Stability and bifurcation of a computer virus propagation model with delay and incomplete antivirus ability

Mathematical Problems in Engineering

Volumn 2014, Issue , 2014, Pages

  Ren, Jianguo ^a   Xu, Yonghong ^a  

^a JIANGSU NORMAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER VIRUSES; LYAPUNOV FUNCTIONS;

COMPUTER VIRUS PROPAGATION; CRITICAL VALUE; EXISTENCE AND STABILITY; GLOBAL DYNAMICS; GLOBALLY ASYMPTOTICALLY STABLE; LYAPUNOV FUNCTIONALS; STABILITY AND BIFURCATION; SUITABLE CONDITIONS;

HOPF BIFURCATION;

EID: 84911869031     PISSN: 1024123X     EISSN: 15635147     Source Type: Journal    
DOI: 10.1155/2014/475934     Document Type: Article

References (24)

1. Kephart J. O., Hogg T., Huberman B. A., Dynamics of computational ecosystems. Physical Review A 1989 40 1 404 421 10.1103/PhysRevA.40.404 MR1004218 2-s2.0-0000808210
2. Wierman J. C., Marchette D. J., Modeling computer virus prevalence with a susceptible-infected-susceptible model with reintroduction. Computational Statistics and Data Analysis 2004 45 1 3 23 10.1016/S0167-9473(03)00113-0 ZBL05373937 2-s2.0-0442280819
3. Piqueira J. R. C., Araujo V. O., A modified epidemiological model for computer viruses. Applied Mathematics and Computation 2009 213 2 355 360 10.1016/j.amc.2009.03.023 MR2536658 ZBL1185.68133 2-s2.0-67349190516
4. Ren J. G., Yang X. F., Zhu Q. Y., Yang L. X., Zhang C., A novel computer virus model and its dynamics. Nonlinear Analysis: Real World Applications 2012 13 1 376 384 10.1016/j.nonrwa.2011.07.048 MR2846848 2-s2.0-80052789013
5. 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 10.1016/j.amc.2006.11.012 MR2335644 2-s2.0-34248175732
6. Draief M., Ganesh A., Massoulié L., Thresholds for virus spread on networks. The Annals of Applied Probability 2008 18 2 359 378 10.1214/07-AAP470 MR2398760 2-s2.0-48849111795
7. Mishra B. K., Jha N., SEIQRS model for the transmission of malicious objects in computer network. Applied Mathematical Modelling 2010 34 3 710 715 10.1016/j.apm.2009.06.011 MR2563351 2-s2.0-70350369682
8. 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 10.1016/j.amc.2007.02.004 ZBL1117.92052 2-s2.0-34250656571
9. Zhu Q., Yang X., Ren J., Modeling and analysis of the spread of computer virus. Communications in Nonlinear Science and Numerical Simulation 2012 17 12 5117 5124 10.1016/j.cnsns.2012.05.030 MR2960303 2-s2.0-84864413758
10. Gan C., Yang X., Liu W., Zhu Q., Zhang X., An epidemic model of computer viruses with vaccination and generalized nonlinear incidence rate. Applied Mathematics and Computation 2013 222 265 274 10.1016/j.amc.2013.07.055 MR3115867 2-s2.0-84882292275
11. Zhang C., Zhao Y., Wu Y., An impulse model for computer viruses. Discrete Dynamics in Nature and Society 2012 2012 13 260962 10.1155/2012/260962 2-s2.0-84864951946
12. Kondakci S., Epidemic state analysis of computers under malware attacks. Simulation Modelling Practice and Theory 2008 16 5 571 584 10.1016/j.simpat.2008.02.011 2-s2.0-42649108776
13. Wang F. G., Zhang Y. K., Wang C. G., Ma J. F., Moon S. J., Stability analysis of a SEIQV epidemic model for rapid spreading worms. Computers and Security 2010 29 4 410 418 10.1016/j.cose.2009.10.002 2-s2.0-77951206095
14. Song L. P., Jin Z., Sun G. Q., Zhang J., Han X., Influence of removable devices on computer worms: dynamic analysis and control strategies. Computers & Mathematics with Applications 2011 61 7 1823 1829 10.1016/j.camwa.2011.02.010 MR2782218 2-s2.0-79952988265
15. Amador J., The stochastic SIRA model for computer viruses. Applied Mathematics and Computation 2014 232 1112 1124 10.1016/j.amc.2014.01.125 MR3181343
16. Fuhrman K. M., Pinter G. A., Berges J. A., Dynamics of a virus-host model with an intrinsic quota. Mathematical and Computer Modelling 2011 53 5-6 716 730 10.1016/j.mcm.2010.10.010 MR2769446 ZBL1217.37080 2-s2.0-78751623568
17. Yang L., Yang X., Wen L., Liu J., A novel computer virus propagation model and its dynamics. International Journal of Computer Mathematics 2012 89 17 2307 2314 10.1080/00207160.2012.715388 MR2999808 ZBL1255.68058 2-s2.0-84867851680
18. Yang X., Yang L.-X., Towards the epidemiological modeling of computer viruses. Discrete Dynamics in Nature and Society 2012 2012 259671 10.1155/2012/259671 2-s2.0-84870050364
19. Yang L., Yang X., Zhu Q., Wen L., A computer virus model with graded cure rates. Nonlinear Analysis: Real World Applications 2013 14 1 414 422 10.1016/j.nonrwa.2012.07.005 MR2969844 2-s2.0-84866383289
20. Kafai Y. B., Understanding virtual epidemics: children's folk conceptions of a computer virus. Journal of Science Education and Technology 2008 17 6 523 529 10.1007/s10956-008-9102-x 2-s2.0-56749178276
21. Zuo Z. H., Zhu Q. X., Zhou M. T., On the time complexity of computer viruses. IEEE Transactions on Information Theory 2005 51 8 2962 2966 10.1109/TIT.2005.851780 MR2238002 2-s2.0-23844438042
22. Li D., Ma W., Asymptotic properties of a HIV-1 infection model with time delay. Journal of Mathematical Analysis and Applications 2007 335 1 683 691 10.1016/j.jmaa.2007.02.006 MR2340347 2-s2.0-34347272262
23. Naresh R., Tripathi A., Sharma D., A nonlinear AIDS epidemic model with screening and time delay. Applied Mathematics and Computation 2011 217 9 4416 4426 10.1016/j.amc.2010.10.036 MR2745124 2-s2.0-78650177284
24. Wang J., Zhang J., Jin Z., Analysis of an SIR model with bilinear incidence rate. Nonlinear Analysis: Real World Applications 2010 11 4 2390 2402 10.1016/j.nonrwa.2009.07.012 MR2661908 2-s2.0-77955768838