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Free Terminal Time Optimal Control Problem of an HIV Model Based on a Conjugate Gradient Method

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Abstract

The minimum duration of treatment periods and the optimal multidrug therapy for human immunodeficiency virus (HIV) type 1 infection are considered. We formulate an optimal tracking problem, attempting to drive the states of the model to a “healthy” steady state in which the viral load is low and the immune response is strong. We study an optimal time frame as well as HIV therapeutic strategies by analyzing the free terminal time optimal tracking control problem. The minimum duration of treatment periods and the optimal multidrug therapy are found by solving the corresponding optimality systems with the additional transversality condition for the terminal time. We demonstrate by numerical simulations that the optimal dynamic multidrug therapy can lead to the long-term control of HIV by the strong immune response after discontinuation of therapy.

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Authors and Affiliations

  1. Department of Mathematics, Inha University, Yonghyundong, Namgu, Incheon, 402-751, Republic of Korea

    Taesoo Jang & Hee-Dae Kwon

  2. Department of Computational Science and Engineering, Yonsei University, Shinchondong, Seodaemungu, Seoul, 120-749, Republic of Korea

    Jeehyun Lee

Authors
  1. Taesoo Jang
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  2. Hee-Dae Kwon
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  3. Jeehyun Lee
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Correspondence to Hee-Dae Kwon.

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Jang, T., Kwon, HD. & Lee, J. Free Terminal Time Optimal Control Problem of an HIV Model Based on a Conjugate Gradient Method. Bull Math Biol 73, 2408–2429 (2011). https://doi.org/10.1007/s11538-011-9630-z

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  • DOI: https://doi.org/10.1007/s11538-011-9630-z

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