Browsing by Author "Adel, Waleed"

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Citation - WoS: 51
Citation - Scopus: 62
Positivity and boundedness preserving numerical algorithm for the solution of fractional nonlinear epidemic model of HIV/AIDS transmission
(Pergamon-elsevier Science Ltd, 2020) Iqbal, Zafar; Baleanu, Dumitru; Ahmed, Nauman; Baleanu, Dumitru; Adel, Waleed; Rafiq, Muhammad; Rehman, Muhammad Aziz-ur; Alshomrani, Ali Saleh; 56389; Matematik
In this article, an integer order nonlinear HIV/AIDS infection model is extended to the non-integer nonlinear model. The Grunwald Letnikov nonstandard finite difference scheme is designed to obtain the numerical solutions. Structure preservence is one of the main advantages of this scheme. Reproductive number R-0 is worked out and its key role in disease dynamics and stability of the system is investigated with the following facts, if R-0 < 1 the disease will be diminished and it will persist in the community for R-0 > 1. On the other hand, it is sought out that system is stable when R-0 < 1 and R-0 > 1 implicates that system is locally asymptotically stable. Positivity and boundedness of the scheme is also proved for the generalized system. Two steady states of the system are computed and verified by computer simulations with the help of some suitable test problem. (C) 2020 Elsevier Ltd. All rights reserved.
Citation - WoS: 17
Citation - Scopus: 18
Stability analysis and numerical simulations of spatiotemporal HIV CD4+T cell model with drug therapy
(Amer inst Physics, 2020) Ahmed, Nauman; Baleanu, Dumitru; Elsonbaty, Amr; Adel, Waleed; Baleanu, Dumitru; Rafiq, Muhammad; 56389; Matematik
In this study, an extended spatiotemporal model of a human immunodeficiency virus (HIV) CD4+ T cell with a drug therapy effect is proposed for the numerical investigation. The stability analysis of equilibrium points is carried out for temporal and spatiotemporal cases where stability regions in the space of parameters for each case are acquired. Three numerical techniques are used for the numerical simulations of the proposed HIV reaction-diffusion system. These techniques are the backward Euler, Crank-Nicolson, and a proposed structure preserving an implicit technique. The proposed numerical method sustains all the important characteristics of the proposed HIV model such as positivity of the solution and stability of equilibria, whereas the other two methods have failed to do so. We also prove that the proposed technique is positive, consistent, and Von Neumann stable. The effect of different values for the parameters is investigated through numerical simulations by using the proposed method. The stability of the proposed model of the HIV CD4+ T cell with the drug therapy effect is also analyzed.
Citation - WoS: 1
Citation - Scopus: 1
Structure Preserving Numerical Analysis of Reaction-Diffusion Models
(Wiley, 2022) Ahmed, Nauman; Jarad, Fahd; Rehman, Muhammad Aziz-ur; Adel, Waleed; Jarad, Fahd; Ali, Mubasher; Rafiq, Muhammad; Akgul, Ali; 234808; Matematik
In this paper, we examine two structure preserving numerical finite difference methods for solving the various reaction-diffusion models in one dimension, appearing in chemistry and biology. These are the finite difference methods in splitting environment, namely, operator splitting nonstandard finite difference (OS-NSFD) methods that effectively deal with nonlinearity in the models and computationally efficient. Positivity of both the proposed splitting methods is proved mathematically and verified with the simulations. A comparison is made between proposed OS-NSFD methods and well-known classical operator splitting finite difference (OS-FD) methods, which demonstrates the advantages of proposed methods. Furthermore, we applied proposed NSFD splitting methods on several numerical examples to validate all the attributes of the proposed numerical designs.