## Description

Deterministic dynamic equations have proved very important in describing the response of HIV-1 to treatment in vivo. This thesis develops estimated local linear mixed-effects methods to estimate the coefficients of a linear differential equation that models the rate of HIV-1 RNA concentration in the patients' plasma. Two methods are developed. In the first, the coefficients are assumed to be constant. In the second, the coefficients are allowed to vary with time. For both methods the first step is to estimate the viral load and the first time derivative of the viral load from the measured value of viral load, where the measured value may have error. A local polynomial kernel estimation with mixed-effects is used for these estimations. The estimates of viral load and the first time derivative of viral load are then used in estimating the coefficients. Where the the coefficients are assumed constant, the second step estimates these coefficients with a linear mixed-effects equation. Where the coefficients are assumed to be time-varying, a local polynomial kernel estimation with mixed-effects is used to estimate the coefficients. We use a real data application and also numerical simulations to illustrate the two estimation methods.'