Browsing by Author "Fatima, Umbreen"

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Citation - WoS: 20
Citation - Scopus: 26
A finite difference scheme to solve a fractional order epidemic model of computer virus
(Amer inst Mathematical Sciences-aims, 2023) Jarad, Fahd; Rehman, Muhammad Aziz-ur; Imran, Muhammad; Ahmed, Nauman; Fatima, Umbreen; Akgul, Ali; Jarad, Fahd; Matematik
In this article, an analytical and numerical analysis of a computer virus epidemic model is presented. To more thoroughly examine the dynamics of the virus, the classical model is transformed into a fractional order model. The Caputo differential operator is applied to achieve this. The Jacobian approach is employed to investigate the model's stability. To investigate the model's numerical solution, a hybridized numerical scheme called the Grunwald Letnikov nonstandard finite difference (GL-NSFD) scheme is created. Some essential characteristics of the population model are scrutinized, including positivity boundedness and scheme stability. The aforementioned features are validated using test cases and computer simulations. The mathematical graphs are all detailed. It is also investigated how the fundamental reproduction number R0 functions in stability analysis and illness dynamics.
Citation - WoS: 5
Citation - Scopus: 8
Modeling of Computer Virus Propagation with Fuzzy Parameters
(Tech Science Press, 2023) Alhebshi, Reemah M.; Baleanu, Dumitru; Ahmed, Nauman; Baleanu, Dumitru; Fatima, Umbreen; Dayan, Fazal; Rafiq, Muhammad; Mahmoud, Emad E.; 56389; Matematik
Typically, a computer has infectivity as soon as it is infected. It is a reality that no antivirus programming can identify and eliminate all kinds of viruses, suggesting that infections would persevere on the Internet. To understand the dynamics of the virus propagation in a better way, a computer virus spread model with fuzzy parameters is presented in this work. It is assumed that all infected computers do not have the same contribution to the virus transmission process and each computer has a different degree of infectivity, which depends on the quantity of virus. Considering this, the parameters beta and gamma being functions of the computer virus load, are considered fuzzy numbers. Using fuzzy theory helps us understand the spread of computer viruses more realistically as these parameters have fixed values in classical models. The essential features of the model, like reproduction number and equilibrium analysis, are discussed in fuzzy senses. Moreover, with fuzziness, two numerical methods, the forward Euler technique, and a nonstandard finite difference (NSFD) scheme, respectively, are developed and analyzed. In the evidence of the numerical simulations, the proposed NSFD method preserves the main features of the dynamic system. It can be considered a reliable tool to predict such types of solutions.
Citation - WoS: 11
Citation - Scopus: 14
Numerical study of computer virus reaction diffusion epidemic model
(Tech Science Press, 2021) Fatima, Umbreen; Baleanu, Dumitru; Baleanu, Dumitru; Ahmed, Nauman; Azam, Shumaila; Raza, Ali; Rafiq, Muhammad; Rehman, Muhammad Aziz-ur; 56389; Matematik
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.