Math. Model. Nat. Phenom.
Volume 11, Number 4, 2016Ecology, Epidemiology and Evolution
|Page(s)||105 - 119|
|Published online||19 July 2016|
The Impact of Hybrid Quarantine Strategies and Delay factor on Viral Prevalence in Computer Networks
Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, China
* Corresponding author. E-mail: email@example.com
Recently, the quarantine approach, which has been applied to infectious disease control, is widely regarded as an effective measure to suppress viral spread in computer networks. Hence, in order to prevent the spread of computer virus in network, and consider the latent period of a latent computer, a new delayed epidemic model of computer virus with hybrid quarantine strategies is presented. By regarding the delay as bifurcating parameter and analyzing the associated characteristic equation, the dynamical behaviors, including local asymptotical stability in which the virus spreading can be controlled, and furthermore, local Hopf bifurcation occurs in the system, which implies computer virus is out of control, are investigated. By applying the normal form and center manifold theorem, the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are also determined. Some numerical simulations are provided to support our theoretical results which also imply that hybrid quarantine strategies can inhibit viral spread effectively, and make the model be asymptotically stable.
Mathematics Subject Classification: 35Q53 / 34B20 / 35G31
Key words: computer virus / delay / intrusion detection systems / hybrid quarantine strategies / Hopf bifurcation
© EDP Sciences, 2016
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