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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.

In this paper, a mathematical model was developed to simulate SARS-CoV-2 dynamics in infected patients. The model considers both the innate and adaptive immune responses and consists of healthy cells, infected cells, viral load, cytokines, natural killer cells, cytotoxic T-lymphocytes, B-lymphocytes, plasma cells, and antibody levels. First, a mathematical analysis was performed to discuss the model’s equilibrium points and compute the basic reproduction number. The accuracy of such mathematical models may be affected by many sources of uncertainties due to the incomplete representation of the biological process and poorly known parameters. This may strongly limit their performance and prediction skills. A state-of-the-art data assimilation technique, the ensemble Kalman filter (EnKF), was then used to enhance the model’s behavior by incorporating available data to determine the best possible estimate of the model’s state and parameters. The proposed assimilation system was applied on the real viral load datasets of six COVID-19 patients. The results demonstrate the efficiency of the proposed assimilation system in improving the model predictions by up to 40%.

The joint state and parameter estimation problem is an important issue in data assimilation. An adjoint free data assimilation method, namely analytical four-dimensional ensemble variational (A-4DEnVar) data assimilation method, was developed to provide a solution for the joint estimation problem. In the algorithm, to estimate the adjoint model reasonably, the ensemble initial conditions and parameters are generated by Gaussian noise whose covariance is constructed by multiplying a very small factor by their background error covariance. The ensemble perturbations are calculated with respect to background states rather than the ensemble mean. Next, the usage of temporal cross covariances makes it possible to avoid the adjoint model and estimate the gradient in 4DVar. Furthermore, we update the solution iteratively with a linear search process to improve the stability and ensure the convergence of the algorithm. The method is tested using the three-variable Lorenz model (Lorenz-1963) to illustrate its efficiency. It is shown that A-4DEnVar results in similar performance with 4DVar. Sensitivity experiments show that A-4DEnVar is able to assimilate observations successfully with different settings. The proposed method is able to work as well as 4DVar and avoid adjoint models for the joint state and parameter estimation.

In this chapter, we develop a fundamental suite of parametrically adaptive processors that form an approach to the model‐based identification problem. They can be thought of as approximations to the optimal solutions based on the prediction error formulation. The approach we take is to introduce the concepts, point out some of the crucial steps in their development, and present the algorithms in tabular form. Here we develop the parametrically adaptive approach from the Bayesian, rather than optimization‐based (prediction error) perspective. Even though the algorithms are developed in order to comprehend their operation, their implementation is quite simple – merely “augment” the state vector with the unknown parameter vector! Besides the nonlinear processors that evolve, we develop the purely Bayesian approach actually solving the joint estimation problem using the particle filter. Finally, we discuss the recursive prediction error approach constrained to the linear, time‐invariant, state‐space model – the innovations representation. This approach will provide some insight as an alternative to the subspace identification techniques.

Summary This study performs an experimental investigation of a novel, semi‐active control strategy for effective vibration mitigation. The implemented approach comprises a combination of the linear quadratic regulator with a nonlinear observer, namely, the unscented Kalman filter, for the control of systems described by uncertainties. Indeed, numerical models of structural systems often result as inadequate because of inherent uncertainties, such as noise, modeling errors, unknown system properties, or influence of varying operational and environmental conditions. In tackling this issue, the unscented Kalman filter is herein employed for adaptive joint state and parameter estimation refining the accuracy of the model employed by the controller and resulting in enhanced vibration mitigation. A scaled five‐story shear frame attached to a hydraulic cylinder comprises the tested structure, where actuation is provided by means of a rotational magnetorheological damper operating on the relative motion between the ground floor and the first floor plate. The experimentally obtained results demonstrate a good agreement with simulations and encourage further implementation of the proposed framework in field applications of structural control. Copyright © 2016 John Wiley & Sons, Ltd.

Mathematical model-based analysis and control of human immunodeficiency virus (HIV) infection have recently provided important advantages in medicine. In this paper, firstly the literature on mathematical models and applied control methods will be surveyed to evaluate the HIV models and therapy. Secondly, a cubature Kalman filter-based nonlinear model predictive control is proposed for the multi-input multi-output control of HIV infection for decreasing the cost of sensory devices and increasing the efficiency of therapy. By doing so both unmeasurable states and personalized parameters of the HIV infection are jointly estimated in a control process to generate suitable drug dosages. In the literature, the applied drug dosages are in continuous or on/off levels. For a practical application of continuous drug dosage-level, it has been discretized into 10 levels of full dosage level. Therefore, the applied drug dosages are in piecewise-continuous levels instead of continuous values or on/off levels. The proposed observer–controller configuration has been applied to the strong and moderate therapy levels of long-term non-progressive as well as fast-progressive patients with personalized parameters, where the application results are discussed for 1-, 5-, 10- and 20-year periods. The computational results show that satisfactory performances are obtained for future applications in terms of the root-mean-squared error of the estimation and control, and in terms of the integral sum of the control input.

Aimed at joint state and parameter estimation problems in hypersonic glide vehicle defense, a novel moving horizon estimation algorithm via Carleman linearization is developed in this paper. First, the maneuver characteristic parameters that reflect the target maneuver law are extended into the state vector, and a dynamic tracking model applicable to various hypersonic glide vehicles is constructed. To improve the estimation accuracy, constraints such as path and parameter change amplitude constraints in flight are taken into account, and the estimation problem is transformed into a nonlinear constrained optimal estimation problem. Then, to solve the problem of high time cost for solving a nonlinear constrained optimal estimation problem, in the framework of moving horizon estimation, nonlinear constrained optimization problems are transformed into bilinear constrained optimization problems by linearizing the nonlinear system via Carleman linearization. For ensuring the consistency of the linearized system with the original nonlinear system, the linearized model is continuously updated as the window slides forward. Moreover, a CKF-based arrival cost update algorithm is also provided to improve the estimation accuracy. Simulation results demonstrate that the proposed joint state and parameter estimation algorithm greatly improves the estimation accuracy while reducing the time cost significantly.

We consider the problem of joint estimation of states and some constant parameters for a class of nonlinear discrete-time systems. This class contains systems that could be transformed into a quasi-LPV (linear parameter varying) polytopic model in the Takagi-Sugeno (T-S) form. Such systems could have unmeasured premise variables, a case usually overlooked in the observer design literature. We assert that, for such systems in discrete-time, the current literature lacks design strategies for joint state and parameter estimation. To this end, we adapt the existing literature on continuous-time linear systems for joint state and time-varying parameter estimation. We first develop the discrete-time version of this result for linear systems. A Lyapunov approach is used to illustrate stability, and bounds for the estimation error are obtained via the bounded real lemma. We use this result to achieve our objective for a design procedure for a class of nonlinear systems with constant parameters. This results in less conservative conditions and a simplified design procedure. A basic waste water treatment plant simulation example is discussed to illustrate the design procedure.

The individual risks faced by banks, insurers, and marketers are less well understood than aggregate risks such as market-price changes. But the risks incurred or carried by individual people, companies, insurance policies, or credit agreements can be just as devastating as macroevents such as share-price fluctuations. A comprehensive introduction,The Econometrics of Individual Riskis the first book to provide a complete econometric methodology for quantifying and managing this underappreciated but important variety of risk. The book presents a course in the econometric theory of individual risk illustrated by empirical examples. And, unlike other texts, it is focused entirely on solving the actual individual risk problems businesses confront today. Christian Gourieroux and Joann Jasiak emphasize the microeconometric aspect of risk analysis by extensively discussing practical problems such as retail credit scoring, credit card transaction dynamics, and profit maximization in promotional mailing. They address regulatory issues in sections on computing the minimum capital reserve for coverage of potential losses, and on the credit-risk measure CreditVar. The book will interest graduate students in economics, business, finance, and actuarial studies, as well as actuaries and financial analysts.