Browsing by Author "Rehman, M. A."

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A FRACTAL FRACTIONAL MODEL FOR CERVICAL CANCER DUE TO HUMAN PAPILLOMAVIRUS INFECTION
(2021) Baleanu, Dumitru; Ahmed, N.; Raza, A.; Iqbal, Z.; Rafiq, M.; Rehman, M. A.; Baleanu, Dumitru; 56389
In this paper, we have investigated women's malignant disease, cervical cancer, by constructing the compartmental model. An extended fractal-fractional model is used to study the disease dynamics. The points of equilibria are computed analytically and verified by numerical simulations. The key role of R-0 in describing the stability of the model is presented. The sensitivity analysis of R-0 for deciding the role of certain parameters altering the disease dynamics is carried out. The numerical simulations of the proposed numerical technique are demonstrated to test the claimed facts.
A novel time efficient structure-preserving splitting method for the solution of two-dimensional reaction-diffusion systems
(2020) Baleanu, Dumitru; Korkmaz, Alper; Rafiq, M.; Baleanu, Dumitru; Alshomrani, Ali Sale; Rehman, M. A.; Iqbal, M. S.; 56389
In this article, the first part is concerned with the important questions related to the existence and uniqueness of solutions for nonlinear reaction-diffusion systems. Secondly, an efficient positivity-preserving operator splitting nonstandard finite difference scheme (NSFD) is designed for such a class of systems. The presented formulation is unconditionally stable as well as implicit in nature and even time efficient. The proposed NSFD operator splitting technique also preserves all the important properties possessed by continuous systems like positivity, convergence to the fixed points of the system, and boundedness. The proposed algorithm is implicit in nature but more efficient in time than the extensively used Euler method.
Spatio-temporal numerical modeling of reaction-diffusion measles epidemic system
(2019) Baleanu, Dumitru; Wei, Zhouchao; Baleanu, Dumitru; Rafiq, M.; Rehman, M. A.; 56389
In this work, we investigate the numerical solution of the susceptible exposed infected and recovered measles epidemic model. We also evaluate the numerical stability and the bifurcation value of the transmission parameter from susceptibility to a disease of the proposed epidemic model. The proposed method is a chaos free finite difference scheme, which also preserves the positivity of the solution of the given epidemic model. Published under license by AIP Publishing.