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

Mathematics

Ibrahim Hoteit¹  Rabih Ghostine²  Sally Hassrouny³  Mohamad Gharamti⁴ 

[1] Applied Mathematics and Computational Science, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia;Department of Mathematics, Kuwait College of Science and Technology, Doha 35001, Kuwait;Department of Science, Kuwait College of Science and Technology, Doha 35001, Kuwait;National Center for Atmospheric Research, Boulder, CO 80305, USA;

关键词: COVID-19 pandemic;    SEIR model;    mathematical modeling;    ensemble Kalman filter;    joint state-parameters estimation;   

DOI  :  10.3390/math9060636

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown