Sequential data assimilation of the stochastic SEIR epidemic model for regional COVID-19 dynamics

Ralf Engbert; Maximilian M. Rabe; Reinhold Kliegl; Sebastian Reich

The contact parameter β is the most critical parameter determining the dynamics of the stochastic SEIR model. After time-resolved estimation of the best fit β * (t k ), we are able to generate simulations from an initial state to predict the future trajectory (Fig. 3 ). Simulations I are started from the first epidemic day in the corresponding region with greater than or equal to 30 cases. The initial numbers of infected I 0 were set to the observed number of cases y obs (t 0 ), while the initial numbers of exposed were set to E 0 = g/a · I 0 , which would hold at epidemic equilibrium for m > 0 (for m = 0 both E and I tend to zero with E/I ≈ g/a). The initial number of infected people was disturbed by noise representing uncertainties in the initial model states. Forward iteration with the estimated time-varying contact parameter show that the slope of the epidemic curve is approximately reproduced by the model (Fig. 3a ,c; grey lines indicate the ensemble of simulated trajectories; blue points are observed data). At March 26th, we started simulations II which exploits the full potential of sequential data assimilation. The sequential data assimilation approach via the ensemble Kalman filter (see Ensemble Kalman filter) is based on the forward modeling of an ensemble of trajectories. After each time step (1 day), the ensemble of trajectory is compared to the next observation and adjusted via a linear regression step. Therefore, we obtained an adapted ensemble of internal model states at each epidemic day. Here we exploit this fact in a forward simulation with initial conditions from the assimilated ensemble of internal model states. The corresponding forward simulations are close to the real timeevolution of the epidemics in the two example regions (