# American Institute of Mathematical Sciences

2013, 2013(special): 311-322. doi: 10.3934/proc.2013.2013.311

## An optimal control problem in HIV treatment

 1 Department of Mathematics and Computer Sciences, Texas Woman's University, Denton, TX 76204 2 Department of Computer Mathematics and Cybernetics, Moscow State Lomonosov University, Moscow, 119992 3 Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, 08193 Bellaterra, Barcelona

Received  September 2012 Revised  February 2013 Published  November 2013

We consider a three-dimensional nonlinear control model, which describes the dynamics of HIV infection with nonlytic immune response and possible effects of controllable medication intake on HIV-infected patients. This model has the following phase variables: populations of the infected and uninfected cells and the concentration of an antiviral drug. The medication intake rate is chosen to be a bounded control function. The optimal control problem of minimizing the infected cells population at the terminal time is stated and solved. The types of the optimal control for different model parameters are obtained analytically. This allowed us to reduce the two-point boundary value problem for the Pontryagin Maximum Principle to one of the finite dimensional optimization. Numerical results are presented to demonstrate the optimal solution.
Citation: Ellina Grigorieva, Evgenii Khailov, Andrei Korobeinikov. An optimal control problem in HIV treatment. Conference Publications, 2013, 2013 (special) : 311-322. doi: 10.3934/proc.2013.2013.311
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