Sequential Data Assimilation of the Stochastic SEIR Epidemic Model for Regional COVID-19 Dynamics
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Sequential Data Assimilation of the Stochastic SEIR Epidemic Model for Regional COVID-19 Dynamics Ralf Engbert1 · Maximilian M. Rabe1 Sebastian Reich3
· Reinhold Kliegl2
·
Received: 13 July 2020 / Accepted: 5 November 2020 © The Author(s) 2020
Abstract Newly emerging pandemics like COVID-19 call for predictive models to implement precisely tuned responses to limit their deep impact on society. Standard epidemic models provide a theoretically well-founded dynamical description of disease incidence. For COVID-19 with infectiousness peaking before and at symptom onset, the SEIR model explains the hidden build-up of exposed individuals which creates challenges for containment strategies. However, spatial heterogeneity raises questions about the adequacy of modeling epidemic outbreaks on the level of a whole country. Here, we show that by applying sequential data assimilation to the stochastic SEIR epidemic model, we can capture the dynamic behavior of outbreaks on a regional level. Regional modeling, with relatively low numbers of infected and demographic noise, accounts for both spatial heterogeneity and stochasticity. Based on adapted models, short-term predictions can be achieved. Thus, with the help of these sequential data assimilation methods, more realistic epidemic models are within reach. Keywords Stochastic epidemic model · Sequential data assimilation · Ensemble Kalman filter · COVID-19
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11538020-00834-8) contains supplementary material, which is available to authorized users.
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Ralf Engbert [email protected] Maximilian M. Rabe [email protected] Reinhold Kliegl [email protected] Sebastian Reich [email protected]
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Department of Psychology, University of Potsdam, Potsdam, Germany
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Division of Training and Movement Sciences, University of Potsdam, Potsdam, Germany
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Institute of Mathematics, University of Potsdam, Potsdam, Germany 0123456789().: V,-vol
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1 Introduction The initial spread of the novel coronavirus in Germany (RKI 2020) resulted in containment measures based on reduced traveling and social distancing (Anderson et al. 2020). In epidemic standard models (Anderson et al. 1992; Kucharski et al. 2020), which provide a dynamical description of epidemic outbreaks (Bolker and Grenfell 1995; Schwartz and Smith 1983), 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, estimating the contact parameter is a key basis for epidemic modeling (Lourenço et al. 2020). From early on, the situation of COVID-19 has been characterized by extreme spatial heterogeneity (RKI 2020). In the initial phase of the outbreak, spatial heterogeneity was caused by random travel-based imports of infectious cases and enhanced by local events with increased contacts; after introduction o
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