Stability and bifurcation of a computer virus propagation model with delay and incomplete antivirus ability
type: Item
instance of: scholarly article
title: Stability and bifurcation of a computer virus propagation model with delay and incomplete antivirus ability
zbMATH Open document ID: 1407.68055
DOI: 10.1155/2014/475934
author: Jianguo Ren
author: Yonghong Xu
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: 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 \(R_0\). 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 \(R_0 < 1\), whereas the virus equilibrium is globally asymptotically stable if \(R_0 > 1\). Numerical examples are presented to illustrate possible behavioral scenarios of the mode.
Mathematics Subject Classification ID: 68M11
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 37C75
Mathematics Subject Classification ID: 92D30
zbMATH DE Number: 7016521
Wikidata QID: Q59067651
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/475934
OpenAlex ID: W2164466097
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description: scientific article; zbMATH DE number 7016521