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

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

Publicly available data on the cumulative number of infected individuals is used to infer the model states X = (S, E, I, R) T and the contact parameter β of the stochastic SEIR model. Note that the cumulative number of infected individuals corresponds to Y = I + R in the SEIR model. In the present study we combine sequential data assimilation for the model states with an approximate log-likelihood function for the contact parameter [20] . The basic algorithmic idea is to propagate an ensemble of M model forecasts using Gillespie's algorithm up to the next available observation point t k . The forecast ensemble is denoted by X . While the forecast ensemble is used to compute the temporary negative log-likelihood L(t k , β) of the model's contact parameter β at time t k , the adjusted model states serve as starting values for the next Gillespie prediction cycle. The above algorithm is run over a fixed range of contact parameters β ∈ [β min , β max ] and over a fixed time window [t initial , t final ] of available data points y obs (t k ). The best fit contact parameter β * (t k ) at any time any t k is found as the one that minimises the temporary negative log-likelihood function, that is, β * (t k ) = arg min β L(t k , β)