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Browsing by Author "Rehman, Muhammad Aziz Ur"

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    Citation Count: Ahmed, Nauman...et al. (2020). "Numerical analysis of diffusive susceptible-infected-recovered epidemic model in three space dimension", Chaos Solitons & Fractals, Vol. 132.
    Numerical analysis of diffusive susceptible-infected-recovered epidemic model in three space dimension
    (2020) Ahmed, Nauman; Ali, Mubasher; Baleanu, Dumitru; Rafiq, Muhammad; Rehman, Muhammad Aziz Ur; 56389
    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.
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    Citation Count: Ahmed, Nauman...et al. (2020). "Numerical Analysis of the Susceptible Exposed Infected Quarantined and Vaccinated (SEIQV) Reaction-Diffusion Epidemic Model", Frontiers in Physics, Vol. 7.
    Numerical Analysis of the Susceptible Exposed Infected Quarantined and Vaccinated (SEIQV) Reaction-Diffusion Epidemic Model
    (2020) Ahmed, Nauman; Fatima, Mehreen; Baleanu, Dumitru; Nisar, Kottakkaran Soopp; Khan, Ilyas; Rafiq, Muhammad; Rehman, Muhammad Aziz Ur; Ahmad, Muhammad Ozair; 56389
    In this paper, two structure-preserving nonstandard finite difference (NSFD) operator splitting schemes are designed for the solution of reaction diffusion epidemic models. The proposed schemes preserve all the essential properties possessed by the continuous systems. These schemes are applied on a diffusive SEIQV epidemic model with a saturated incidence rate to validate the results. Furthermore, the stability of the continuous system is proved, and the bifurcation value is evaluated. A comparison is also made with the existing operator splitting numerical scheme. Simulations are also performed for numerical experiments.