Browsing by Author "Azam, Shumaila"

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Citation Count: Fatima, Umbreen...et al. (2021). "Numerical study of computer virus reaction diffusion epidemic model", Computers, Materials and Continua, Vol. 66, No. 3, pp. 3183-3194.
Numerical study of computer virus reaction diffusion epidemic model
(2021) Fatima, Umbreen; Baleanu, Dumitru; Ahmed, Nauman; Azam, Shumaila; Raza, Ali; Rafiq, Muhammad; Rehman, Muhammad Aziz-Ur; 56389
Reaction–diffusion systems are mathematical models which link to several physical phenomena. The most common is the change in space and time of the meditation of one or more materials. Reaction–diffusion modeling is a substantial role in the modeling of computer propagation like infectious diseases. We investigated the transmission dynamics of the computer virus in which connected to each other through network globally. The current study devoted to the structure-preserving analysis of the computer propagation model. This manuscript is devoted to finding the numerical investigation of the reaction–diffusion computer virus epidemic model with the help of a reliable technique. The designed technique is finite difference scheme which sustains the important physical behavior of continuous model like the positivity of the dependent variables, the stability of the equilibria. The theoretical analysis of the proposed method like the positivity of the approximation, stability, and consistency is discussed in detail. A numerical example of simulations yields the authentication of the theoretical results of the designed technique.
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.