Hopf bifurcation analysis of a delayed viral infection model in computer networks

Feng, Liping; Liao, Xiaofeng; Li, Huaqing; Han, Qi

doi:10.1016/j.mcm.2011.12.010

Cited by 83 publications

(47 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Based on the discussion about the distribution of the root of (19) in [25,26], we obtain the expression of cos , say…”

Section: Stability Of the Viral Equilibrium And Existence Of Hopf Bifmentioning

confidence: 99%

“…For example, Feng et al [19] studied the Hopf bifurcation of a delayed SIRS viral infection model in computer networks by taking the time delay due to the latent and temporary immune period as the bifurcation parameter. Dong et al [9] proposed a delayed SEIR computer virus model with multistate antivirus and studied the Hopf bifurcation of the model by choosing the delay where the infectious nodes use antivirus software to clean the viruses as the bifurcation parameter.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Delay Induced Hopf Bifurcation of an Epidemic Model with Graded Infection Rates for Internet Worms

Zhao

2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

A delayed SEIQRS worm propagation model with different infection rates for the exposed computers and the infectious computers is investigated in this paper. The results are given in terms of the local stability and Hopf bifurcation. Sufficient conditions for the local stability and the existence of Hopf bifurcation are obtained by using eigenvalue method and choosing the delay as the bifurcation parameter. In particular, the direction and the stability of the Hopf bifurcation are investigated by means of the normal form theory and center manifold theorem. Finally, a numerical example is also presented to support the obtained theoretical results.

show abstract

“…Based on the discussion about the distribution of the root of (19) in [25,26], we obtain the expression of cos , say…”

Section: Stability Of the Viral Equilibrium And Existence Of Hopf Bifmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Delay Induced Hopf Bifurcation of an Epidemic Model with Graded Infection Rates for Internet Worms

Zhao

2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…To this end, many dynamical models describing propagation of computer viruses have been established by scholars at home and abroad. Particularly the classic epidemic models, such as SIRS [3][4][5] model, SEIRS model [6], and SEIQRS model [7,8], are used to investigate the spreading law of computer viruses due to the common feature between the computer virus and the biological virus. Some computer virus models with infectivity in both seizing and latent computers have been also proposed by Yang et al [9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Stability and Hopf Bifurcation for a Delayed Computer Virus Model with Antidote in Vulnerable System

Zhang

Wang

Феррара

2017

Journal of Control Science and Engineering

View full text Add to dashboard Cite

A delayed computer virus model with antidote in vulnerable system is investigated. Local stability of the endemic equilibrium and existence of Hopf bifurcation are discussed by analyzing the associated characteristic equation. Further, direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are investigated by using the normal form theory and the center manifold theorem. Finally, numerical simulations are presented to show consistency with the obtained results.

show abstract

“…In response to this call, Kephart and White [4,5] explored a few earliest malware epidemic models. Toward this direction, a variety of novel computer infection propagation models, ranging from conventional models such as the SIRS models [6], the SEIRS models [7], and the SICS models [8] to unconventional models such as the delayed models [9,10], the stochastic models [11], and the network-based models [12][13][14], have been frequently reported in the literature.…”

Section: Introductionmentioning

confidence: 99%

The impact of nonlinear infection rate on the spread of computer virus

Yang

Xiao

2015

Nonlinear Dyn

View full text Add to dashboard Cite

The dominating majority of previous computer virus epidemic models assume a bilinear infection rate. This assumption, however, ignores the fact that, due to reasons such as overcrowded infected nodes and active protection measures taken at a high level of viral prevalence, the infection rate typically rises in a nonlinear fashion. This paper is devoted to understanding the impact of nonlinear infection rate on the propagation of computer infections. For that purpose, a new computer virus epidemic model is proposed by introducing a generic nonlinear infection rate into a traditional SLBS model. Theoretical analysis shows that, under moderate conditions, the proposed model admits a (viral) globally asymptotically stable equilibrium, fully demonstrating the robustness of stability of the equilibrium to the details of infections. The new model is justified through simulation experiments. We also determine the influence of some model parameters on the viral equilibrium. Our results extend some previously known results.

show abstract

Hopf bifurcation analysis of a delayed viral infection model in computer networks

Cited by 83 publications

References 14 publications

Delay Induced Hopf Bifurcation of an Epidemic Model with Graded Infection Rates for Internet Worms

Delay Induced Hopf Bifurcation of an Epidemic Model with Graded Infection Rates for Internet Worms

Stability and Hopf Bifurcation for a Delayed Computer Virus Model with Antidote in Vulnerable System

The impact of nonlinear infection rate on the spread of computer virus

Contact Info

Product

Resources

About