Estimation of HIV/AIDS parameters. (English) Zbl 1046.93013
The author proposes an estimation procedure for parameters of the simplest three-dimensional model of HIV/AIDS dynamics. The model takes into account the dynamics of uninfected and infected CD4+T cells and the evolution of the concentration of free virions. The author assumes that only measurements of the viral load and the healthy CD4+T cells counts in plasma are available and that at least five measurements of the former and four of the latter could be obtained. The estimators used in the study are based on the well-known techniques of adaptive identifiers and adaptive observers and the author demonstrates their efficiency in the early infection stage as well as in the asymptotic stage after using anti-retrovirus drugs. On the other hand, in the asymptotic stage of HIV without therapy and in the short period after treatment, determination of all parameters is impossible. The analytical results and hypotheses are verified by simulation studies carried out in the Matlab/Simulink environment.
Reviewer: A. Šwierniak (Gliwice)
MSC:
| 93B30 | System identification |
| 93C95 | Application models in control theory |
| 92C45 | Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) |
| 92C50 | Medical applications (general) |
| 93C10 | Nonlinear systems in control theory |
| 92D30 | Epidemiology |
| 93B07 | Observability |
Keywords:
adaptive identifier; adaptive observer; biomedical study; HIV/AIDS; identifiability; nonlinear systems; observabilityReferences:
| [1] | Alvarez-Ramirez, J.; Meraz, M.; Velasco-Hernandez, J. X., Feedback control of the chemotherapy of HIV, International Journal of Bifurcation and Chaos, 10, 2207-2219 (2000) · Zbl 0956.92021 |
| [2] | CDC Working Group (2003). Guidelines for laboratory test result reporting of human immunodeficiency virus type i ribonucleic acid determination. [on-line], http://www.cdc.gov/; CDC Working Group (2003). Guidelines for laboratory test result reporting of human immunodeficiency virus type i ribonucleic acid determination. [on-line], http://www.cdc.gov/ |
| [3] | Conte, G.; Moog, C. H.; Perdon, A. M., Nonlinear control systems: An algebraic setting (1999), Springer: Springer London · Zbl 0920.93002 |
| [4] | Covert, D.; Kirschner, D., Revisiting early models of the host-pathogen interactions in HIV infection, Comments Theoretical Biology, 5, 383-411 (2000) |
| [5] | Ho, D. D., Neumann, A. U., Perelson, A. S., Chen, W., Leonard, J. M., & Markowitz, M. (1995). Rapid turnover of plasma virions and CD4 lymphocytes in HIV-1 infection. Nature273; Ho, D. D., Neumann, A. U., Perelson, A. S., Chen, W., Leonard, J. M., & Markowitz, M. (1995). Rapid turnover of plasma virions and CD4 lymphocytes in HIV-1 infection. Nature273 |
| [6] | Kirschner, D.; Lenhart, S.; Serbin, S., Optimal control of the chemotherapy of HIV, Journal of Mathematical Biology, 35, 775-792 (1997) · Zbl 0876.92016 |
| [7] | Ljung, L.; Glad, T., On global identifiability for arbitrary model parameterizations, Automatica, 30, 265-276 (1994) · Zbl 0795.93026 |
| [8] | Marino, R.; Tomei, P., Nonlinear control design: Geometric, adaptive and robust (1995), Prentice-Hall: Prentice-Hall New York · Zbl 0833.93003 |
| [9] | Marino, R., & Tomei, P. (2000). Global estimation of \(n\)IEEE 39th conference on decision and control; Marino, R., & Tomei, P. (2000). Global estimation of \(n\)IEEE 39th conference on decision and control |
| [10] | Nowak, M. A.; Bangham, C. R.M., Population dynamics of immune responses to persistent viruses, Science, 272, 74-79 (1996) |
| [11] | Nowak, M. A.; May, R. M., Virus dynamics: Mathematical principles of immunology and virology (2000), Oxford University Press: Oxford University Press New York · Zbl 1101.92028 |
| [12] | Perelson, A. S.; Kirschner, D.; De Boer, R., Dynamics of HIV infection of CD4+T cells, Mathematical Biosciences, 114, 81-125 (1993) · Zbl 0796.92016 |
| [13] | Perelson, A. S.; Nelson, P. W., Mathematical analysis of HIV-1 dynamics in vivo, SIAM Review, 41, 3-44 (1999) · Zbl 1078.92502 |
| [14] | Perelson, A. S.; Neumann, A. U.; Markowitz, M.; Leonard, J. M.; Ho, D. D., HIV-1 dynamics in vivoVirion clearance rate, infected cell life-span, and viral generation time, Science, 271, 1582-1586 (1996) |
| [15] | Sastry, S.; Bodson, M., Adaptive control: Stability, convergence, and robustness (1989), Prentice-Hall: Prentice-Hall London · Zbl 0721.93046 |
| [16] | Wei, X., Ghosh, S.K., Taylor, M.E., Johnson, V.A., Emini, E.A., Deutsch, P., Lifson, J.D., et al. (1995). Viral dynamics in HIV-1 infection. Nature273; Wei, X., Ghosh, S.K., Taylor, M.E., Johnson, V.A., Emini, E.A., Deutsch, P., Lifson, J.D., et al. (1995). Viral dynamics in HIV-1 infection. Nature273 |
| [17] | Wein, L. M.; Zenios, S. A.; Nowak, M. A., Dynamic multidrug therapies for HIVA control theoretic approach, Journal of Theoretical Biology, 185, 15-29 (1997) |
| [18] | Xia, X. (2000). Global frequency estimators through Marino-Tomei observers. In I. K. Craig, & F. R. Camisani-Calzolari (Eds.), Proceedings of IFAC conference on technology transfer in developing countries: Automation in infrastructure creation; Xia, X. (2000). Global frequency estimators through Marino-Tomei observers. In I. K. Craig, & F. R. Camisani-Calzolari (Eds.), Proceedings of IFAC conference on technology transfer in developing countries: Automation in infrastructure creation |
| [19] | Xia, X.; Moog, C. H., Identifiability of nonlinear systems with application to HIV/AIDS models, IEEE Transactions on Automatic Control, 48, 330-336 (2003) · Zbl 1364.93838 |
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