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

Author

Listed:
  • Rabih Ghostine

    (Department of Mathematics, Kuwait College of Science and Technology, Doha 35001, Kuwait)

  • Mohamad Gharamti

    (National Center for Atmospheric Research, Boulder, CO 80305, USA)

  • Sally Hassrouny

    (Department of Science, Kuwait College of Science and Technology, Doha 35001, Kuwait)

  • Ibrahim Hoteit

    (Applied Mathematics and Computational Science, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia)

Abstract

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.

Suggested Citation

  • Rabih Ghostine & Mohamad Gharamti & Sally Hassrouny & Ibrahim Hoteit, 2021. "An Extended SEIR Model with Vaccination for Forecasting the COVID-19 Pandemic in Saudi Arabia Using an Ensemble Kalman Filter," Mathematics, MDPI, vol. 9(6), pages 1-16, March.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:636-:d:518689
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    References listed on IDEAS

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    1. Cooper, Ian & Mondal, Argha & Antonopoulos, Chris G., 2020. "A SIR model assumption for the spread of COVID-19 in different communities," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Sarkar, Kankan & Khajanchi, Subhas & Nieto, Juan J., 2020. "Modeling and forecasting the COVID-19 pandemic in India," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Ndaïrou, Faïçal & Area, Iván & Nieto, Juan J. & Torres, Delfim F.M., 2020. "Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    4. Nkwayep, C. Hameni & Bowong, S. & Tewa, J.J. & Kurths, J., 2020. "Short-term forecasts of the COVID-19 pandemic: a study case of Cameroon," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
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    Cited by:

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    2. Svetozar Margenov & Nedyu Popivanov & Iva Ugrinova & Tsvetan Hristov, 2022. "Mathematical Modeling and Short-Term Forecasting of the COVID-19 Epidemic in Bulgaria: SEIRS Model with Vaccination," Mathematics, MDPI, vol. 10(15), pages 1-28, July.
    3. Xuan Leng & Asad Khan & Anwarud Din, 2023. "Probability Analysis of a Stochastic Non-Autonomous SIQRC Model with Inference," Mathematics, MDPI, vol. 11(8), pages 1-18, April.

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