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Dynamic multidrug therapies for HIV: Optimal and STI control approaches. (English) Zbl 1060.92034

Summary: 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.

MSC:

92C50 Medical applications (general)
49N90 Applications of optimal control and differential games
37M05 Simulation of dynamical systems
34H05 Control problems involving ordinary differential equations
49K15 Optimality conditions for problems involving ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
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