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Optimal Control Strategy for a Fully Determined HIV Model
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Intelligent Control and Automation·Volume 01 (2010)·Pages 15–19·Published 27 August 2010·DOI10.4236/ica.2010.11002
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Abstract
This paper shows how mathematical methods can be implemented to formulate guidelines for clinical testing and monitoring of HIV/AIDS disease. First, a mathematical model for HIV infection is presented which the measurement of the CD4+T cells and the viral load counts are needed to estimate all its parameters. Next, through an analysis of model properties, the minimal number of measurement samples is obtained. In the sequel, the effect of Reverse Transcriptase enzyme Inhibitor (RTI) on HIV progression is demonstrated by using a control function. Also the total cost of treatment by this kind of drugs has been minimized. The numerical results are obtained by a numerical method in discretization issue, called AVK.
KeywordsHIV/AIDSMathematical ModelingSystem IdentificationControl TheoryImmunotherapy
- D. Covert and D. Kirschner, “Revisiting Early Models of the HostPathogen Interactions in HIV Infection,” Comments Theoretical Biology, Vol. 5, No. 6, 2000, pp. 383 411.
- M. A. Nowak and R.M. May, “Virus Dynamics: Mathematical Principles of Immunology and Virology,” Oxford University Press, New York, 2000.
- A. S. Perelson and P. W. Nelson, “Mathematical Analysis of HIV1 Dynamics in Vivo,” SIAM Review, Vol. 41, No. 1, 1999, pp. 344.
- W.Y. Tan and H. Wu, “Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention,” World Scientific, Singapore, 2005.
- M. A. Nowak and C. R. M. Bangham, “Population Dynamics of Immune Responses to Persistent Viruses,” Science, Vol. 272, No. 5758, 1996, pp. 7479.
- X. Wei, S. K. Ghosh, M. E. Taylor, V. A. Johnson, E. A. Emini, P. Deutsch and J. D. Lifson, “Viral Dynamics in HIV1 Infection”, Nature, Vol. 273, No. 6510, 1995, pp. 117122.
- X. Xia, “Estimation of HIV/AIDS parameters,” Automatica, Vol. 39, No. 11, 2003, pp. 19831988.
- R. Pattman, M. Snow, P. Handy, K. N. Sankar and B. Elawad, “Oxford Handbook of Genitourinary Medicine, HIV and AIDS,” Oxford University Press, USA, 2005.
- X. Xia, “Modelling of HIV Infection: Vaccine Readiness, Drug Effectiveness and Therapeutical Failures,” Journal of Process Control, Vol. 17, No. 3, 2007, pp. 253260.
- K. R. Fister and S. Lenhart, “Optimizing Chemotherapy in an HIV Model,” Journal of Differential Equations, Vol. 1998, No. 32, 1998, pp. 112.
- K. P. Badakhshan and A. V. Kamyad, “Numerical Solution of Nonlinear Optimal Control Problems Using Non linear Programming,” Applied Mathematics and Computation, Vol. 187, No. 2, 2007, pp. 15111519.