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

Mathematical and Computer Modelling

Volumn 56, Issue 7-8, 2012, Pages 167-179

  Feng, Liping ^a,b   Liao, Xiaofeng ^a   Li, Huaqing ^a   Han, Qi ^a  

^a CHONGQING UNIVERSITY   (China)

^b XINZHOU TEACHERS UNIVERSITY   (China)

Author keywords

Computer virus; Hopf bifurcation; Stability; Time delay; Virus model

Indexed keywords

ANTI VIRUS; BIFURCATING PERIODIC SOLUTIONS; CENTER MANIFOLD THEOREM; COMPUTER VIRUS PROPAGATION; CRITICAL VALUE; EXPLICIT FORMULA; HOPF BIFURCATION ANALYSIS; MULTI-STATE; NORMAL FORM THEORY; STABILITY AND BIFURCATION; THEORETICAL BASIS; VIRAL INFECTION MODEL; VIRUS MODEL; VIRUS PROPAGATION;

COMPUTER VIRUSES; CONVERGENCE OF NUMERICAL METHODS; HOPF BIFURCATION; TIME DELAY;

STABILITY;

EID: 84861987353     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2011.12.010     Document Type: Article

References (19)

1. Gordon L.A., Loeb M.P., Lucyshyn W., Richardson R. 2005 CSI/FBI crime and security survey. Computer Security Institute 2005.
2. National computer virus emergency response center: report, 2009, Online, Available: (in Chinese). http://www.antivirus-china.org.cn/index.asp.
3. J.O. Kephart, S.R White, Directed-graph epidemiological models of computer viruses, in: IEEE Symposium on Security and Privacy, 1991, pp. 343-361.
4. J.O. Kephart, S.R White, Measuring and modeling computer virus prevalence, in: IEEE Computer Security Symposium on Research in Security and Privacy, IEEE, 1993, pp. 2-15.
5. De P., Liu Y.H, Das S.K. An epidemic theoretic framework for vulnerability analysis of broadcast protocols in wireless sensor networks. IEEE Transactions on Mobile Computing 2009, 8(3):413-425.
6. Moreno Y., Pastor-Satorras R., Vespignani A. Epidemic outbreaks in complex heterogeneous networks. European Physical Journal B 2002, 26:521-529.
7. Garetto M., Gong W.B., Towsley D. Modeling malware spreading dynamics. Twenty-Second Annual Joint Conference of the IEEE Computer and Communications 2003, 1869-1879.
8. C.C. Zou, W.B. Gong, D. Towsley, D. Towsley, Code red worm propagation modeling and analysis, CCS'02 (2002) 18-22.
9. Zou C.C., Gong W.B., Towsley D., Gao L.X. The monitoring and early detection of internet worms. IEEE/ACM Transactions on Networking 2005, 13(5):961-974.
10. Zou C.C., Towsley D., Gong W.B. On the performance of Internet worm scanning strategies. Performance Evaluation 2006, 63:700-723.
11. Song X.Y., Wang S.L., Dong J. Stability properties and Hopf bifurcation of a delayed viral infection model with lytic immune response. Journal of Mathematical Analysis and Applications 2011, 373:345-355.
12. Li J.Q., Wang K.F., Yang Y.L. Dynamical behaviors of an HBV infection model with logistic hepatocyte growth. Mathematical and Computer Modelling 2011, 54:704-711.
13. Huang G., Takeuchi Y., Ma W.B., Wei D.J. Global stability for delay SIR and SEIR epidemic models with nonlinear incidence rate. Bulletin of Mathematical Biology 2010, 72:1192-1207.
14. Pang J.H., Cui J.A., Hui J. Rich dynamics of epidemic model with sub-optimal immunity and nonlinear recovery rate. Mathematical and Computer Modelling 2011, 54:440-448.
15. Li X.Z., Li W.S., Ghosh M. Stability and bifurcation of an SIS epidemic model with treatment. Chaos, Solitons and Fractals 2009, 42:2822-2832.
16. Blyuss K.B., Kyrychko Y.N. Stability and bifurcations in an epidemic model with varying immunity period. Bulletin of Mathematical Biology 2010, 72:490-505.
17. Kermack W.O., McKendrick A.G. Contributions to the mathematical theory of epidemics. Proceedings of the Royal Society of London Series A 1927, 115:700-721.
18. Hale J., Verduyn Lunel S.M. Introduction to Functional Differential Equations 1993, Springer-Verlag.
19. Hassard B.D., Kazarinoff N.D., Wan Y.H. Theory and Applications of Hopf Bifurcation 1981, Cambridge University Press, Cambridge, MA.