An optimal control problem in HIV treatment

Pages: 311 - 322, Issue special, November 2013

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Ellina Grigorieva - Department of Mathematics and Computer Sciences, Texas Woman's University, Denton, TX 76204, United States (email)
Evgenii Khailov - Department of Computer Mathematics and Cybernetics, Moscow State Lomonosov University, Moscow, 119992, Russian Federation (email)
Andrei Korobeinikov - Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, 08193 Bellaterra, Barcelona, Spain (email)

Abstract: 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.

Keywords:  HIV treatment, nonlinear control system, Pontryagin Maximum Principle, Valee-Poussin Theorem.
Mathematics Subject Classification:  49J15, 58E25, 92D30.

Received: September 2012;      Revised: February 2013;      Published: November 2013.