Control of infection dynamics, with applications to the HIV disease

Abstract

The human immunodeficiency virus (HIV) infection, that causes acquired immune deficiency syndrome (AIDS), is a dynamic process that can be modeled via differential equations. The primary goal of this thesis is to show how to drive any initial state into an equilibrium, called the long-term nonprogressor, in which the infected patient does not develop symptoms of AIDS. We first propose three control methods for HIV treatment. These methods are designed for antiretroviral drug therapy and are based on the understanding of the system dynamics. We apply these control strategies to several HIV dynamic models as well as a general disease dynamic model. Then we derive a new output feedback control scheme from one of the proposed methods. To show the feasibility of the output feedback control, the HIV model is studied analytically. This control method guarantees that the immune state is enhanced to a certain level, which is enough for a typical patient to be driven into the long-term nonprogressor. We also investigate methods to estimate approximately the state of the immune system based on the available outputs of the HIV model. The feasibility and effectiveness of the control strategies and estimation ideas are demonstrated by computer simulations.

Key Words. HIV dynamic model, AIDS, output feedback control, drug scheduling, biological system analysis.