Modeling, Analysis, and Estimation of an in vitro HIV Infection Using Functional Differential Equations

Abstract

This dissertation focuses on developing mathematical and computational tools for use as an aid in understanding the cellular population dynamics of an in vitro HIV experiment. We carefully develop a functional differential equation model which incorporates mathematical mechanisms that account for both the biological delays and the parameter uncertainty inherent in the system. We present the theoretical foundations for our methodology which then allow us to develop a numerical approximation scheme and perform parameter identifications (even on the delay distributions) and sensitivity analyses. We summarize the results of a numerical investigation of the delays followed by the results from the nonlinear least squares inverse problem. We then present a statistical significance argument for the importance of the delay mechanism as well as the results of a sample sensitivity analysis of the system with respect to select parameters.