IJPAM: Volume 57, No. 3 (2009)

HIV MODEL ANALYSIS AND ESTIMATION
IMPLEMENTATION UNDER OPTIMAL CONTROL
BASED TREATMENT STRATEGIES

John David$^1$, Hien Tran$^2$, H.T. Banks$^3$
$^{1,2,3}$Center for Research in Scientific Computation
North Carolina State University
Raleigh, NC 27695-8205, USA
$^3$e-mail: htbanks@ncsu.edu


Abstract.This paper illustrates the methodology necessary to ultimately implement the feedback control of HIV infection. To that end we describe a model of the immunologic response of the human immunodeficiency virus (HIV) in individuals. We illustrate how optimal control methodology can produce a drug dosing strategy and how this treatment strategy possesses features of structured treatment interruptions (STI). We then perform a sensitivity analysis of the model, illustrating use of both classical sensitivity functions and generalized sensitivity functions. We also investigate the use of stochastic estimation to develop filters and estimate states and parameters from noisy data. In the course of this analysis, we show that automatic differentiation (AD) can be a powerful tool in this type of analysis.

Received: November 12, 2009

AMS Subject Classification: 92C50, 92C60

Key Words and Phrases: HIV model, control, sensitivity, extended Kalman filter

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 57
Issue: 3