In this paper, we present an application of optimal control theory on a two-dimensional spatial-temporal SEIR (susceptible, exposed, infected, and restored) epidemic model, in the form of a partial differential equation. Our goal is to minimize the number of susceptible and infected individuals and to maximize recovered individuals by reducing the cost of vaccination. In addition, the existence of the optimal control and solution of the state system is proven. The characterization of the control is given in terms of state function and adjoint. Numerical results are provided to illustrate the effectiveness of our adopted approach.
In this work, we are interested in studying a spatiotemporal two-dimensional SIR epidemic model, in the form of a system of partial differential equations (PDE). A distribution of a vaccine in the form of a control variable is considered to force immunity. The purpose is to characterize a control that minimizes the number of susceptible, infected individuals and the costs associated with vaccination over a nite space and time domain. In addition, the existence of the solution of the state system and the optimal control is proved. The characterization of the control is given in terms of state function and adjoint function. The numerical resolution of the state system shows the effectiveness of our control strategy.
In this paper, we proposed and analyzed a non-linear mathematical model for scholar Drop out and we advanced an optimal control policy for this model by considering three variables namely the numbers of school-age children who are in school, school-age children who are out of school, and school-age children in non-formal education. The model is examined using the stability theory of differential equations. The optimal control analysis for the proposed scholar Drop out model is performed using Pontryagin's maximum principle. The conditions for optimal control of the problem with effective use of implemented policies to counter this scourge are derived and analyzed.
Dans ce travail, on présente une méthode de décomposition de domaine pour résoudre les équations de Navier Stokes. Deux applications sont présentées pour illustrer ses avantages: la première concerne le jet par le fond dans un canal à surface libre et la seconde est celle du soutirage latéral. Ces deux applications concernent la problématique de la création de la circulation artificielle des masses d'eau en vue d'homogénéiser les paramètres physique du milieu. Dans l'application de la méthode de décomposition, le domaine d'étude est décomposé en sous domaines en vue de mieux prendre en compte des processus physiques et les méthodes numériques adaptés à leurs applications. Deux méthodes numériques sont utilisées, une méthode des différences finies près de la paroi et une méthode particulaire dans les zones de forte circulation. Dans les interfaces des sous domaines, on utilise des conditions de couplage par la méthode Particule-Maillage.
How to cite this paper: MORDANE S., ADNAOUI K., LOUKILI M., TOUNSI N., CHAGDALI M. (2016). Abstract:In this work, we present The method of decomposition domain to solve the NavierStokes equations. Two applications are presented to illustrate the advantages of the method: the first concerns the jet emitted from the bottom in an open channel and the second deals with the lateral racking problem. These two applications concern the problem of creating artificial circulation of the water masses in order to homogenize the physical parameters of the medium. In applying the decomposition method, the field of studies is broken down into sub areas to take better account of the physical processes and the numerical methods suited to their applications. Two numerical methods are used, a finite difference near the wall and a particle method in high traffic areas. In the interfaces of sub-domains, using coupling conditions by the particle-mesh method.
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