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

Taesoo Jang, Hee Dae Kwon, Jeehyun Lee

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15 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)2408-2429
Number of pages22
JournalBulletin of Mathematical Biology
Volume73
Issue number10
DOIs
Publication statusPublished - 2011 Oct

Bibliographical note

Funding Information:
Acknowledgements The work of Hee-Dae Kwon was supported in part by the National Research Foundation of Korea (NRF) Grant funded by the Korean government (MEST) (2009-0065241) and in part by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-331-C00053). The work of Jeehyun Lee was supported by the Korea Research Foundation Grant funded by the Korean government (KRF-2008-531-C00012) and in part by the WCU program through NRF (R31-2008-000-10049-0).

All Science Journal Classification (ASJC) codes

  • Neuroscience(all)
  • Immunology
  • Mathematics(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Environmental Science(all)
  • Pharmacology
  • Agricultural and Biological Sciences(all)
  • Computational Theory and Mathematics

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