Extrapolated nonstandard numerical schemes for solving an epidemiological model for computer viruses

Abstract

Abstract— The aim of this work is to construct high-order numerical schemes that preserve the dynamical properties of a mathematical model describing the spread of computer viruses on the Internet. For this purpose, we first apply Mickens’ methodology to formulate a dynamically consistent nonstandard finite difference (NSFD) scheme for the model under consid­eration. After that, the constructed NSFD scheme is combined with Richardson’s extrapolation method to generate higher-accuracy numerical approximations. The result is that we obtain extrapolated numerical schemes that not only preserve the dynamical proper­ties of the computer virus propagation model but also provide higher-accuracy numerical approximations. In addition, a set of numerical examples is conducted to illustrate and support the theoretical findings and to show the advantages of the proposed numerical schemes.