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Prof. Nasser H. Sweilam
Cairo University, Egypt
Numerical Studies for the Multi-Strain Tuberculosis Model
In this talk, numerical studies for the multi-strain Tuberculosis (TB) model, that incorporates three strains, i.e., drug-sensitive, emerging multi-drug resistant (MDR) and extensively drug-resistant (XDR), which developed by J. Arino and I. soliman (2014), are introduced. The adopted model is described by a system of nonlinear ordinary differential equations(ODEs). Special class of numerical methods, known as nonstandard finite difference method (NSFDM) is introduced. The obtained results of using NSFDM are compared with other known numerical methods such as implicit Euler method and fourth-order Runge-Kutta (RK4) method. Also, the fractional order multi-strain TB model (FOTBM) as a novelmodel is presented . The fractional derivative is defined in the sense of Grünwald-Letinkovdefinition. Two numerical methods are presented to study this model, the standard finite difference method (SFDM) and NSFDM. The stability of equilibrium points is studied. As anextension of FOTBM, the variable-order fractional multi-strain TB model (VOFTBM) is presented. The variable-order fractional derivative is defined in this sense of Grünwald-Letinkov definition. Two numerical methods are presented for this model, SFDM and NSFDM. The stability of equilibrium points is studied. Finally, The optimal control for multi strain TB model is presented. TB control problem is formulated and studied theoretically using the Pontryagin maximum principle. Different optimal control strategies are proposed to minimize the cost of interventions.
Nasser Sweilam bornin August 21, 1959, Suez, Egypt. He graduated from Mathematics Department, Faculty of Science, Cairo University, Egypt; B. Sc. 1981, and M. Sc., 1988. He was a DAAD-channel system Ph.D. student between Cairo University, Egypt, and TU-Munich, Germany. He received his Ph.D. from Cairo University in ”Optimal Control of Variational Inequalities, the Dam Problem”. He is a professor of numerical analysis at Cairo University, science 2007. Currently, he is the chair of the Department of Mathematics, Faculty of Science, Cairo University and the vice president of the national committee of mathematics. He is a referee and editor of several international journals, in the frame of pure and applied Mathematics. Prof. Sweilam’s research interests include: optimal control of differential equations, fractional and variable order calculus, bio-informatics and cluster computing, ill-posed problems.
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