Hopf bifurcation of an improved SLBS model under the influence of latent period

Mathematical Problems in Engineering

Volumn 2013, Issue , 2013, Pages

  Zhang, Chunming ^a   Liu, Wanping ^b   Xiao, Jing ^a   Zhao, Yun ^a  

^a GUANGDONG MEDICAL UNIVERSITY   (China)

^b CHONGQING UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATING PARAMETER; BIFURCATING PERIODIC SOLUTIONS; CENTER MANIFOLD THEOREM; CHARACTERISTIC EQUATION; DYNAMICAL BEHAVIORS; LOCAL ASYMPTOTICAL STABILITIES; LOCAL HOPF BIFURCATIONS; NORMAL FORM METHODS;

COMPUTER VIRUSES; TIME DELAY;

HOPF BIFURCATION;

EID: 84887387649     PISSN: 1024123X     EISSN: 15635147     Source Type: Journal    
DOI: 10.1155/2013/196214     Document Type: Article

References (19)

1. Kephart J. O., White S. R., Chess D. M., Computers and epidemiology. IEEE Spectrum 1993 20 26
2. Cohen F., Computer viruses. Theory and experiments. Computers and Security 1987 6 1 22 35 2-s2.0-0023294949
3. Han X., Tan Q., Dynamical behavior of computer virus on Internet. Applied Mathematics and Computation 2010 217 6 2520 2526 2-s2.0-77957993272 10.1016/j.amc.2010.07.064
4. Mishra B. K., Jha N., Fixed period of temporary immunity after run of anti-malicious software on computer nodes. Applied Mathematics and Computation 2007 190 2 1207 1212 2-s2.0-34250656571 10.1016/j.amc.2007.02.004 (Pubitemid 46935863)
5. Mishra B. K., Pandey S. K., Fuzzy epidemic model for the transmission of worms in computer network. Nonlinear Analysis: Real World Applications 2010 11 5 4335 4341 2-s2.0-77955517848 10.1016/j.nonrwa.2010.05.018
6. Ren J., Yang X., Yang L.-X., Xu Y., Yang F., A delayed computer virus propagation model and its dynamics. Chaos, Solitons and Fractals 2012 45 1 74 79 2-s2.0-82255191358 10.1016/j.chaos.2011.10.003
7. Ren J., Yang X., Zhu Q., Yang L.-X., Zhang C., A novel computer virus model and its dynamics. Nonlinear Analysis: Real World Applications 2012 13 1 376 384 2-s2.0-80052789013 10.1016/j.nonrwa.2011.07.048
8. Mishra B. K., Pandey S. K., Dynamic model of worms with vertical transmission in computer network. Applied Mathematics and Computation 2011 217 21 8438 8446 2-s2.0-79956061729 10.1016/j.amc.2011.03.041
9. Yuan H., Chen G., Network virus-epidemic model with the point-to-group information propagation. Applied Mathematics and Computation 2008 206 1 357 367 2-s2.0-55949131751 10.1016/j.amc.2008.09.025
10. Mishra B. K., Saini D. K., SEIRS epidemic model with delay for transmission of malicious objects in computer network. Applied Mathematics and Computation 2007 188 2 1476 1482 2-s2.0-34248175732 10.1016/j.amc.2006.11.012 (Pubitemid 46710039)
11. Wang F., Zhang Y., Wang C., Ma J., Moon S., Stability analysis of a SEIQV epidemic model for rapid spreading worms. Computers and Security 2010 29 4 410 418 2-s2.0-77951206095 10.1016/j.cose.2009.10.002
12. Mishra B. K., Jha N., SEIQRS model for the transmission of malicious objects in computer network. Applied Mathematical Modelling 2010 34 3 710 715 2-s2.0-70350369682 10.1016/j.apm.2009.06.011
13. Yang X., Yang L.-X., Towards the epidemiological modeling of computer viruses. Discrete Dynamics in Nature and Society 2012 2012 11 259671 10.1155/2012/259671
14. Yang L.-X., Yang X., Wen L., Liu J., A novel computer virus propagation model and its dynamics. International Journal of Computer Mathematics 2012 10.1080/00207160.2012.715388
15. Yang L.-X., Yang X., Zhu Q., Wen L., A computer virus model with graded cure rates. Nonlinear Analysis: Real World Applications 2012 10.1016/j.nonrwa.2012.07.005
16. Britten N. F., Essential Mathematical Biology 2003 Springer
17. Hassard B. D., Kazarinoff N. D., Wan Y. H., Theory and Applications of Hopf Bifurcation 1981 41 Cambridge, UK Cambridge University Press
18. Freedman H. L., Sree Hari Rao V., The trade-off between mutual interference and time lags in predator-prey systems. Bulletin of Mathematical Biology 1983 45 6 991 1004 2-s2.0-0001352326 10.1007/BF02458826
19. Hale J. K., Theory of Functional Differential Equations 1977 New York, NY, USA Springer