Browsing by Author "Iqbal, Muhammad Sajid"

Now showing 1 - 8 of 8

Citation - WoS: 3
Citation - Scopus: 2
Analysis and numerical effects of time-delayed rabies epidemic model with diffusion
(Walter de Gruyter Gmbh, 2023) Jawaz, Muhammad; Baleanu, Dumitru; Rehman, Muhammad Aziz-Ur; Ahmed, Nauman; Baleanu, Dumitru; Iqbal, Muhammad Sajid; Rafiq, Muhammad; Raza, Ali; 56389; Matematik
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 tau on infected individuals is also examined, graphically. Moreover, a fruitful conclusion of the study is submitted.
Citation - WoS: 12
Citation - Scopus: 13
Analysis of the Fractional Diarrhea Model With Mittag-Leffler Kernel
(Amer inst Mathematical Sciences-aims, 2022) Jarad, Fahd; Ahmed, Nauman; Akgul, Ali; Raza, Ali; Shahzad, Muhammad; Iqbal, Zafar; Jarad, Fahd; Matematik
In this article, we have introduced the diarrhea disease dynamics in a varying population. For this purpose, a classical model of the viral disease is converted into the fractional-order model by using Atangana-Baleanu fractional-order derivatives in the Caputo sense. The existence and uniqueness of the solutions are investigated by using the contraction mapping principle. Two types of equilibrium points i.e., disease-free and endemic equilibrium are also worked out. The important parameters and the basic reproduction number are also described. Some standard results are established to prove that the disease-free equilibrium state is locally and globally asymptotically stable for the underlying continuous system. It is also shown that the system is locally asymptotically stable at the endemic equilibrium point. The current model is solved by the Mittag-Leffler kernel. The study is closed with constraints on the basic reproduction number R-0 and some concluding remarks.
Citation - WoS: 11
Citation - Scopus: 12
Investigation of Electromagnetic Wave Structures for a Coupled Model in Anti-ferromagnetic Spin Ladder Medium
(Frontiers Media Sa, 2020) Younis, Muhammad; Baleanu, Dumitru; Yousaf, Umair; Ahmed, Nauman; Rizvi, Syed Tahir Raza; Iqbal, Muhammad Sajid; Baleanu, Dumitru; 56389; Matematik
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.
Citation - WoS: 10
Citation - Scopus: 11
Novel numerical analysis for nonlinear advection-reaction-diffusion systems
(de Gruyter Poland Sp Z O O, 2020) Shahid, Naveed; Baleanu, Dumitru; Ahmed, Nauman; Baleanu, Dumitru; Alshomrani, Ali Saleh; Iqbal, Muhammad Sajid; Rehman, Muhammad Aziz-ur; Malik, Muhammad Rafiq; 56389; Matematik
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 - WoS: 2
Citation - Scopus: 2
Numerical investigation for the nonlinear model of hepatitis-B virus with the existence of optimal solution
(Amer inst Mathematical Sciences-aims, 2021) Shahid, Naveed; Baleanu, Dumitru; Rehman, Muhammad Aziz-ur; Ahmed, Nauman; Baleanu, Dumitru; Iqbal, Muhammad Sajid; Rafiq, Muhammad; 56389; Matematik
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 - WoS: 8
Citation - Scopus: 8
Optimality of solution with numerical investigation for coronavirus epidemic model
(Tech Science Press, 2021) Shahid, Naveed; Baleanu, Dumitru; Baleanu, Dumitru; Ahmed, Nauman; Shaikh, Tahira Sumbal; Raza, Ali; Iqbal, Muhammad Sajid; Rehman, Muhammad Aziz-ur; 56389; Matematik
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 compartmental models that a numerical design must 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.
Citation - WoS: 14
Citation - Scopus: 14
Structure preserving computational technique for fractional order Schnakenberg model
(Springer Heidelberg, 2020) Iqbal, Zafar; Baleanu, Dumitru; Ahmed, Nauman; Baleanu, Dumitru; Rafiq, Muhammad; Iqbal, Muhammad Sajid; Rehman, Muhammad Aziz-ur; 56389; Matematik
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 - WoS: 2
Citation - Scopus: 2
Structure preserving numerical scheme for spatio-temporal epidemic model of plant disease dynamics
(Elsevier, 2021) Azam, Shumaila; Baleanu, Dumitru; Ahmed, Nauman; Akgul, Ali; Iqbal, Muhammad Sajid; Rafiq, Muhammad; Ahmad, Muhammad Ozair; Baleanu, Dumitru; 56389; Matematik
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.