Joint-state and parameters estimation using nudging and SEIK filters for HIV mechanistic models

Various methods have been used in the statistical field to estimate parameters in mechanistic models. In particular, approach based on penalised likelihood for estimation of parameters in ordinary differential equations with non linear models on parameters (ODENLME) has proven successful. We will consider the NIMROD program [Prague2013] as a benchmark for estimation in these models. However, such approach is time consuming. We propose to consider data assimilation which historically arose in the context of geophysics. We propose a Luenberger (also called nudging) state observer coupled with a parameter Kalman-based observer (RoUKF filter, also called SEIK filter) to perform a joint state and parameter estimation on a dataset composed of longitudinal observations of biomarkers for multiples patients. We compare these methods in term of performances and computation time. We discuss how the concept of random effect can be modelled using Kalman-based filter and its limitations. We illustrate both methods in simulation and on two datasets