A Reliable numerical scheme for a computer virus propagation model

Abstract

n this paper, we develop the Mickens’ methodology to construct a dynamically consistent Non-Standard FiniteDifference (NSFD) scheme for a recognized computer virus propagation model. It is proved that the constructed NSFD scheme correctly preserves essential mathematical features of the continuous-time model, which are positivity, boundedness and asymptotic stability. As an important consequence, we obtain an effective numerical scheme that has the ability to provide reliable approximations, meanwhile, some typical standard finite difference schemes fail to preserve the essential properties of the computer virus propagation model; hence, they can generate numerical approximations which are not only negative but also unstable. Finally, a set of numerical experiments is performed to support the theoretical results as well as to demonstrate the advantage of the NSFD scheme over standard ones. As we expected, there is a good agreement between the numerical results and theoretical assertions.