Stability and Hopf Bifurcation of a Delayed Epidemic Model of Computer Virus with Impact of Antivirus Software
In this paper, we investigate an SLBRS computer virus model with time delay and impact of antivirus software. The proposed model considers the entering rates of all computers since every computer can enter or leave the Internet easily. It has been observed that there is a stability switch and the sy...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2018/8239823 |
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| author | Zizhen Zhang Ranjit Kumar Upadhyay Dianjie Bi Ruibin Wei |
| author_facet | Zizhen Zhang Ranjit Kumar Upadhyay Dianjie Bi Ruibin Wei |
| author_sort | Zizhen Zhang |
| collection | DOAJ |
| description | In this paper, we investigate an SLBRS computer virus model with time delay and impact of antivirus software. The proposed model considers the entering rates of all computers since every computer can enter or leave the Internet easily. It has been observed that there is a stability switch and the system becomes unstable due to the effect of the time delay. Conditions under which the system remains locally stable and Hopf bifurcation occurs are found. Sufficient conditions for global stability of endemic equilibrium are derived by constructing a Lyapunov function. Formulae for the direction, stability, and period of the bifurcating periodic solutions are conducted with the aid of the normal form theory and center manifold theorem. Numerical simulations are carried out to analyze the effect of some of the parameters in the system on the dynamic behavior of the system. |
| format | Article |
| id | doaj-art-4b94f3e9d89d4ad49f7aba2119a21b89 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-4b94f3e9d89d4ad49f7aba2119a21b892025-02-03T01:02:14ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/82398238239823Stability and Hopf Bifurcation of a Delayed Epidemic Model of Computer Virus with Impact of Antivirus SoftwareZizhen Zhang0Ranjit Kumar Upadhyay1Dianjie Bi2Ruibin Wei3School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, ChinaDepartment of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, IndiaSchool of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, ChinaSchool of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, ChinaIn this paper, we investigate an SLBRS computer virus model with time delay and impact of antivirus software. The proposed model considers the entering rates of all computers since every computer can enter or leave the Internet easily. It has been observed that there is a stability switch and the system becomes unstable due to the effect of the time delay. Conditions under which the system remains locally stable and Hopf bifurcation occurs are found. Sufficient conditions for global stability of endemic equilibrium are derived by constructing a Lyapunov function. Formulae for the direction, stability, and period of the bifurcating periodic solutions are conducted with the aid of the normal form theory and center manifold theorem. Numerical simulations are carried out to analyze the effect of some of the parameters in the system on the dynamic behavior of the system.http://dx.doi.org/10.1155/2018/8239823 |
| spellingShingle | Zizhen Zhang Ranjit Kumar Upadhyay Dianjie Bi Ruibin Wei Stability and Hopf Bifurcation of a Delayed Epidemic Model of Computer Virus with Impact of Antivirus Software Discrete Dynamics in Nature and Society |
| title | Stability and Hopf Bifurcation of a Delayed Epidemic Model of Computer Virus with Impact of Antivirus Software |
| title_full | Stability and Hopf Bifurcation of a Delayed Epidemic Model of Computer Virus with Impact of Antivirus Software |
| title_fullStr | Stability and Hopf Bifurcation of a Delayed Epidemic Model of Computer Virus with Impact of Antivirus Software |
| title_full_unstemmed | Stability and Hopf Bifurcation of a Delayed Epidemic Model of Computer Virus with Impact of Antivirus Software |
| title_short | Stability and Hopf Bifurcation of a Delayed Epidemic Model of Computer Virus with Impact of Antivirus Software |
| title_sort | stability and hopf bifurcation of a delayed epidemic model of computer virus with impact of antivirus software |
| url | http://dx.doi.org/10.1155/2018/8239823 |
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