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Zbl 1237.37067
Dong, Tao; Liao, Xiaofeng; Li, Huaqing
Stability and Hopf bifurcation in a computer virus model with multistate antivirus. (English)
[J] Abstr. Appl. Anal. 2012, Article ID 841987, 16 p. (2012). ISSN 1085-3375; ISSN 1687-0409/e

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.

MSC 2000:: *37N35 Dynamical systems in control
68M10 Computer networks
92D30 Epidemiology

Keywords: SEIR model; computer virus; Hopf bifurcation

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Zentralblatt MATH Berlin [Germany]