Mathematical analysis and design of the nonstandard computational method for an epidemic model of computer virus with delay Effect: Application of mathematical biology in computer science

Abstract

Mathematical modeling with nonlinear delay differential equations (DDES) impart a significant role in the different disciplines such as epidemiology, computer modeling, immunology, physiology, neural networks, social sciences, bio-medical engineering, and many more. In this manuscript, a nonlinear delayed model is investigated to study the dynamics of a virus in a computer network. Many important results are established for the stability of equilibria of the model using the Routh Hurwitz criterion, Volterra Lyapunov function, and Lasalle invariance principle. Also, a nonstandard finite difference method is presented for the computational analysis of the model. The delay tactics like, be cautious while opening the email attachments, disable image previews in your email client, use an anti-malware solution, monitor all devices proactively, utilize administrator rights, pay attention to virus-related warnings and notifications, are precautionary measures which can help us in removing the virus from network. The impact of delay tactics on the threshold number is also analyzed. In the end, numerical results are presented to strengthen the theoretical analysis of the model.