Optimal Control Of An Hiv Model
Volume 2, Issue 4, pp 650 - 658
Publication Date: May 30, 2011
H. R. Erfanian
- Department of Mathematics & Statistics, University of Science and Culture, Tehran, Iran.
M. H. Noori Skandari
- Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
We consider an HIV model, based on optimal control, for identifying the best treatment strategy in order to maximize the healthy cells by using chemotherapies with minimum side effects. In this paper, a new approach is introduced which transform the constraints of problem to the integral constraints. By an approximation, we obtain a finite dimensional linear programming problem which give us an approximate solution for original problem.
- HIV Model
- Optimal Control
- Linear programming
- Measure theory
- Chemotherapy .
 A.A.Ejigu , An Efficient Treatment Strategy for HIV Patients Using Optimal Control , African Institute for Mathematical Sciences (AIMS), Supervised by: Prof. Kailash C. Patidar,University of the Western Cape, South Africa,Submitted in partial fulfilment of a postgraduate diploma at AIMS, 22 May 2008.
 H. R. Erfanian, A. V. Kamyad and S. Effati, The optimal method for solving continuous linear and nonlinear programs, Applied mathematical sciences, Vol. 3, No. 25, pp 1209-1217, 2009.
 A.B. Gumel, P.N. Shivakumar, B.M. Sahai, A mathematical model for the dynamics of HIV-1 during the typical course of infection, in: Third World Congress of Nonlinear Analysts, vol. 47, pp. 2073–2083, 2001.
 A.Heydari, M.H.Farahi, A.A.Heydari, Chemotherapy in an HIV model by a pair of optimal control, Proceedings of the 7th WSEAS International Conference on Simulation, Modelling and Optimization, Beijing, China, September 15-17, 2007.
 H.R.Joshi, Optimal control of an HIV immunology model, Optimal Control Applications and Methods, No.23, pp 199-213, 2002.
 J. Karrakchou, M. Rachik, and S. Gourari. Optimal control and Infectiology: Application to an HIV/AIDS Model. Applied Mathematics and Computation, 177:807–818, 2006.
. A. V. Kamyad, J. E. Rubio and D. A. Wilson, An optimal control problem for the multidimensional diffusion equation with a generalized control variable, Journal of Optimization Theory and Applications , No.75(1), pp.101-132,1992.
 A. V. Kamyad, J. E. Rubio, and D. A. Wilson, The optimal control of the multidimensional diffusion equation, Journal of Optimization theory and Application , No.70 (1991), pp.191-209,1991.
 J. E. Rubio, Control and Optimization the Linear Treatment of Non-linear Problems, Manchester, U. K., Manchester University Press, 1986.
 H. Zarei, A. V. Kamyad, S. Effati , Maximizing of Asymptomatic Stage of Fast Progressive HIV Infected Patient Using Embedding Method Intelligent Control and Automation , No.1, pp.48-58 , 2010.