Sequential Data Assimilation of the Stochastic SEIR Epidemic Model for Regional COVID-19 Dynamics

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.

Dynamics of epidemic spreading on connected graphs

“…The above equation ( 4.4 ) can be interpreted as the counter-part on graphs to equations that were already derived in a spatially continuous setting (Diekmann 1978 ; Berestycki et al. 2020 ). In our case, we can rewrite ( 4.4 ) as where and .…”

“…In a first approximation, we will assume that infected populations are only subject to spatial diffusion along the lines, as it is traditionally assumed in classical spatial SIR models (Aronson 1977 ; Diekmann 1978 ; Reluga 2004 ; Berestycki et al. 2020 ). As a consequence, in our model, the dynamics of the epidemic only takes place in the cities.…”

“…Our framework is at the crossroad of models that take into account lines of transportation such as recent reaction-diffusion models that study propagation of epidemics along lines with fast diffusion (Berestycki et al. 2020 ) and models that incorporate networks with more sophisticated interactions dynamics (Britton et al. 2008 ; Sahneh et al.…”

“…On a formal level, our proposed model can be thought of as being a one-dimensional version of the planar reaction-diffusion system of Berestycki et al. ( 2020 ) with a line of fast diffusion in the case of one city and one line of transportation. Actually, the graph structure of the transportation network provides a natural embedding into a planar spatial domain.…”

An Extended SEIR Model with Vaccination for Forecasting the COVID-19 Pandemic in Saudi Arabia Using an Ensemble Kalman Filter

“…In epidemiology, previous studies have used data assimilation in the context of both variational and Kalman filter methods [35][36][37][38]. The Reference [39] used the EnKF to estimate the parameters of a stochastic SEIR model. The Reference [40] applied a deterministic variant of the EnKF, the Ensemble Adjustment Kalman Filter (EAKF), in combination with a network of SEIR models, simulating different connected cities.…”