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

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 636
Author(s):  
Rabih Ghostine ◽  
Mohamad Gharamti ◽  
Sally Hassrouny ◽  
Ibrahim Hoteit
Keyword(s):  
Saudi Arabia ◽  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Numerical Models ◽  
Parameters Estimation ◽  
Disease Spread ◽  
Model Parameters ◽  
Equilibrium Existence ◽  
Seir Model ◽  
Proposed Model

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.

scholarly journals Research and application of parameter estimation method in hydrological model based on dual ensemble Kalman filter

2021 ◽  
Author(s):  
Mengtian Lu ◽  
Sicheng Lu ◽  
Weihong Liao ◽  
Xiaohui Lei ◽  
Zhaokai Yin ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Assimilation Efficiency ◽  
Estimation Method ◽  
Initial Distribution ◽  
Parameters Estimation ◽  
Model Parameters ◽  
Multiple Parameters ◽  
Basin Surface

Abstract Although field measurements and using long hydrological datasets provide a reliable method for parameters' calibration, changes in the underlying basin surface and lack of hydrometeorological data may affect parameter accuracy in streamflow simulation. The ensemble Kalman filter (EnKF) can be used as a real-time parameter correction method to solve this problem. In this study, five representative Xin'anjiang model parameters are selected to study the effects of the initial parameter ensemble distribution and the specific function form of the parameter on EnKF parameter estimation process for both single and multiple parameters. Results indicate: (1) the method of parameter calibration to determine the initial distribution mean can improve the assimilation efficiency; (2) there is mutual interference among the parameters during multiple parameters' estimation which invalidates some conclusions of single-parameter estimation. We applied and evaluated the EnKF method in Jinjiang River Basin, China. Compared to traditional approaches, our method showed a better performance in both basins with long hydrometeorological dataset (an increase of Kling–Gupta efficiency (KGE) from 0.810 to 0.887 and a decrease of bias from −1.08% to −0.74%); and in basins with a lack of hydrometeorological data (an increase of KGE from 0.536 to 0.849 and a decrease of bias from −15.55% to −11.42%).

scholarly journals Assimilation of Dynamic Combined Finite Discrete Element Methods Using the Ensemble Kalman Filter

2021 ◽  
Vol 11 (7) ◽  
pp. 2898
Author(s):  
Humberto C. Godinez ◽  
Esteban Rougier
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Failure Modes ◽  
Split Hopkinson Pressure Bar ◽  
Peak Stress ◽  
Discrete Element ◽  
Material Behavior ◽  
Model Parameters ◽  
Hopkinson Pressure Bar ◽  
Parameter Values

Simulation of fracture initiation, propagation, and arrest is a problem of interest for many applications in the scientific community. There are a number of numerical methods used for this purpose, and among the most widely accepted is the combined finite-discrete element method (FDEM). To model fracture with FDEM, material behavior is described by specifying a combination of elastic properties, strengths (in the normal and tangential directions), and energy dissipated in failure modes I and II, which are modeled by incorporating a parameterized softening curve defining a post-peak stress-displacement relationship unique to each material. In this work, we implement a data assimilation method to estimate key model parameter values with the objective of improving the calibration processes for FDEM fracture simulations. Specifically, we implement the ensemble Kalman filter assimilation method to the Hybrid Optimization Software Suite (HOSS), a FDEM-based code which was developed for the simulation of fracture and fragmentation behavior. We present a set of assimilation experiments to match the numerical results obtained for a Split Hopkinson Pressure Bar (SHPB) model with experimental observations for granite. We achieved this by calibrating a subset of model parameters. The results show a steady convergence of the assimilated parameter values towards observed time/stress curves from the SHPB observations. In particular, both tensile and shear strengths seem to be converging faster than the other parameters considered.

scholarly journals Modifying the network-based stochastic SEIR model to account for quarantine: an application to COVID-19

2021 ◽  
Vol 10 (s1) ◽  
Author(s):  
Chris Groendyke ◽  
Adam Combs
Keyword(s):  
Network Model ◽  
Transmission Rate ◽  
Disease Spread ◽  
Contact Network ◽  
Model Parameters ◽  
Seir Model ◽  
Disease States ◽  
Potential Contact ◽  
The Mean ◽  
Infectious State

Abstract Objectives: Diseases such as SARS-CoV-2 have novel features that require modifications to the standard network-based stochastic SEIR model. In particular, we introduce modifications to this model to account for the potential changes in behavior patterns of individuals upon becoming symptomatic, as well as the tendency of a substantial proportion of those infected to remain asymptomatic. Methods: Using a generic network model where every potential contact exists with the same common probability, we conduct a simulation study in which we vary four key model parameters (transmission rate, probability of remaining asymptomatic, and the mean lengths of time spent in the exposed and infectious disease states) and examine the resulting impacts on various metrics of epidemic severity, including the effective reproduction number. We then consider the effects of a more complex network model. Results: We find that the mean length of time spent in the infectious state and the transmission rate are the most important model parameters, while the mean length of time spent in the exposed state and the probability of remaining asymptomatic are less important. We also find that the network structure has a significant impact on the dynamics of the disease spread. Conclusions: In this article, we present a modification to the network-based stochastic SEIR epidemic model which allows for modifications to the underlying contact network to account for the effects of quarantine. We also discuss the changes needed to the model to incorporate situations where some proportion of the individuals who are infected remain asymptomatic throughout the course of the disease.

scholarly journals Parameters Estimation and Prediction of Water Movement and Solute Transport in Layered, Variably Saturated Soils Using the Ensemble Kalman Filter

Water ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 1520
Author(s):  
Zheng Jiang ◽  
Quanzhong Huang ◽  
Gendong Li ◽  
Guangyong Li
Keyword(s):  
Kalman Filter ◽  
Solute Transport ◽  
Ensemble Kalman Filter ◽  
Water Movement ◽  
Parameters Estimation ◽  
Saturated Soils ◽  
Hydrological Models ◽  
State Variables ◽  
Ensemble Size ◽  
Highly Nonlinear

The parameters of water movement and solute transport models are essential for the accurate simulation of soil moisture and salinity, particularly for layered soils in field conditions. Parameter estimation can be achieved using the inverse modeling method. However, this type of method cannot fully consider the uncertainties of measurements, boundary conditions, and parameters, resulting in inaccurate estimations of parameters and predictions of state variables. The ensemble Kalman filter (EnKF) is well-suited to data assimilation and parameter prediction in Situations with large numbers of variables and uncertainties. Thus, in this study, the EnKF was used to estimate the parameters of water movement and solute transport in layered, variably saturated soils. Our results indicate that when used in conjunction with the HYDRUS-1D software (University of California Riverside, California, CA, USA) the EnKF effectively estimates parameters and predicts state variables for layered, variably saturated soils. The assimilation of factors such as the initial perturbation and ensemble size significantly affected in the simulated results. A proposed ensemble size range of 50–100 was used when applying the EnKF to the highly nonlinear hydrological models of the present study. Although the simulation results for moisture did not exhibit substantial improvement with the assimilation, the simulation of the salinity was significantly improved through the assimilation of the salinity and relative solutetransport parameters. Reducing the uncertainties in measured data can improve the goodness-of-fit in the application of the EnKF method. Sparse field condition observation data also benefited from the accurate measurement of state variables in the case of EnKF assimilation. However, the application of the EnKF algorithm for layered, variably saturated soils with hydrological models requires further study, because it is a challenging and highly nonlinear problem.

scholarly journals Modeling the impact of drought on canopy carbon and water fluxes through parameter optimization using an ensemble Kalman filter

2009 ◽  
Vol 6 (4) ◽  
pp. 8279-8309 ◽  
Author(s):  
W. Ju ◽  
S. Wang ◽  
G. Yu ◽  
Y. Zhou ◽  
H. Wang
Keyword(s):  
Kalman Filter ◽  
Parameter Optimization ◽  
Ensemble Kalman Filter ◽  
Terrestrial Ecosystems ◽  
Model Parameters ◽  
Interannual Variations ◽  
Atmospheric Water ◽  
Model Parameterization ◽  
Coniferous Plantation ◽  
The Impact

Abstract. Soil and atmospheric water deficits have significant influences on CO2 and energy exchanges between the atmosphere and terrestrial ecosystems. Model parameterization significantly affects the ability of a model to simulate carbon, water, and energy fluxes. In this study, an ensemble Kalman filter (EnKF) and observations of gross primary productivity (GPP) and latent heat (LE) fluxes were used to optimize model parameters significantly affecting the calculation of these fluxes for a subtropical coniferous plantation in southeastern China. The optimized parameters include the maximum carboxylation rate (Vcmax), the Ball-Berry coefficient (m) and the coefficient determining the sensitivity of stomatal conductance to atmospheric water vapor deficit D0). Optimized Vcmax and m showed larger seasonal and interannual variations than D0. Seasonal variations of Vcmax and m are more pronounced than the interannual variations. Vcmax and m are associated with soil water content (SWC). During dry periods, SWC at the 20 cm depth can explain 61% and 64% of variations of Vcmax and m, respectively. EnKF parameter optimization improves the simulations of GPP, LE and sensible heat (SH), mainly during dry periods. After parameter optimization using EnKF, the variations of GPP, LE and SH explained by the model increased by 1% to 4% at half-hourly steps and by 3% to 5% at daily time steps. Efforts are needed to develop algorithms that can properly describe the variations of these parameters under different environmental conditions.

scholarly journals Identification of hydrological model parameter variation using ensemble Kalman filter

2016 ◽  
Vol 20 (12) ◽  
pp. 4949-4961 ◽  
Author(s):  
Chao Deng ◽  
Pan Liu ◽  
Shenglian Guo ◽  
Zejun Li ◽  
Dingbao Wang
Keyword(s):  
Kalman Filter ◽  
Temporal Variation ◽  
Ensemble Kalman Filter ◽  
Water Conservation ◽  
Hydrological Model ◽  
Anthropogenic Activities ◽  
Temporal Variations ◽  
Balance Model ◽  
Model Parameters ◽  
Water Storage Capacity

Abstract. Hydrological model parameters play an important role in the ability of model prediction. In a stationary context, parameters of hydrological models are treated as constants; however, model parameters may vary with time under climate change and anthropogenic activities. The technique of ensemble Kalman filter (EnKF) is proposed to identify the temporal variation of parameters for a two-parameter monthly water balance model (TWBM) by assimilating the runoff observations. Through a synthetic experiment, the proposed method is evaluated with time-invariant (i.e., constant) parameters and different types of parameter variations, including trend, abrupt change and periodicity. Various levels of observation uncertainty are designed to examine the performance of the EnKF. The results show that the EnKF can successfully capture the temporal variations of the model parameters. The application to the Wudinghe basin shows that the water storage capacity (SC) of the TWBM model has an apparent increasing trend during the period from 1958 to 2000. The identified temporal variation of SC is explained by land use and land cover changes due to soil and water conservation measures. In contrast, the application to the Tongtianhe basin shows that the estimated SC has no significant variation during the simulation period of 1982–2013, corresponding to the relatively stationary catchment properties. The evapotranspiration parameter (C) has temporal variations while no obvious change patterns exist. The proposed method provides an effective tool for quantifying the temporal variations of the model parameters, thereby improving the accuracy and reliability of model simulations and forecasts.

Data Assimilation of Coupled Fluid Flow and Geomechanics Using the Ensemble Kalman Filter

SPE Journal ◽  
2010 ◽  
Vol 15 (02) ◽  
pp. 382-394 ◽  
Author(s):  
Haibin Chang ◽  
Yan Chen ◽  
Dongxiao Zhang
Keyword(s):  
Fluid Flow ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Material Properties ◽  
Ensemble Kalman Filter ◽  
Oil Field ◽  
Reservoir Rock ◽  
Model Parameters ◽  
Stress Strain ◽  
Reservoir Flow

Summary In reservoir history matching or data assimilation, dynamic data, such as production rates and pressures, are used to constrain reservoir models and to update model parameters. As such, even if under certain conceptualization the model parameters do not vary with time, the estimate of such parameters may change with the available observations and, thus, with time. In reality, the production process may lead to changes in both the flow and geomechanics fields, which are dynamically coupled. For example, the variations in the stress/strain field lead to changes in porosity and permeability of the reservoir and, hence, in the flow field. In weak formations, such as the Lost Hills oil field, fluid extraction may cause a large compaction to the reservoir rock and a significant subsidence at the land surface, resulting in huge economic losses and detrimental environmental consequences. The strong nonlinear coupling between reservoir flow and geomechanics poses a challenge to constructing a reliable model for predicting oil recovery in such reservoirs. On the other hand, the subsidence and other geomechanics observations can provide additional insight into the nature of the reservoir rock and help constrain the reservoir model if used wisely. In this study, the ensemble-Kalman-filter (EnKF) approach is used to estimate reservoir flow and material properties by jointly assimilating dynamic flow and geomechanics observations. The resulting model can be used for managing and optimizing production operations and for mitigating the land subsidence. The use of surface displacement observations improves the match to both production and displacement data. Localization is used to facilitate the assimilation of a large amount of data and to mitigate the effect of spurious correlations resulting from small ensembles. Because the stress, strain, and displacement fields are updated together with the material properties in the EnKF, the issue of consistency at the analysis step of the EnKF is investigated. A 3D problem with reservoir fluid-flow and mechanical parameters close to those of the Lost Hills oil field is used to test the applicability.

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