State estimation of the time-space propagation of COVID-19 using a distributed parameter observer based on a SEIR-type model.

The real-time prediction and estimation of the spread of diseases, such as COVID-19 is of paramount importance as evidenced by the recent pandemic. This work is concerned with the distributed parameter estimation of the time-space propagation of such diseases using a diffusion-reaction epidemiological model of the susceptible-exposed-infected-recovered (SEIR) type. State estimation is based on continuous measurements of the number of infections and deaths per unit of time and of the host spatial domain. The observer design method is based on positive definite matrices to parameterize a class of Lyapunov functionals, in order to stabilize the estimation error dynamics. Thus, the stability conditions can be expressed as a set of matrix inequality constraints which can be solved numerically using sum of squares (SOS) and standard semi-definite programming (SDP) tools. The observer performance is analyzed based on a simplified case study corresponding to the situation in France in March 2020 and shows promising results.