Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 5Citation - Scopus: 7New Applications Related To Hepatitis C Model(Amer inst Mathematical Sciences-aims, 2022) Raza, Ali; Akgul, Ali; Iqbal, Zafar; Rafiq, Muhammad; Ahmad, Muhammad Ozair; Jarad, Fahd; Ahmed, NaumanThe main idea of this study is to examine the dynamics of the viral disease, hepatitis C. To this end, the steady states of the hepatitis C virus model are described to investigate the local as well as global stability. It is proved by the standard results that the virus-free equilibrium state is locally asymptotically stable if the value of R-0 is taken less than unity. Similarly, the virus existing state is locally asymptotically stable if R-0 is chosen greater than unity. The Routh-Hurwitz criterion is applied to prove the local stability of the system. Further, the disease-free equilibrium state is globally asymptotically stable if R-0 < 1. The viral disease model is studied after reshaping the integer-order hepatitis C model into the fractal-fractional epidemic illustration. The proposed numerical method attains the fixed points of the model. This fact is described by the simulated graphs. In the end, the conclusion of the manuscript is furnished.Article Citation - WoS: 1Citation - Scopus: 1Structure Preserving Numerical Analysis of Reaction-Diffusion Models(Wiley, 2022) Rehman, Muhammad Aziz-ur; Adel, Waleed; Jarad, Fahd; Ali, Mubasher; Rafiq, Muhammad; Akgul, Ali; Ahmed, NaumanIn 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.Article Citation - WoS: 18Citation - Scopus: 19Construction and Numerical Analysis of a Fuzzy Non-Standard Computational Method for the Solution of an Seiqr Model of Covid-19 Dynamics(Amer inst Mathematical Sciences-aims, 2022) Ahmed, Nauman; Rafiq, Muhammad; Akgul, Ali; Raza, Ali; Ahmad, Muhammad Ozair; Jarad, Fahd; Dayan, FazalThis current work presents an SEIQR model with fuzzy parameters. The use of fuzzy theory helps us to solve the problems of quantifying uncertainty in the mathematical modeling of diseases. The fuzzy reproduction number and fuzzy equilibrium points have been derived focusing on a model in a specific group of people having a triangular membership function. Moreover, a fuzzy non-standard finite difference (FNSFD) method for the model is developed. The stability of the proposed method is discussed in a fuzzy sense. A numerical verification for the proposed model is presented. The developed FNSFD scheme is a reliable method and preserves all the essential features of a continuous dynamical system.Article Citation - WoS: 9Citation - Scopus: 15Numerical Simulations on Scale-Free and Random Networks for the Spread of Covid-19 in Pakistan(Elsevier, 2023) Nizami, Abdul Rauf; Baleanu, Dumitru; Ahmad, Nadeem; Rafiq, MuhammadEpidemiology is the study of how and why an infectious disease occurs in a group of peo-ple. Several epidemiological models have been developed to get information on the spread of a dis-ease in society. That information is used to plan strategies to prevent illness and manage patients. But, most of these models consider only random diffusion of the disease and hence ignore the num-ber of interactions among people. To take into account the interactions among individuals, the net-work approach is becoming increasingly popular. It is novel to consider the dynamics of infectious disease using various networks rather than classical differential equation models. In this paper, we numerically simulate the Susceptible-Infected-Recoverd (SIR) model on Barabasi-Albert network and Erd delta s-Re acute accent nyi network to analyze the spread of COVID-19 in Pakistan so that we know the severity of the disease. We also show how a situation becomes alarming if hubs in a network get infected.(c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).Article Citation - WoS: 2Citation - Scopus: 2Structure Preserving Numerical Scheme for Spatio-Temporal Epidemic Model of Plant Disease Dynamics(Elsevier, 2021) Ahmed, Nauman; Akgul, Ali; Iqbal, Muhammad Sajid; Rafiq, Muhammad; Ahmad, Muhammad Ozair; Baleanu, Dumitru; Azam, ShumailaIn this article, an implicit numerical design is formulated for finding the numerical solution of spatiotemporal nonlinear dynamical system with advection. Such type of problems arise in many fields of life sciences, mathematics, physics and engineering. The epidemic model describes the population densities that have some special types of features. These features should be maintained by the numerical design. The proposed scheme, not only solves the nonlinear physical system but also preserves the structure of the state variables. Von-Neumann criteria, M-matrix theory and Taylor's expansion are used for proving some standard results. Basic reproduction number is evaluated and its key role in deciding the stability at the equilibrium points is also investigated. Graphical solutions are also presented against the test problem.Article Citation - WoS: 8Citation - Scopus: 8Numerical 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 AzizHIV/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.Article Citation - WoS: 2Citation - Scopus: 3Numerical Investigation for the Nonlinear Model of Hepatitis-B Virus With the Existence of Optimal Solution(Amer inst Mathematical Sciences-aims, 2021) Rehman, Muhammad Aziz-ur; Ahmed, Nauman; Baleanu, Dumitru; Iqbal, Muhammad Sajid; Rafiq, Muhammad; Shahid, NaveedIn the recent article, a reaction-advection-diffusion model of the hepatitis-B virus (HBV) is studied. Existence and uniqueness of the optimal solution for the proposed model in function spaces is analyzed. The advection and diffusion terms make the model more generic than the simple model. So, the numerical investigation plays a vital role to understand the behavior of the solutions. To find the existence and uniqueness of the optimal solutions, a closed and convex subset (closed ball) of the Banach space is considered. The explicit estimates regarding the solution of the system for the admissible auxiliary data is computed. On the other hand, for the numerical approximation of the solution, an elegant numerical technique is devised to find the approximate solutions. After constructing the discrete model, some fundamental properties must necessarily be possessed by the proposed numerical scheme. For instance, consistency, stability, and positivity of the solutions. These properties are carefully studied in the current article. To prove the positivity of the proposed scheme, M-matrix theory is used. All the above mentioned properties are verified by sketching the graph via simulations. Furthermore, these plots are helpful to understand the true behavior of the solutions. For this purpose, a fruitful discussion is included about the simulations to justify our results.Article Citation - WoS: 28Citation - Scopus: 32New Applications Related To Covid-19(Elsevier, 2021) Ahmed, Nauman; Raza, Ali; Iqbal, Zafar; Rafiq, Muhammad; Baleanu, Dumitru; Rehman, Muhammad Aziz-ur; Akgul, AliAnalysis of mathematical models projected for COVID-19 presents in many valuable outputs. We analyze a model of differential equation related to Covid-19 in this paper. We use fractal-fractional derivatives in the proposed model. We analyze the equilibria of the model. We discuss the stability analysis in details. We apply very effective method to obtain the numerical results. We demonstrate our results by the numerical simulations.Article Citation - WoS: 9Citation - Scopus: 11An Accurate Predictor-Corrector Nonstandard Finite Difference Scheme for an Seir Epidemic Model(Hindawi Ltd, 2020) Ahmad, Riaz; Farooqi, Rashada; Alharbi, Sayer O.; Baleanu, Dumitru; Rafiq, Muhammad; Ahmad, M. O.; Farooqi, AsmaThe present work deals with the construction, development, and analysis of a viable normalized predictor-corrector-type nonstandard finite difference scheme for the SEIR model concerning the transmission dynamics of measles. The proposed numerical scheme double refines the solution and gives realistic results even for large step sizes, thus making it economical when integrating over long time periods. Moreover, it is dynamically consistent with a continuous system and unconditionally convergent and preserves the positive behavior of the state variables involved in the system. Simulations are performed to guarantee the results, and its effectiveness is compared with well-known numerical methods such as Runge-Kutta (RK) and Euler method of a predictor-corrector type.Article Citation - WoS: 5Citation - Scopus: 6Numerical 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, NaumanIn 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.