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Article

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

1
Department of Mathematics, Kuwait College of Science and Technology, Doha 35001, Kuwait
2
National Center for Atmospheric Research, Boulder, CO 80305, USA
3
Department of Science, Kuwait College of Science and Technology, Doha 35001, Kuwait
4
Applied Mathematics and Computational Science, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia
*
Author to whom correspondence should be addressed.
Academic Editor: J. Alberto Conejero
Mathematics 2021, 9(6), 636; https://doi.org/10.3390/math9060636
Received: 29 January 2021 / Revised: 24 February 2021 / Accepted: 25 February 2021 / Published: 17 March 2021
(This article belongs to the Special Issue Mathematical and Computational Methods against the COVID-19 Pandemics)
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. View Full-Text
Keywords: COVID-19 pandemic; SEIR model; mathematical modeling; ensemble Kalman filter; joint state-parameters estimation COVID-19 pandemic; SEIR model; mathematical modeling; ensemble Kalman filter; joint state-parameters estimation
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MDPI and ACS Style

Ghostine, R.; Gharamti, M.; Hassrouny, S.; Hoteit, I. An Extended SEIR Model with Vaccination for Forecasting the COVID-19 Pandemic in Saudi Arabia Using an Ensemble Kalman Filter. Mathematics 2021, 9, 636. https://doi.org/10.3390/math9060636

AMA Style

Ghostine R, Gharamti M, Hassrouny S, Hoteit I. An Extended SEIR Model with Vaccination for Forecasting the COVID-19 Pandemic in Saudi Arabia Using an Ensemble Kalman Filter. Mathematics. 2021; 9(6):636. https://doi.org/10.3390/math9060636

Chicago/Turabian Style

Ghostine, Rabih, Mohamad Gharamti, Sally Hassrouny, and Ibrahim Hoteit. 2021. "An Extended SEIR Model with Vaccination for Forecasting the COVID-19 Pandemic in Saudi Arabia Using an Ensemble Kalman Filter" Mathematics 9, no. 6: 636. https://doi.org/10.3390/math9060636

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