Abstract
Mathematical modeling is used for individual patients to help for an early diagnosis of the evolution of the infection. The feasibility of the method is depicted on some patients who start a HAART (Highly Active AntiRetroviral Therapy). It is shown how this mathematical study can be used in the early diagnosis of the immunological failure for HIV patients.
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References
A. M. Jeffrey. A control theoretic approach to HIV/AIDS drug dosage desing and timing the initiation of therapy. PhD thesis, University of Preotria, South Africa, July 2006.
R. Zurakowski and R. A. Teel. A model predictive control based scheduling method for HIV therapy. Journal of Theoretical Biology, pages 368–382, July 2006.
A. S. Perelson and P. W. Nelson. Mathematical analysis of HIV-1 dynamics in vivo. SIAM Review, 41(1):3–44, 1999.
A. S. Perelson et al. Decay characteristics of HIV-1 infected compartment during combination therapy. Nature, 387:188–191, 1997.
David D. Ho et al. Rapid turnover of plasma virion and CD4 lymphocytes in HIV-1 infection. Nature, 373:123–126, January 1995.
Xiping Wei et al. Viral dynamics in human immunodeficiency virus type 1 infection. Nature, 373:117–122, January 1995.
R. Arnaout, M. A. Nowak, and D. Wodarz. HIV-1 dynamics revisited: Biphasic decay by cytotoxic T lymphocyte killing. Proc. Royal Society, 267:1347–1354, 2000.
R. A. Filter, X. Xia, and I. K. Gray. Dynamic HIV/AIDS parameter estimation with application to a vaccine readiness study in southern Africa. IEEE Transactions on Biomedical Engineering, 52(5):284–291, May 2005.
M. A. Nowak and R. M. May. Virus dynamics: Mathematical principles of immunology and virology. Oxford University Press, 2002.
D. Kirschner and G. F. Webb. Understanding drug resistance for monotherapy treatment of HIV infection. Bulletin of Mathematical Biology, 59(4):763–785, 1997.
D. A. Ouattara. Mathematical analysis of the HIV-1 infection: Parameter estimation, therapies effectiveness, and therapeutical failures. In 27th Annual International Conference of the IEEE Engineering in Medecine and Biology Society (EMBC’05), Shanghai, China, September 2005.
D. Wodarz et al. A new therory of cytotoxic T-lymphocyte memory: Implication for the HIV treatement. Phil. Trans. R. Soc. Lond., 355:329–343, 2000.
X. Xia and C. H. Moog. Identifiability of nonlinear systems with application to HIV/AIDS models. IEEE Transactions on Automatic Control, 48(2):330–336, February 2003.
Eric Walter. Identifiability of Parametric Models. Pergamon Press, London, U.K., 1987. Edited, Updated and Expanded papers of the 7th IFAC/IFCOR Symposium on Identification and System Parameter Estimation, July 1985 in York, England.
E. T. Tunali and T.-J. Tarn. New results for identifiability of nonlinear systems. IEEE Transactions on Automatic Control, AC-32(2):146–154, Febr. 1987.
G. Conte, C. H. Moog, and A. M. Perdon. Nonlinear Control Systems. Springer-Verlag, London, U.K., 1999.
J. Kim, W. H. Kim, H. B. Chung, and C. C. Chung. Constant drug dose leading long-term non-progressor for HIV-infected patients with RTI and PI. In 44th IEEE Conference on Decision and Control, and the European Control Conference 2005, Seville, Spain, December 2005.
D. Wodarz and M. A. Nowak. CD8 memory, immuonodominance, and antigenic escape. Eur. J. Immunol., 30:2704–2712, 2000.
JF. Delfraissy. Prise en charge des personnes infectées par le VIH: Recommandations du groupe d’experts. Médecine Science, Paris, flammarion edition, 2004. Available at http://www.ladocumentationfrancaise.fr/brp/notices/044000467.shtml.
U.S. Dept. Health and Human Services. Guidelines for the use of antiretroviral agents in HIV-1-infected adults and adolescents, May 2006. Available at http://www.aidsinfo.nih.gov/guidelines.
I. T. Prud’homme et al. Amplicor HIV Monitor, NASBA HIV-1 RNA QT and Quantiplex HIV RNA version 2.0 viral load assays: a Canadian evaluation. Journal of Clinical Virology, 11:189–202, 1998.
A. Berger et al. Comparative evaluation of the COBAS Amplicor HIV-1 Monitor™ ultrasensitive test, the new COBAS AmpliPrep/COBAS Amplicor HIV-1 Monitor™ and the versant HIV RNA 3.0 assays for quantitation of HIV-1 RNA in plasma samples. Journal of Clinical Virology, 33:43–51, 2005.
R. Galli, L. Merrick, M. Friesenhahn, and R. Ziermann. Comprehensive comparison of the Versant® HIV-1 RNA 3.0 (bDNA) and COBAS Amplicor HIV-1 Monitor® 1.5 assays on 1000 clinical specimens. Journal of Clinical Virology, 34:245–252, 2005.
K. Israel-Ballard et al. Taqman rt-pcr and Versant® HIV-1 RNA 3.0 (bDNA) assay quantification of HIV-1 RNA viral load in breast milk. Journal of Clinical Virology, 34:253–256, 2005.
Fiches Techniques de la Firme Roche. Available at http://www.roche-diagnostics.fr.
R. A. Filter and X. Xia. A penalty function to HIV/AIDS model parameter estimation. In 13th IFAC Symposium on System Identification, Rotterdam, 2003.
D. A. Ouattara, F. Bugnon, F. Raffi, and C. H. Moog. Parameter identification of an HIV/AIDS model. In 13th International Symposium on HIV and Emerging Infectious Diseases, Toulon, France, September 2004.
S. Nõmm. Realization and Identifiability of Discret-time Nonlinear Systems. PhD thesis, Tallinn University of Technology (Estonia), Ecole Centrale de Nantes (France), 2004. ISBN: 9985-59-440-1 / ISSN: 1406-4723.
D. A. Ouattara. Modélisation de l’infection par le VIH, identification et aide au diagnostic. PhD thesis, Ecole Centrale de Nantes & Université de Nantes, Nantes, France, September 2006.
IRCCyN Web software for the computation HIV infection parameters. Available at http://www.irccyn.ec-nantes.fr/hiv.
D. Kirschner, S. Lenhart, and S. Serbin. Optimal control of the chemotherapy of HIV. J. Math. Biol, 35:775–792, 1997.
M. A. Jeffrey, X. Xia, and I. K. Graig. When to initiate HIV therapy: A control theoretic approach. IEEE Transactions on Biomedical Engineering, 50(11): 1213–1220, 2003.
F. Biafore and C. E. D’Attellis. Exact linearisation and control of an HIV-1 predator-prey model. In 27th Annual International Conference of the IEEE Engineering in Medecine and Biology Society, Shanghai, China, September 2005.
D. A. Ouattara and C. H. Moog. Identification, linéarisation et commande optimale du modèle 3D de l’infection VIH-1. In Conférence International Francophone d’Autotmatique, CIFA 2006, Bordeaux, France, 2006.
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Ouattara, D.A., Moog, C.H. (2007). Modeling of the HIV/AIDS Infection: An Aid for an Early Diagnosis of Patients. In: Queinnec, I., Tarbouriech, S., Garcia, G., Niculescu, SI. (eds) Biology and Control Theory: Current Challenges. Lecture Notes in Control and Information Sciences, vol 357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71988-5_2
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DOI: https://doi.org/10.1007/978-3-540-71988-5_2
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