Browsing by Author "Iqbal, Muhammad Sajid"

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Citation Count: Jawaz, Muhammad;...et.al. (2023). "Analysis and numerical effects of time-delayed rabies epidemic model with diffusion", International Journal of Nonlinear Sciences and Numerical Simulation, Vol.24, No.6, pp.2179-2194.
Analysis and numerical effects of time-delayed rabies epidemic model with diffusion
(2023) Jawaz, Muhammad; Rehman, Muhammad Aziz-Ur; Ahmed, Nauman; Baleanu, Dumitru; Iqbal, Muhammad Sajid; Rafiq, Muhammad; Raza, Ali; 56389
The current work is devoted to investigating the disease dynamics and numerical modeling for the delay diffusion infectious rabies model. To this end, a non-linear diffusive rabies model with delay count is considered. Parameters involved in the model are also described. Equilibrium points of the model are determined and their role in studying the disease dynamics is identified. The basic reproduction number is also studied. Before going towards the numerical technique, the definite existence of the solution is ensured with the help of the Schauder fixed point theorem. A standard result for the uniqueness of the solution is also established. Mapping properties and relative compactness of the operator are studied. The proposed finite difference method is introduced by applying the rules defined by R.E. Mickens. Stability analysis of the proposed method is done by implementing the Von-Neumann method. Taylor's expansion approach is enforced to examine the consistency of the said method. All the important facts of the proposed numerical device are investigated by presenting the appropriate numerical test example and computer simulations. The effect of τ on infected individuals is also examined, graphically. Moreover, a fruitful conclusion of the study is submitted.
Citation Count: Younis, Muhammad...et al. (2020). "Investigation of Electromagnetic Wave Structures for a Coupled Model in Anti-ferromagnetic Spin Ladder Medium", Frontiers in Physics, Vol. 8.
Investigation of Electromagnetic Wave Structures for a Coupled Model in Anti-ferromagnetic Spin Ladder Medium
(2020) Younis, Muhammad; Yousaf, Umair; Ahmed, Nauman; Rizvi, Syed Tahir Raza; Iqbal, Muhammad Sajid; Baleanu, Dumitru; 56389
The article studies the extraction of electromagnetic wave structures in a spin ladder anti-ferromagnetic medium with a coupled generalized non-linear Schrodinger model. The direct algebraic technique is used to extract the wave solutions. The solutions are obtained in the form of dark, singular, kink, and dark-singular under different constraint conditions. Moreover, the dynamic behavior of the structures have depicted in 3D graphs and their corresponding counterplots. The results are helpful for the understanding of wave propagation study and are also vital for numerical and experimental verifications in the field of electromagnetic wave theory. © Copyright © 2020 Younis, Yousaf, Ahmed, Rizvi, Iqbal and Baleanu.
Citation Count: Shahid, Naveed...et al. (2020). "Novel numerical analysis for nonlinear advection-reaction-diffusion systems", Open Physics, Vol. 18, No. 1, pp. 112-125.
Novel numerical analysis for nonlinear advection-reaction-diffusion systems
(2020) Shahid, Naveed; Ahmed, Nauman; Baleanu, Dumitru; Alshomrani, Ali Saleh; Iqbal, Muhammad Sajid; Rehman, Muhammad Aziz-u; Shaikh, Tahira Sumbal; Malik, Muhammad Rafiq; 56389
In this article, a numerical model for a Brusselator advection-reaction-diffusion (BARD) system by using an elegant numerical scheme is developed. The consistency and stability of the proposed scheme is demonstrated. Positivity preserving property of the proposed scheme is also verified. The designed scheme is compared with the two well-known existing classical schemes to validate the certain physical properties of the continuous system. A test problem is also furnished for simulations to support our claim. Prior to computations, the existence and uniqueness of solutions for more generic problems is investigated. In the underlying system, the nonlinearities depend not only on the desired solution but also on the advection term that reflects the pivotal importance of the study.
Citation Count: Ali, Muhammad Tariq;...et.al. (2023). "Numerical Analysis for the Effect of Irresponsible Immigrants on HIV/AIDS Dynamics", Intelligent Automation and Soft Computing, Vol.36, no.2, pp.1479-1496.
Numerical Analysis for the Effect of Irresponsible Immigrants on HIV/AIDS Dynamics
(2023) Ali, Muhammad Tariq; Baleanu, Dumitru; Rafiq, Muhammad; Awrejcewicz, Jan; Ahmed, Nauman; Raza, Ali; Iqbal, Muhammad Sajid; Ahmad, Muhammad Ozair; 56389
The human immunodeficiency viruses are two species of Lentivirus that infect humans. Over time, they cause acquired immunodeficiency syndrome, a condition in which progressive immune system failure allows life-threatening opportunistic infections and cancers to thrive. Human immunodeficiency virus infection came from a type of chimpanzee in Central Africa. Studies show that immunodeficiency viruses may have jumped from chimpanzees to humans as far back as the late 1800s. Over decades, human immunodeficiency viruses slowly spread across Africa and later into other parts of the world. The SusceptibleInfected-Recovered (SIR) models are significant in studying disease dynamics. In this paper, we have studied the effect of irresponsible immigrants on HIV/AIDS dynamics by formulating and considering different methods. Euler, Runge Kutta, and a Non-standard finite difference (NSFD) method are developed for the same problem. Numerical experiments are performed at disease-free and endemic equilibria points at different time step sizes ‘ℎ’. The results reveal that, unlike Euler and Runge Kutta, which fail for large time step sizes, the proposed Non-standard finite difference (NSFD) method gives a convergence solution for any time step size. Our proposed numerical method is bounded, dynamically consistent, and preserves the positivity of the continuous solution, which are essential requirements when modeling a prevalent disease.
Citation Count: Shahid, Naveed...et al. (2021). "Numerical investigation for the nonlinear model of hepatitis-B virus with the existence of optimal solution". AIMS MATHEMATICS. Vol: 6, No: 8, pp. 8294-8314.
Numerical investigation for the nonlinear model of hepatitis-B virus with the existence of optimal solution
(2021) Shahid, Naveed; Rehman, Muhammad Aziz-ur; Ahmed, Nauman; Baleanu, Dumitru; Iqbal, Muhammad Sajid; Rafiq, Muhammad; 56389
In 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.
Citation Count: Shahid, Naveeda...et al. (2021). "Optimality of solution with numerical investigation for coronavirus epidemic model", Computers, Materials and Continua, Vol. 67, no. 2, pp. 1713-1728.
Optimality of solution with numerical investigation for coronavirus epidemic model
(2021) Shahid, Naveeda; Baleanu, Dumitru; Ahmed, Nauman; Shaikh, Tahira Sumbal; Raza, Ali; Iqbal, Muhammad Sajid; Rafiq, Muhammad; Aziz-Ur Rehman, Muhammad; 56389
The novel coronavirus disease, coined as COVID-19, is a murderous and infectious disease initiated from Wuhan, China. This killer disease has taken a large number of lives around the world and its dynamics could not be controlled so far. In this article, the spatio-Temporal compartmental epidemic model of the novel disease with advection and diffusion process is projected and analyzed. To counteract these types of diseases or restrict their spread, mankind depends upon mathematical modeling and medicine to reduce, alleviate, and anticipate the behavior of disease dynamics. The existence and uniqueness of the solution for the proposed system are investigated. Also, the solution to the considered system is made possible in a well-known functions space. For this purpose, a Banach space of function is chosen and the solutions are optimized in the closed and convex subset of the space. The essential explicit estimates for the solutions are investigated for the associated auxiliary data. The numerical solution and its analysis are the crux of this study.Moreover, the consistency, stability, and positivity are the indispensable and core properties of the compartmentalmodels that a numerical designmust possess. To this end, a nonstandard finite difference numerical scheme is developed to find the numerical solutions which preserve the structural properties of the continuous system. The M-matrix theory is applied to prove the positivity of the design. The results for the consistency and stability of the design are also presented in this study. The plausibility of the projected scheme is indicated by an appropriate example. Computer simulations are also exhibited to conclude the results. © 2021 Tech Science Press. All rights reserved.
Citation Count: Iqbal, Zafar...et al. (2020). "Structure preserving computational technique for fractional order Schnakenberg model", Computational & Applied Mathematics, Vol. 39, No. 2.
Structure preserving computational technique for fractional order Schnakenberg model
(2020) Iqbal, Zafar; Ahmed, Nauman; Baleanu, Dumitru; Rafiq, Muhammad; Iqbal, Muhammad Sajid; Rehman, Muhammad Aziz-ur; 56389
The current article deals with the analysis and numerical solution of fractional order Schnakenberg (S-B) model. This model is a system of autocatalytic reactions by nature, which arises in many biological systems. This study is aiming at investigating the behavior of natural phenomena with a more realistic and practical approach. The solutions are obtained by applying the Grunwald-Letnikov (G-L) finite difference (FD) and the proposed G-L nonstandard finite difference (NSFD) computational schemes. The proposed formulation is explicit in nature, strongly structure preserving as well as it is independent of the time step size. One very important feature of our proposed scheme is that it preserves the positivity of the solution of continuous fractional order S-B model because the unknown variables involved in this system describe the chemical concentrations of different substances. The comparison of the proposed scheme with G-L FD method reflects the significance of the said method.
Citation Count: Azam, Shumaila...et al. (2021). "Structure preserving numerical scheme for spatio-temporal epidemic model of plant disease dynamics", Results in Physics, Vol. 30.
Structure preserving numerical scheme for spatio-temporal epidemic model of plant disease dynamics
(2021) Azam, Shumaila; Ahmed, Nauman; Akgül, Ali; Iqbal, Muhammad Sajid; Rafiq, Muhammad; Ahmad, Muhammad Ozair; Baleanu, Dumitru; 56389
In 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.