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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 475934, 9 pages
http://dx.doi.org/10.1155/2014/475934
Research Article

Stability and Bifurcation of a Computer Virus Propagation Model with Delay and Incomplete Antivirus Ability

1College of Computer, Jiangsu Normal University, Xuzhou 221116, China
2College of Live Science, Jiangsu Normal University, Xuzhou 221116, China

Received 12 March 2014; Revised 11 August 2014; Accepted 11 August 2014; Published 30 September 2014

Academic Editor: José R. C. Piqueira

Copyright © 2014 Jianguo Ren and Yonghong Xu. 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

A new computer virus propagation model with delay and incomplete antivirus ability is formulated and its global dynamics is analyzed. The existence and stability of the equilibria are investigated by resorting to the threshold value . By analysis, it is found that the model may undergo a Hopf bifurcation induced by the delay. Correspondingly, the critical value of the Hopf bifurcation is obtained. Using Lyapunov functional approach, it is proved that, under suitable conditions, the unique virus-free equilibrium is globally asymptotically stable if , whereas the virus equilibrium is globally asymptotically stable if . Numerical examples are presented to illustrate possible behavioral scenarios of the mode.