Dynamic Multidrug Therapies for HIV: Optimal and STI Control Approaches

B. M. Adams; H. T. Banks; Hee-Dae Kwon; Hien T. Tran; B. M. Adams; H. T. Banks; Hee-Dae Kwon; Hien T. Tran

doi:10.3934/mbe.2004.1.223

Mathematical Biosciences and Engineering

2004, Volume 1, Issue 2: 223-241. doi: 10.3934/mbe.2004.1.223

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Dynamic Multidrug Therapies for HIV: Optimal and STI Control Approaches

1.
Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695
2.
Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695-8212

Accepted: 29 June 2018 Published: 01 July 2004
MSC : 34H05, 37M05, 49K15, 65L05, 92B05, 92C60.

We formulate a dynamic mathematical model that describes the interaction of the immune system with the human immunodeficiency virus (HIV) and that permits drug ''cocktail'' therapies. We derive HIV therapeutic strategies by formulating and analyzing an optimal control problem using two types of dynamic treatments representing reverse transcriptase (RT) inhibitors and protease inhibitors (PIs). Continuous optimal therapies are found by solving the corresponding optimality systems. In addition, using ideas from dynamic programming, we formulate and derive suboptimal structured treatment interruptions (STI) in antiviral therapy that include drug-free periods of immune-mediated control of HIV. Our numerical results support a scenario in which STI therapies can lead to long-term control of HIV by the immune response system after discontinuation of therapy.
- nonlinear modeling,
- HIV dynamics,
- optimal control.,
- structured treatment interruption
Citation: B. M. Adams, H. T. Banks, Hee-Dae Kwon, Hien T. Tran. Dynamic Multidrug Therapies for HIV: Optimal and STI Control Approaches[J]. Mathematical Biosciences and Engineering, 2004, 1(2): 223-241. doi: 10.3934/mbe.2004.1.223

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Abstract

We formulate a dynamic mathematical model that describes the interaction of the immune system with the human immunodeficiency virus (HIV) and that permits drug ''cocktail'' therapies. We derive HIV therapeutic strategies by formulating and analyzing an optimal control problem using two types of dynamic treatments representing reverse transcriptase (RT) inhibitors and protease inhibitors (PIs). Continuous optimal therapies are found by solving the corresponding optimality systems. In addition, using ideas from dynamic programming, we formulate and derive suboptimal structured treatment interruptions (STI) in antiviral therapy that include drug-free periods of immune-mediated control of HIV. Our numerical results support a scenario in which STI therapies can lead to long-term control of HIV by the immune response system after discontinuation of therapy.
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