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

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

The evolving spread of the novel coronavirus in Germany [1] resulted in containment measures based on reduced traveling and social distancing [3] . In epidemic standard models [2, 15] , which provide a dynamical description of epidemic outbreaks [7, 21] , containment measures aim at a reduction of the contact parameter. Since the contact parameter is one of the critical parameters that determine the speed of increase of the number of infectious individuals, estimation of the contact parameter is a key basis of epidemic modeling [18] . The current situation of COVID-19 is characterized by extreme spatial heterogeneity [1] . In the initial phase of the outbreak, this heterogeneity is caused by random travel-based imports of infectious cases and enhanced by local events with increased contacts. As a consequence, the assumption of homogeneous mixing must be relaxed [13] and coupled dynamics of regional models seem to be a more adequate description [16] . However, when modeling a relatively small region with population size N = 10 5 compared to the country level with N = 10 7 to 10 9 , demographic stochasticity [10, 13] must be addressed (see The stochastic SEIR model). The combination of dynamical modeling with substantial fluctuations calls for sequential data assimilation methods for parameter inference [5, 20] . We investigate the stochastic SEIR epidemic model [2] for application to regional data of COVID-19 incidence. The model assumes S, E, I, and R compartments representing susceptible, exposed, S E I R !SI aE gI Figure 1 : The SEIR model. The population is composed of four compartments that represent susceptible, exposed, infectious, and recovered individuals. The contact parameter β is critical for disease transmission, 1/a and 1/g are the average duration of exposed and infectious periods, resp. Different from the standard model, birth and death processes are neglected for the short-term simulations discussed throughout the current study.