Browsing by Author "Rehman, Muhammad Aziz Ur"

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Citation - WoS: 3
Citation - Scopus: 6
Mathematical and Numerical Investigations of the Fractional-Order Epidemic Model With Constant Vaccination Strategy
(Editura Acad Romane, 2021) Iqbal, Zafar; Baleanu, Dumitru; Rehman, Muhammad Aziz Ur; Baleanu, Dumitru; Ahmed, Nauman; Raza, Ali; Rafiq, Muhammad; Matematik
This work is devoted to find the reliable numerical solution of an epidemic model with constant vaccination strategy. For this purpose, a structure preserving numerical scheme called the Grunwald-Letnikov nonstandard finite difference scheme is designed. The proposed technique retains all the important properties of the continuous epidemic model like boundedness, positivity, and stability. This behavior of the proposed numerical scheme is validated mathematically and graphically. The role of the vaccination in controlling the disease dynamics in the population is verified through numerical simulations. The stability of the system under discussion is also examined at the disease free equilibrium point and the endemic equilibrium point. Finally, the outcome of this study is furnished with concluding remarks and future directions of research.
Citation - WoS: 5
Citation - Scopus: 6
Numerical Analysis of Diffusive Susceptible-Infected Epidemic Model in Three Space Dimension
(Pergamon-elsevier Science Ltd, 2020) Ali, Mubasher; Baleanu, Dumitru; Rafiq, Muhammad; Rehman, Muhammad Aziz Ur; Ahmed, Nauman
In this article, numerical solution of three dimensional susceptible-infected-recovered (SIR) reaction-diffusion epidemic system is furnished with a time efficient operator splitting nonstandard finite difference (OS-NSFD) method. We perform the comparison of proposed OS-NSFD method with popular forward Euler explicit finite difference (FD) method and time efficient backward Euler operator splitting finite difference (OS-FD) implicit method. The proposed OS-NSFD method is implicit in nature but computationally efficient as compared to forward Euler explicit (FD) scheme. The numerical stability and bifurcation value of transmission coefficient for SIR reaction-diffusion epidemic system is also investigated with the aid of Routh-Hurwitz method. At the end, we give two numerical experiments and simulation. In first experiment, all the numerical schemes are compared with the help of simulations. In second experiment we show the simulations of proposed NSFD technique at different values of parameters. Also we discuss the importance of transmission rate to control the spread of disease with the help of simulations. (C) 2019 Elsevier Ltd. All rights reserved.
Citation - WoS: 8
Citation - Scopus: 8
Numerical and Bifurcation Analysis of Spatio-Temporal Delay Epidemic Model
(Elsevier, 2021) Rehman, Muhammad Aziz Ur; Ahmed, Nauman; Baleanu, Dumitru; Rafiq, Muhammad; Jawaz, Muhammad; ur Rehman, Muhammad Aziz
HIV/AIDS is a distressing and incurable disease of the human beings. In this article, we have proposed a numerical structure for the HIV/AIDS compartmental model with diffusion and delay process. The proposed scheme has the proficiency to preserve the positivity of the state variables. Also, the proposed scheme leads to the consistency and stability. Two equilibrium states of the model have been described. Moreover, the stability of the scheme is examined at these two states. The contribution of the basic reproductive number R-0, in stability analysis is also investigated. The bifurcation value of the infection parameter gamma, for different situations of tau is also investigated. Graphical solutions with the aid of computer simulations are presented to clarify the paramount features of the proposed numerical design.