Winston Garira, Senelani D. Musekwa, Tinevimbo Shiri
Abstract:
Highly active antiretroviral therapy (HAART) is administered to symptomatic
human immunodeficiency virus (HIV) infected individuals to improve their
health. Various administration schemes are used to improve patients'
lives and at the same time suppressing development of drug resistance,
reduce evolution of new viral strains, minimize serious side effects,
improve patient adherence and also reduce the costs of drugs.
We deduce an optimal drug administration scheme useful in improving patients'
health especially in poor resourced settings. In this paper we use
the Pontryagin's Maximum Principle to derive optimal drug dosages based
on a mathematical dynamical model. We use methods of optimal control
to determine optimal controls analytically, and then use the Runge-Kutta
scheme of order four to numerically simulate different therapy effects.
We simulate the different effects of a drug regimen composed of a protease
inhibitor and a nucleoside reverse transcriptase inhibitor.
Our results indicate that for highly toxic drugs, small dosage sizes and
allowing drug holidays make a profound impact in both improving the quality
of life and reducing economic costs of therapy. The results show that for
drugs with less toxicity, continuous therapy is beneficial.
Submitted April 16, 2005. Published May 17, 2005.
Math Subject Classifications: 93C15, 92D30, 49K15, 49J15, 34B15.
Key Words: HIV; mathematical model; optimal control, combined therapy.
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Winston Garira Department of Applied Mathematics National University of Science and Technology P O Box AC939 Ascot, Bulawayo, Zimbabwe email: wgarira@nust.ac.zw |
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Senelani D. Musekwa Department of Applied Mathematics National University of Science and Technology P O Box AC939 Ascot, Bulawayo, Zimbabwe email: sdmusekwa@nust.ac.zw |
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Tinevimbo Shiri Department of Applied Mathematics National University of Science and Technology P O Box AC939 Ascot, Bulawayo, Zimbabwe email: tshiri@nust.ac.zw |
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