Identification of Hiv-1 Dynamics - Estimating the Noise Model, Constant and Time-varying Parameters of Long-term Clinical Data

The importance of a system theory based approach in understanding immunological diseases, in particular the HIV-1 infection, is being increasingly recognized. This is because the dynamics of virus infection may be effectively represented by relatively compact state space models in the form of nonlinear ordinary differential equations. This work focuses on the identification of constant and time-varying parameters in long-term dynamic HIV-1 data.We introduce a novel strategy for parameter identification. Constant parameters were estimated using Particle Swarm Optimization (PSO), and time-varying parameters were captured with Extended Kalman Filter (EKF). As EKF relies on the noise strongly, the measurement noise was also inferred. The results are convincing on clinical data: similar noise parameters were detected for two different subjects, a good overall fit was reached to the data, and EKF was found efficient in estimating the time-varying parameters, overcoming drawbacks and limitations of existing methods.