Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

Browse

Filters

2020 - 20225

Settings

Author: search.filters.author.Ahmed, NaumanSubject: search.filters.subject.Positivity

Search Results

Now showing 1 - 5 of 5
  • Article
    Citation - WoS: 13
    Citation - Scopus: 12
    Design, Analysis and Comparison of a Nonstandard Computational Method for the Solution of a General Stochastic Fractional Epidemic Model
    (Mdpi, 2022) Macias-Diaz, Jorge E.; Raza, Ali; Baleanu, Dumitru; Rafiq, Muhammad; Iqbal, Zafar; Ahmad, Muhammad Ozair; Ahmed, Nauman
    Malaria is a deadly human disease that is still a major cause of casualties worldwide. In this work, we consider the fractional-order system of malaria pestilence. Further, the essential traits of the model are investigated carefully. To this end, the stability of the model at equilibrium points is investigated by applying the Jacobian matrix technique. The contribution of the basic reproduction number, R-0, in the infection dynamics and stability analysis is elucidated. The results indicate that the given system is locally asymptotically stable at the disease-free steady-state solution when R-0 < 1. A similar result is obtained for the endemic equilibrium when R-0 > 1. The underlying system shows global stability at both steady states. The fractional-order system is converted into a stochastic model. For a more realistic study of the disease dynamics, the non-parametric perturbation version of the stochastic epidemic model is developed and studied numerically. The general stochastic fractional Euler method, Runge-Kutta method, and a proposed numerical method are applied to solve the model. The standard techniques fail to preserve the positivity property of the continuous system. Meanwhile, the proposed stochastic fractional nonstandard finite-difference method preserves the positivity. For the boundedness of the nonstandard finite-difference scheme, a result is established. All the analytical results are verified by numerical simulations. A comparison of the numerical techniques is carried out graphically. The conclusions of the study are discussed as a closing note.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 13
    Positivity Preserving Technique for the Solution of Hiv/Aids Reaction Diffusion Model With Time Delay
    (Frontiers Media Sa, 2020) Ahmed, Nauman; Baleanu, Dumitru; Rafiq, Muhammad; Rehman, Muhammad Aziz-ur; Jawaz, Muhammad Jawaz
    This study is concerned with finding a numerical solution to the delay epidemic model with diffusion. This is not a simple task as variables involved in the model exhibit some important physical features. We have therefore designed an efficient numerical scheme that preserves the properties acquired by the given system. We also further develop Euler's technique for a delayed epidemic reaction-diffusion model. The proposed numerical technique is also compared with the forward Euler technique, and we observe that the forward Euler technique demonstrates the false behavior at certain step sizes. On the other hand, the proposed technique preserves the true behavior of the continuous system at all step sizes. Furthermore, the effect of the delay factor is discussed graphically by using the proposed technique.
  • Article
    Citation - WoS: 16
    Citation - Scopus: 17
    Numerical Analysis of the Susceptible Exposed Infected Quarantined and Vaccinated (Seiqv) Reaction-Diffusion Epidemic Model
    (Frontiers Media Sa, 2020) Fatima, Mehreen; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Khan, Ilyas; Rafiq, Muhammad; Ahmad, Muhammad Ozair; Ahmed, Nauman
    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.
  • Article
    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.
  • Article
    Citation - WoS: 12
    Citation - Scopus: 13
    A Novel Time Efficient Structure-Preserving Splitting Method for the Solution of Two-Dimensional Reaction-Diffusion Systems
    (Springer, 2020) Korkmaz, Alper; Rafiq, M.; Baleanu, Dumitru; Alshomrani, Ali Saleh; Rehman, M. A.; Iqbal, M. S.; Ahmed, Nauman
    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.