Estimation for dynamical systems using a population-based Kalman filter – Applications in computational biology

International audience; Estimation of dynamical systems - in particular, identification of their parameters - is fundamental in computational biology, e.g., pharmacology, virology, or epidemiology, to reconcile model runs with available measurements. Unfortunately, the mean and variance priorities of the parameters must be chosen very appropriately to balance our distrust of the measurements when the data are sparse or corrupted by noise. Otherwise, the identification procedure fails. One option is to use repeated measurements collected in configurations with common priorities - for example, with multiple subjects in a clinical trial or clusters in an epidemiological investigation. This shared information is beneficial and is typically modeled in statistics using nonlinear mixed-effects models. In this paper, we present a data assimilation method that is compatible with such a mixed-effects strategy without being compromised by the potential curse of dimensionality. We define population-based estimators through maximum likelihood estimation. We then develop an equivalent robust sequential estimator for large populations based on filtering theory that sequentially integrates data. Finally, we limit the computational complexity by defining a reduced-order version of this population-based Kalman filter that clusters subpopulations with common observational backgrounds. The performance of the resulting algorithm is evaluated against classical pharmacokinetics benchmarks. Finally, the versatility of the proposed method is tested in an epidemiological study using real data on the hospitalisation of COVID-19 patients in the regions and departments of France.