Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014, Article ID 784684, 14 pages
http://dx.doi.org/10.1155/2014/784684
Research Article

Stability and Bifurcation Analysis of a Modified Epidemic Model for Computer Viruses

1College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China
2Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Hong Kong
3Department of Mathematics, Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar

Received 8 January 2014; Accepted 10 May 2014; Published 5 June 2014

Academic Editor: He Huang

Copyright © 2014 Chuandong Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We extend the three-dimensional SIR model to four-dimensional case and then analyze its dynamical behavior including stability and bifurcation. It is shown that the new model makes a significant improvement to the epidemic model for computer viruses, which is more reasonable than the most existing SIR models. Furthermore, we investigate the stability of the possible equilibrium point and the existence of the Hopf bifurcation with respect to the delay. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when the delay passes through a sequence of critical values. An analytical condition for determining the direction, stability, and other properties of bifurcating periodic solutions is obtained by using the normal form theory and center manifold argument. The obtained results may provide a theoretical foundation to understand the spread of computer viruses and then to minimize virus risks.