The importance of a system theory based approach in understanding immunological diseases, in particular the HIV-1 infection, is being increasingly recognized. The dynamics of virus infection may be effectively represented by compact state space models in the form of nonlinear ordinary differential equations (ODEs).
Nonlinear Bayesian filtering offers various online tools for system identification of parametric ordinary differential equation models. Since parameters may change with time, it is a relevant question to assess how well time-varying parameters can be estimated from data.
For this purpose two different filtering methods, Extended Kalman Filter and Particle Filter were applied for state and time-varying parameter estimation. After evaluating the methods on simulated time-series we applied them to long-term clinical datasets. Estimated time-varying parameters on clinical data are consistent with previously reported results with offline algorithms.