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.
SUMMARYThe present work addresses the numerical prediction of discontinuous shallow water flows by the application of a second-order Runge-Kutta discontinuous Galerkin scheme (RKDG2). The unsteady flow of water in a one-dimensional approach is described by the Saint Venant's model which incorporates source terms in practical applications. Therefore, the RKDG2 scheme is reformulated with a simple way to integrate source terms. Further, an adequate boundary conditions handling, by the theory of characteristics, was overviewed to be adapted to the external points of the mesh, as well as to some points of local invalidity of the Saint Venant's model. To validate the proposed technique, steady and transient test problems (all having a reference solution) were considered and computed by means of the overall method. The results were illustrated jointly with the reference solution and the results carried out by a traditional second-order finite volume (FV2) scheme implemented with the same techniques as the RKDG2. The proposed method has proven its practical consideration when solving discontinuous shallow water flow involving: non-prismatic channels, various cross-sections, smoothly varying bed topography and internal boundary conditions.
International audienceIn this study, a comparison between the 1D and 2D numerical simulation of transitional flow in open-channel networks is presented and completely described allowing for a full comprehension of the modeling water flow. For flow in an open-channel network, mutual effects exist among the channel branches joining at a junction. Therefore, for the 1D study, the whole system (branches and junction) cannot be treated individually. The 1D Saint Venant equations calculating the flow in the branches are then supplemented by various equations used at the junction: a discharge flow conservation equation between the branches arriving and leaving the junction, and a momentum or energy conservation equation. The disadvantages of the 1D study are that the equations used at the junction are of empirical nature due to certain parameters given by experimental results and moreover they often present a reduced field of validity. On the contrary, for the 2D study, the entire network is considered as a single unit and the flow in all the branches and junctions is solved simultaneously. Therefore, we simply apply the 2D Saint Venant equations, which are solved by a second-order Runge-Kutta discontinuous Galerkin method. Finally, the experimental results obtained by Hager are used to validate and to compare the two approaches 1D and 2D
Accurate water level forecasts during flood events are crucial to mitigate the loss of human lives and economic damages. However, the accuracy of flood models can be affected by various factors, including the complexity of the terrain geometry and bathymetry, imperfect physics as well as uncertainties in the inflows and parameters. This paper describes a practical implementation of an ensemble Kalman filter (EnKF) based data assimilation system that is aimed towards enhancing the forecasting skill of flood models.
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