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Journal of Mathematical Biology

, Volume 35, Issue 7, pp 775–792 | Cite as

Optimal control of the chemotherapy of HIV

  • Denise Kirschner
  • Suzanne Lenhart
  • Steve Serbin

Abstract.

 Using an existing ordinary differential equation model which describes the interaction of the immune system with the human immunodeficiency virus (HIV), we introduce chemotherapy in an early treatment setting through a dynamic treatment and then solve for an optimal chemotherapy strategy. The control represents the percentage of effect the chemotherapy has on the viral production. Using an objective function based on a combination of maximizing benefit based on T cell counts and minimizing the systemic cost of chemotherapy (based on high drug dose/strength), we solve for the optimal control in the optimality system composed of four ordinary differential equations and four adjoint ordinary differential equations.

Key words: Chemotherapy HIV Optimal control Ordinary differential equation system 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Denise Kirschner
    • 1
  • Suzanne Lenhart
    • 2
  • Steve Serbin
    • 2
  1. 1.Department of Mathematics, Texas A and M University, College Station, TX 77843, USA e-mail: dek@math.tamu.eduUS
  2. 2.Department of Mathematics, University of Tennessee at Knoxville, Knoxville, TN 37996, USA e-mails: lenhart@math.utk.edu; serbin@sugarbowl.math.utk.eduUS

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