Estimating and predicting the numbers of free HIV and T cells by nonlinear Kalman filter method

In this paper we have developed a state space model for the HIV pathogenesis at the cellular level involving free HIV and different types of T cells. In this state space model, the stochastic system model is the stochastic model of the HIV pathogenesis developed by Tan and Wu (1996) whereas the observation model is a statistic model based on the log of observed total numbers of CD4⁺ T-cell counts at different times. This is a continuous time-discrete time nonlinear Kalman filter model. For this model we have developed procedures for estimating and predicting the numbers of different types of T cells and free HIV through extended Kalman filter method. As an illustration, we have applied the method of this paper to a hemophilia patient from NCI/NIH with observed CD4⁺ T-cell counts at 16 occasions