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

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...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2012-01, Vol.2012 (2012), p.1212-1227-682
Main Authors: Dong, Tao, Liao, Xiaofeng, Li, Huaqing
Format: Article
Language:English
Subjects:
Computer viruses
Cybersecurity
Mathematical models
Software
Studies
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Summary: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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2012/841987