Stability and Hopf Bifurcation Analysis for a Computer Virus Propagation Model with Two Delays and Vaccination. (20th March 2017)

• Record Type: Journal Article
• Authors: Zhang, Zizhen; Wang, Yougang; Bi, Dianjie; Guerrini, Luca
• Other Names: Yang Lu-Xing Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2017(2017)
• Publication Date: 2017-03-20
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2017/3536125
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : A further generalization of an SEIQRS-V (susceptible-exposed-infectious-quarantined-recovered-susceptible with vaccination) computer virus propagation model is the main topic of the present paper. This paper specifically analyzes effects on the asymptotic dynamics of the computer virus propagation model when two time delays are introduced. Sufficient conditions for the asymptotic stability and existence of the Hopf bifurcation are established by regarding different combination of the two delays as the bifurcation parameter. Moreover, explicit formulas that determine the stability, direction, and period of the bifurcating periodic solutions are obtained with the help of the normal form theory and center manifold theorem. Finally, numerical simulations are employed for supporting the obtained analytical results.