Reconstructing Governing Equations of Influenza Virus Dynamics from Incomplete Measurements

Accurate dynamic models of virus infection processes are highly relevant for the optimization of vaccine production processes. However, fitting their parameters onto or even designing novel dynamic models from an existing set of biological measurement data is challenging as it is common that entire quantities are missing due to sub-optimal measurement setups. This work targets identifying virus dynamics models based on incomplete measurement data and domain knowledge. To this end, we unite sparse identification of non-linear dynamics (SINDy) with a commonly used approach to identify non-linear dynamical systems from incomplete measurements, namely an extended Kalman filter (EKF). This yields a hybrid model that is able to identify governing equations that describe the dynamic non-linear processes. The capabilities of this model are demonstrated on a set of incomplete artificial measurement data of an existing infection dynamics model.