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

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

Parameter recovery from simulated data To test the inference scheme, we simulated data for 20 days. In Figure 6 , the black line indicates the evolution of the SEIR model's predicted cumulative numbers of infected individuals, Y (t k ) = HX(t k ) = I(t k ) + R(t k ). Red dots represent the daily number of reported cases as in real data. In the simulation, the contact rate was chosen as β true = 0.6. In the following, we analyzed whether this true value could be recovered using the inference procedures described above. We varied the contact rate β and determined the cumulative negative log likelihood values L cum (β), Eq. (14) . The position of the minimum of L cum (β) indicates the best estimate for the numerical value of the underlying contact rate β * , Eq. (15) . The position of the minimum turns out to be close to the true value, β * ≈ β true = 0.6 (Fig. 6b) . Thus, parameter recovery can be demonstrated for a relatively short time series of 10 observations, which represents a typical data-set in the early phase of newly emerging epidemics. Next, we apply our inference scheme to real data.