A Nonstandard Finite Difference Scheme for a SEI Epidemic Model

Abstract

In this paper we propose a nonstandard finite difference scheme for an epidemic model which considers the effect of media coverage on the spread of some infectious diseases. We show that this scheme preserves equilibrium points of the corresponding continuous system. Furthere more we study the qualitative properties of the system, such as, positivity, stability of the equilibria and Neimark-Sacker bifurcation. The results demonstrates that the discretized epidemic model is dynamically consistent with the continuous system.