Qualitative Study of a Dynamical System for Computer Virus Propagation—A Nonstandard Finite‐Difference‐Methodological View

ABSTRACT In this article, we consider a nonlinear model that was originally proposed for computer virus propagation by Gan and coauthors in 2013. As our first contribution, we re‐examined and extended some analytical results regarding this dynamical system. Secondly, we reformulated it by one nonlinear, nonautonomous differential equation. Thirdly, we showed that we can use a classical Newton‐based optimization approach that converges quadratically under mild assumptions for finding the unique equilibrium state of the dynamical system. Fourthly, we proposed a nonstandard finite‐difference‐method based on nonlocal approximations for numerical discretization of our reformulation. Fifthly, we showed that our time‐discrete model possesses the same properties as the time‐continuous model, that is, that namely boundedness and nonnegativity are conserved for arbitrary time‐step sizes. Then we proved convergence towards the time‐continuous solution in the asymptotic sense of letting the time‐step size tend to zero. We finally underlined our theoretical findings by numerical experiments.