Electron. J. Diff. Eqns., Vol. 1998(1998), No. 32, pp. 1-12.

Optimizing chemotherapy in an HIV model

K. Renee Fister, Suzanne Lenhart, & Joseph Scott McNally

We examine an ordinary differential system modeling the interaction of the HIV virus and the immune system of the human body. The optimal control represents a percentage effect the chemotherapy has on the interaction of the CD4+T cells with the virus. We maximize the benefit based on the T cell count and minimize the systemic cost based on the percentage of chemotherapy given. Existence of an optimal control is proven, and the optimal control is uniquely characterized in terms of the solution of the optimality system, which is the state system coupled with the adjoint system. In addition, numerical examples are given for illustration.

Submitted April 15, 1998. Published December 4, 1998.
Math Subject Classification: 34B15, 49K15, 92D30.
Key Words: Chemotherapy, HIV, Optimal Control.

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K. Renee Fister
Department of Mathematics and Statistics, Murray State University
Murray, KY 42071 USA
e-mail: kfister@math.mursuky.edu

Suzanne Lenhart
Department of Mathematics, University of Tennessee
Knoxville, TN 37996 USA
e-mail : lenhart@math.utk.edu

Joseph Scott McNally
School of Medicine, Emory University
Atlanta, GA 30322 USA
e-mail: jmcnall@learnlink.emory.edu

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