A finite difference scheme to solve a fractional order epidemic model of computer virus

Abstract

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 $ \mathfrak{R}_0 $ functions in stability analysis and illness dynamics.

Keywords

• computer virus
• fractional order system
• grunwald letinkov technique
• nonstandard finite differences
• simulations