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

In this paper, an extended SEIR model with a vaccination compartment is proposed to simulate the novel coronavirus disease (COVID-19) spread in Saudi Arabia. The model considers seven stages of infection: susceptible (S), exposed (E), infectious (I), quarantined (Q), recovered (R), deaths (D), and vaccinated (V). Initially, a mathematical analysis is carried out to illustrate the non-negativity, boundedness, epidemic equilibrium, existence, and uniqueness of the endemic equilibrium, and the basic reproduction number of the proposed model. Such numerical models can be, however, subject to various sources of uncertainties, due to an imperfect description of the biological processes governing the disease spread, which may strongly limit their forecasting skills. A data assimilation method, mainly, the ensemble Kalman filter (EnKF), is then used to constrain the model outputs and its parameters with available data. We conduct joint state-parameters estimation experiments assimilating daily data into the proposed model using the EnKF in order to enhance the model’s forecasting skills. Starting from the estimated set of model parameters, we then conduct short-term predictions in order to assess the predicability range of the model. We apply the proposed assimilation system on real data sets from Saudi Arabia. The numerical results demonstrate the capability of the proposed model in achieving accurate prediction of the epidemic development up to two-week time scales. Finally, we investigate the effect of vaccination on the spread of the pandemic.

[2]  P. Dormitzer,et al.  Safety and Efficacy of the BNT162b2 mRNA Covid-19 Vaccine , 2020, The New England journal of medicine.

[3]  Samuel Kortas,et al.  A fault-tolerant HPC scheduler extension for large and operational ensemble data assimilation: Application to the Red Sea , 2018, J. Comput. Sci..

[4]  I. Cooper,et al.  A SIR model assumption for the spread of COVID-19 in different communities , 2020, Chaos, Solitons & Fractals.

[5]  Ibrahim Hoteit,et al.  Assessing a robust ensemble-based Kalman filter for efficient ecosystem data assimilation of the Cretan Sea , 2013 .

[6]  J. Watmough,et al.  Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. , 2002, Mathematical biosciences.

[7]  Katriona Shea,et al.  The SEIRS model for infectious disease dynamics , 2020, Nature Methods.

[8]  Laurent Bertino,et al.  Insights on multivariate updates of physical and biogeochemical ocean variables using an Ensemble Kalman Filter and an idealized model of upwelling , 2018, Ocean Modelling.

[9]  Jorn Lothar Sesterhenn,et al.  Adjoint-based Data Assimilation of an Epidemiology Model for the Covid-19 Pandemic in 2020 , 2020, ArXiv.

[10]  Ibrahim Hoteit,et al.  Regional ocean data assimilation. , 2015, Annual review of marine science.

[11]  Olwijn Leeuwenburgh,et al.  Forecasting hospitalization and ICU rates of the COVID-19 outbreak: an efficient SEIR model , 2020 .

[12]  Maia Martcheva,et al.  An Introduction to Mathematical Epidemiology , 2015 .

[13]  Ibrahim Hoteit,et al.  Calibrating land hydrological models and enhancing their forecasting skills using an ensemble Kalman filter with one-step-ahead smoothing , 2020 .

[14]  Jaline Gerardin,et al.  Identifying the measurements required to estimate rates of COVID-19 transmission, infection, and detection, using variational data assimilation , 2020, Infectious Disease Modelling.

[15]  I. Hoteit,et al.  A two-update ensemble Kalman filter for land hydrological data assimilation with an uncertain constraint. , 2017 .

[16]  I. Hoteit,et al.  Enhanced flood forecasting through ensemble data assimilation and joint state-parameter estimation , 2019, Journal of Hydrology.

[17]  Ceyhun Eksin,et al.  Systematic biases in disease forecasting - The role of behavior change. , 2019, Epidemics.

[18]  Punit Sharma,et al.  Using Data Assimilation Technique and Epidemic Model to Predict TB Epidemic , 2015 .

[19]  Dinh-Tuan Pham,et al.  A simplified reduced order Kalman filtering and application to altimetric data assimilation in Tropical Pacific , 2002 .

[20]  Ruiyun Li,et al.  Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV-2) , 2020, Science.

[21]  Peter M. Atkinson,et al.  Flood inundation model updating using an ensemble Kalman filter and spatially distributed measurements , 2007 .

[22]  Tim Lant,et al.  Towards Real Time Epidemiology: Data Assimilation, Modeling and Anomaly Detection of Health Surveillance Data Streams , 2007, BioSurveillance.

[23]  Michael Ghil,et al.  Meteorological data assimilation for oceanographers. Part I: Description and theoretical framework☆ , 1989 .

[24]  Ibrahim Hoteit,et al.  Combining Hybrid and One-Step-Ahead Smoothing for Efficient Short-Range Storm Surge Forecasting with an Ensemble Kalman Filter , 2019, Monthly Weather Review.

[25]  Ibrahim Hoteit,et al.  An iterative ensemble Kalman filter with one-step-ahead smoothing for state-parameters estimation of contaminant transport models , 2015 .

[26]  T D Hollingsworth,et al.  Variational data assimilation with epidemic models. , 2009, Journal of theoretical biology.

[27]  Geir Evensen,et al.  The Ensemble Kalman Filter: theoretical formulation and practical implementation , 2003 .

[28]  M. Trawicki Deterministic Seirs Epidemic Model for Modeling Vital Dynamics, Vaccinations, and Temporary Immunity , 2017 .

[29]  S. Reich,et al.  Sequential Data Assimilation of the Stochastic SEIR Epidemic Model for Regional COVID-19 Dynamics , 2020, Bulletin of mathematical biology.

[30]  Mark Buehner,et al.  An Ensemble Kalman Filter for Numerical Weather Prediction Based on Variational Data Assimilation: VarEnKF , 2017 .

[31]  C. Scoglio,et al.  Short-term forecasts and long-term mitigation evaluations for the COVID-19 epidemic in Hubei Province, China , 2020, Infectious Disease Modelling.

[32]  Ibrahim Hoteit,et al.  A Comparison of Ensemble Kalman Filters for Storm Surge Assimilation , 2014 .

[33]  N. Kimura,et al.  A river flash flood forecasting model coupled with ensemble Kalman filter , 2016 .

[34]  Patrick Heimbach,et al.  A MITgcm/DART ensemble analysis and prediction system with application to the Gulf of Mexico , 2013 .

[35]  Isaac Chun-Hai Fung,et al.  Cholera transmission dynamic models for public health practitioners , 2014, Emerging Themes in Epidemiology.

[36]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[37]  C. K. R. T. Jones,et al.  An international assessment of the COVID-19 pandemic using ensemble data assimilation , 2020, medRxiv.

[38]  William R. Holland,et al.  Assimilation of Altimeter Data into an Ocean Circulation Model: Space versus Time Resolution Studies , 1989 .

[39]  M. Bentsen,et al.  Ensemble data assimilation for ocean biogeochemical state and parameter estimation at different sites , 2017 .

[40]  D. McLaughlin,et al.  Hydrologic Data Assimilation with the Ensemble Kalman Filter , 2002 .

[41]  Devendra Kumar,et al.  An Efficient Numerical Method for Fractional SIR Epidemic Model of Infectious Disease by Using Bernstein Wavelets , 2020, Mathematics.

[42]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .

[43]  Ibrahim Hoteit,et al.  Constraining a compositional flow model with flow‐chemical data using an ensemble‐based Kalman filter , 2014 .

[44]  Delfim F. M. Torres,et al.  Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan , 2020, Chaos, Solitons & Fractals.

[45]  Ibrahim Hoteit,et al.  A Bayesian Consistent Dual Ensemble Kalman Filter for State-Parameter Estimation in Subsurface Hydrology , 2015, 1511.02178.

[46]  O. Diekmann,et al.  On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations , 1990, Journal of mathematical biology.

[47]  Günter Bärwolff,et al.  Mathematical Modeling and Simulation of the COVID-19 Pandemic , 2020, Syst..

[48]  C. Hameni Nkwayep,et al.  Short-term forecasts of the COVID-19 pandemic: a study case of Cameroon , 2020, Chaos, Solitons & Fractals.