TY  - JOUR
A1  - Engbert, Ralf
A1  - Rabe, Maximilian Michael
A1  - Kliegl, Reinhold
A1  - Reich, Sebastian
T1  - Sequential data assimilation of the stochastic SEIR epidemic model for regional COVID-19 dynamics
JF  - Bulletin of mathematical biology : official journal of the Society for Mathematical Biology
N2  - 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.
KW  - Stochastic epidemic model
KW  - Sequential data assimilation
KW  - Ensemble Kalman
KW  - filter
KW  - COVID-19
Y1  - 2020
U6  - https://doi.org/10.1007/s11538-020-00834-8
SN  - 0092-8240
SN  - 1522-9602
VL  - 83
IS  - 1
PB  - Springer
CY  - New York
ER  - 
TY  - GEN
A1  - Wiljes, Jana de
A1  - Tong, Xin T.
T1  - Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For spatial-temporal models, the ensemble Kalman filter with proper localisation techniques is considered to be a state-of-the-art DA methodology. This article proposes and investigates a localised ensemble Kalman Bucy filter for nonlinear models with short-range interactions. We derive dimension-independent and component-wise error bounds and show the long time path-wise error only has logarithmic dependence on the time range. The theoretical results are verified through some simple numerical tests.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1221 
KW  - data assimilation
KW  - stability and accuracy
KW  - dimension independent bound
KW  - localisation
KW  - high dimensional
KW  - filter
KW  - nonlinear
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-540417
SN  - 1866-8372
VL  - 33
IS  - 9
SP  - 4752
EP  - 4782
PB  - IOP Publ.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Wiljes, Jana de
A1  - Tong, Xin T.
T1  - Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations
JF  - Nonlinearity
N2  - Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For spatial-temporal models, the ensemble Kalman filter with proper localisation techniques is considered to be a state-of-the-art DA methodology. This article proposes and investigates a localised ensemble Kalman Bucy filter for nonlinear models with short-range interactions. We derive dimension-independent and component-wise error bounds and show the long time path-wise error only has logarithmic dependence on the time range. The theoretical results are verified through some simple numerical tests.
KW  - data assimilation
KW  - stability and accuracy
KW  - dimension independent bound
KW  - localisation
KW  - high dimensional
KW  - filter
KW  - nonlinear
Y1  - 2020
U6  - https://doi.org/10.1088/1361-6544/ab8d14
SN  - 0951-7715
SN  - 1361-6544
VL  - 33
IS  - 9
SP  - 4752
EP  - 4782
PB  - IOP Publ.
CY  - Bristol
ER  -