Numerical dynamics of nonstandard finite difference schemes for a computer virus propagation model

In this paper, we construct and analyze nonstandard finite difference (NSFD) schemes for a computer virus propagation model. We prove theoretically that the proposed NSFD schemes preserve essential qualitative properties of the continuous model. These properties are positivity and boundedness of solutions, equilibria and their stability properties. The performed numerical simulations support the theoretical results. The numerical experiments also show that standard finite difference schemes fail to preserve the essential properties of the continuous model for large step sizes. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.