.archives-ouvertes.fr/inserm-00156907

A. Leone, M. Rohankhedkar, A. Okoye, A. Legasse, M. K. Axthelm et al., Increased CD4 + T cell levels during IL-7 administration of antiretroviral therapy-treated simian immunodeficiency virus-positive macaques are not dependent on strong proliferative responses, J Immunol, vol.185, issue.3, pp.1650-1659, 2010.

Y. Levy, C. Lacabaratz, L. Weiss, J. P. Viard, C. Goujard et al., Enhanced T cell recovery in HIV-infected adults through IL-7 treatment, J Clin Investig, vol.119, issue.4, p.997, 2009.
URL : https://hal.archives-ouvertes.fr/inserm-00484803

Y. Levy, I. Sereti, G. Tambussi, J. Routy, J. Lelievre et al., 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, placebocontrolled, multicenter study, Clin Infect Dis, vol.55, issue.2, pp.291-300, 2012.

C. Lewden, G. Chêne, P. Morlat, F. Raffi, M. Dupon et al., 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 J Acquir Immune Defic Syndr, vol.46, issue.1, pp.72-77, 2007.
URL : https://hal.archives-ouvertes.fr/inserm-00170726

C. L. Mackall, T. J. Fry, C. Bare, P. Morgan, A. Galbraith et al., Il-7 increases both thymic-dependent and thymic-independent T-cell regeneration after bone marrow transplantation, Blood, vol.97, issue.5, pp.1491-1497, 2001.

Y. Okamoto, D. C. Douek, R. D. Mcfarland, and R. A. Koup, Effects of exogenous interleukin-7 on human thymus function, Blood, vol.99, issue.8, pp.2851-2858, 2002.

F. Pappalardo, M. Pennisi, F. Castiglione, and S. Motta, Vaccine protocols optimization: in silico experiences, Biotechnol Adv, vol.28, issue.1, pp.82-93, 2010.

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, Comput Methods Programs Biomed, vol.111, issue.2, pp.447-458, 2013.
URL : https://hal.archives-ouvertes.fr/inserm-00939447

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

J. T. Tan, E. Dudl, E. Leroy, R. Murray, J. Sprent et al., Il-7 is critical for homeostatic proliferation and survival of naive T cells, Proc Nat Acad Sci, vol.98, issue.15, pp.8732-8737, 2001.

R. Thiebaut, J. Drylewicz, M. Prague, C. Lacabaratz, S. Beq et al., Quantifying and predicting the effect of exogenous interleukin-7 on CD4 + T cells in HIV-1 infection, PLoS Comput Biol, vol.10, issue.5, p.630, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01108204

, Controlling IL-7 Injections in HIV-Infected Patients

R. Thiébaut, A. Jarne, J. P. Routy, I. Sereti, M. Fischl et al., Repeated cycles of recombinant human interleukin 7 in HIV-infected patients with low CD4, 2016.

, T-cell reconstitution on antiretroviral therapy: results of 2 phase II multicenter studies, Clin Infect Dis, vol.62, issue.9, pp.1178-1185

A. T. Vella, S. Dow, T. A. Potter, J. Kappler, and P. Marrack, Cytokine-induced survival of activated T cells in vitro and in vivo, Proc Nat Acad Sci, vol.95, issue.7, pp.3810-3815, 1998.

, FIGURE 4 Boxplot of time spent under 500 CD4, number of visits, mean number of CD4, and number of injections for each protocol at the threshold 0.05. ACI, adaptive criterion of injection protocol; ATI, adaptive time of injection protocol; ORI, original protocol

, However, these cycles are unnecessary as the decrease of CD4 in this patient is very slow. The ACI protocol correctly predicts that a new cycle will be necessary only at the fifth visit. The ATI protocol predicts a new cycle at a slightly larger time and has the advantage of having only two visits for a control, instead of eight for the other protocols. Patient 2 has an opposite problem, as the ORI protocol fails to detect that a new cycle was necessary, eg, at the first visit, resulting in a long time spent under 500 CD4. In contrast, the ACI and ATI protocols correctly predict that a new cycle is necessary. Again, the number of control visits is reduced in the ATI protocol, which yields accurate times of control. In Web Supplementary 3, the rate of error, defined as the number of times the decision made is not the optimal, is analyzed. Overall, the rate of time when the algorithm made a decision causing the patient to spend some time under 500 CD4 is extremely low for the ACI and ACIC protocols (between 0.1% and 6%). For the ATI and ATIC protocols, The rate of REFERENCES 1. Haase AT. Population biology of HIV-1 infection: viral and CD4+ T cell demographics and dynamics in lymphatic tissues, vol.17, 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, N Engl J Med, 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, Ann Intern Med, 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, The Antiretroviral Therapy, vol.372, pp.293-299, 2008.

. , 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. F. Delfraissy, and J. Theze, Interleukin-7 (IL-7): immune function, involvement in the pathogenesis of HIV infection and therapeutic potential, Eur Cytokine Netw, 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, Proc Natl Acad Sci USA, 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, J Clin Invest, vol.119, issue.4, pp.997-1007, 2009.
URL : https://hal.archives-ouvertes.fr/inserm-00484803

Y. Lévy, 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, Clin Infect Dis, vol.55, issue.2, pp.291-300, 2012.

I. Sereti, R. 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, J Acquir Immune Defic Syndr, 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, Clin Infect Dis, vol.62, issue.9, pp.1178-1185, 2016.

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

D. Boer, R. J. Perelson, and A. S. , Quantifying T lymphocyte turnover, J Theor Biol, vol.327, pp.45-87, 2013.

M. Lavielle, A. Samson, A. K. Fermin, and F. Mentré, 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, J Viral Hepat, vol.17, issue.12, pp.825-833, 2010.

R. Ke, C. Loverdo, H. Qi, R. Sun, L. et al., Rational design and adaptive management of combination therapies for hepatitis C virus infection, PLoS Comput Biol, 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, Math Comput Model, 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, J Theor Biol, 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 Comput Biol, vol.10, issue.5, p.1003630, 2014.

S. A. Murphy, Optimal dynamic treatment regimes, J R Stat Soc Ser B Stat Methodol, vol.65, issue.2, pp.331-355, 2003.

J. M. Robins, Optimal structural nested models for optimal sequential decisions, Proceedings of the Second Seattle Symposium in Biostatistics: Analysis of Correlated Data, pp.189-326, 2004.

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

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

M. L. Petersen, S. G. Deeks, and M. J. Van-der-laan, Individualized treatment rules: generating candidate clinical trials, Statist Med, vol.26, issue.25, pp.4578-4601, 2007.

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

B. Rich, E. Moodie, and D. A. Stephens, Optimal individualized dosing strategies: a pharmacologic approach to developing dynamic treatment regimens for continuous-valued treatments, Biom J, 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-01670680

E. S. Rosenberg, M. Davidian, and H. T. Banks, Using mathematical modeling and control to develop structured treatment interruption strategies for HIV infection, Drug Alcohol Depend, vol.88, pp.41-51, 2007.

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

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

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

A. M. Croicu, Short-and long-term optimal control of a mathematical model for HIV infection of CD4 + T cells, Bull Math Biol, vol.77, issue.11, pp.2035-2071, 2015.

B. Chakraborty and S. A. Murphy, Dynamic treatment regimes, Annu Rev Stat Its Appl, 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, Scand J Stat, vol.34, issue.1, pp.33-52, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00194275

D. Commenges, H. Jacqmin-gadda, C. Proust, and J. A. Guedj, Newton-like algorithm for likelihood maximization: the robust-variance scoring algorithm. arXiv preprint math/0610402, 2006.

, van der Vaart AW. Asymptotic Statistics. Cambrigde, 2000.

W. R. Gilks, N. G. Best, and K. Tan, Adaptive rejection metropolis sampling within Gibbs sampling, Appl Stat, vol.45, issue.4, 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, J Stat Softw, issue.9, 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

D. Commenges, C. Pasin, M. Prague, and R. Thiébaut, Adaptive protocols based on predictions from a mechanistic model of the effect of IL7 on CD4 counts, SUPPORTING INFORMATION Additional supporting information may be found online in the Supporting Information section at the end of the article. How to cite this article: Villain L, pp.1-15, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01973877

M. Plummer, N. Best, K. Cowles, and K. Vines, CODA: convergence diagnosis and output analysis for, MCMC. R news, vol.6, issue.1, pp.7-11, 2006.

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

L. Villain, D. Commenges, M. Prague, C. Pasin, and T. R. , Adaptive protocols based on predictions from a mechanistic model of the effect of IL7 on CD4 counts, Statistics in Medicine, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01973877