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HIV dynamics: Modeling, data analysis, and optimal treatment protocols. (English) Zbl 1075.92030

Summary: We present an overview of some concepts and methodologies we believe useful in modeling HIV pathogenesis. After a brief discussion of motivation for and previous efforts in the development of mathematical models for progression of HIV infection and treatment, we discuss mathematical and statistical ideas relevant to Structured Treatment Interruptions (STI). Among these are model development and validation procedures including parameter estimation, data reduction and representation, and optimal control relative to STI. Results from initial attempts in each of these areas by an interdisciplinary team of applied mathematicians, statisticians and clinicians are presented.

MSC:

92C50 Medical applications (general)
62P10 Applications of statistics to biology and medical sciences; meta analysis
49N90 Applications of optimal control and differential games
92C60 Medical epidemiology
49J15 Existence theories for optimal control problems involving ordinary differential equations
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