Dynamic Multidrug Therapies for HIV: Optimal and STI Control Approaches
We formulate a dynamic mathematical model that describes theinteraction of the immune system with the human immunodeficiencyvirus (HIV) and that permits drug ''cocktail'' therapies. Wederive HIV therapeutic strategies by formulating and analyzing anoptimal control problem using t...
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AIMS Press
2004-06-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2004.1.223 |
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| author | B. M. Adams H. T. Banks Hee-Dae Kwon Hien T. Tran |
| author_facet | B. M. Adams H. T. Banks Hee-Dae Kwon Hien T. Tran |
| author_sort | B. M. Adams |
| collection | DOAJ |
| description | We formulate a dynamic mathematical model that describes theinteraction of the immune system with the human immunodeficiencyvirus (HIV) and that permits drug ''cocktail'' therapies. Wederive HIV therapeutic strategies by formulating and analyzing anoptimal control problem using two types of dynamic treatmentsrepresenting reverse transcriptase (RT) inhibitors and proteaseinhibitors (PIs). Continuous optimal therapies are found bysolving the corresponding optimality systems. In addition, usingideas from dynamic programming, we formulate and derive suboptimalstructured treatment interruptions (STI) in antiviral therapy thatinclude drug-free periods of immune-mediated control of HIV. Ournumerical results support a scenario in which STI therapies canlead to long-term control of HIV by the immune response systemafter discontinuation of therapy. |
| format | Article |
| id | doaj-art-a5218b50b62348a1a883b7a97e271afe |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2004-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-a5218b50b62348a1a883b7a97e271afe2025-01-24T01:46:53ZengAIMS PressMathematical Biosciences and Engineering1551-00182004-06-011222324110.3934/mbe.2004.1.223Dynamic Multidrug Therapies for HIV: Optimal and STI Control ApproachesB. M. Adams0H. T. Banks1Hee-Dae Kwon2Hien T. Tran3Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695-8212Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695We formulate a dynamic mathematical model that describes theinteraction of the immune system with the human immunodeficiencyvirus (HIV) and that permits drug ''cocktail'' therapies. Wederive HIV therapeutic strategies by formulating and analyzing anoptimal control problem using two types of dynamic treatmentsrepresenting reverse transcriptase (RT) inhibitors and proteaseinhibitors (PIs). Continuous optimal therapies are found bysolving the corresponding optimality systems. In addition, usingideas from dynamic programming, we formulate and derive suboptimalstructured treatment interruptions (STI) in antiviral therapy thatinclude drug-free periods of immune-mediated control of HIV. Ournumerical results support a scenario in which STI therapies canlead to long-term control of HIV by the immune response systemafter discontinuation of therapy.https://www.aimspress.com/article/doi/10.3934/mbe.2004.1.223nonlinear modelinghiv dynamicsoptimal control.structured treatment interruption |
| spellingShingle | B. M. Adams H. T. Banks Hee-Dae Kwon Hien T. Tran Dynamic Multidrug Therapies for HIV: Optimal and STI Control Approaches Mathematical Biosciences and Engineering nonlinear modeling hiv dynamics optimal control. structured treatment interruption |
| title | Dynamic Multidrug Therapies for HIV: Optimal and STI Control Approaches |
| title_full | Dynamic Multidrug Therapies for HIV: Optimal and STI Control Approaches |
| title_fullStr | Dynamic Multidrug Therapies for HIV: Optimal and STI Control Approaches |
| title_full_unstemmed | Dynamic Multidrug Therapies for HIV: Optimal and STI Control Approaches |
| title_short | Dynamic Multidrug Therapies for HIV: Optimal and STI Control Approaches |
| title_sort | dynamic multidrug therapies for hiv optimal and sti control approaches |
| topic | nonlinear modeling hiv dynamics optimal control. structured treatment interruption |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2004.1.223 |
| work_keys_str_mv | AT bmadams dynamicmultidrugtherapiesforhivoptimalandsticontrolapproaches AT htbanks dynamicmultidrugtherapiesforhivoptimalandsticontrolapproaches AT heedaekwon dynamicmultidrugtherapiesforhivoptimalandsticontrolapproaches AT hienttran dynamicmultidrugtherapiesforhivoptimalandsticontrolapproaches |