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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 841987, 16 pages
http://dx.doi.org/10.1155/2012/841987
Research Article

Stability and Hopf Bifurcation in a Computer Virus Model with Multistate Antivirus

1State Key Laboratory of Power Transmission Equipment and System Security, College of Computer Science, Chongqing University, Chongqings 400044, China
2College of Software and Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Received 9 January 2012; Accepted 6 February 2012

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 Tao Dong 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

By considering that people may immunize their computers with countermeasures in susceptible state, exposed state and using anti-virus software may take a period of time, a computer virus model with time delay based on an SEIR model is proposed. We regard time delay as bifurcating parameter to study the dynamical behaviors which include local asymptotical stability and local Hopf bifurcation. By analyzing the associated characteristic equation, Hopf bifurcation occurs when time delay passes through a sequence of critical value. The linerized model and stability of the bifurcating periodic solutions are also derived by applying the normal form theory and the center manifold theorem. Finally, an illustrative example is also given to support the theoretical results.