Stability Analysis of Delayed SIE Computer Virus Propagation Model

doi:10.3969/j.issn.1006-2475.2016.01.010

Abstract

Abstract: Based on the SIE computer virus propagation model, and considering that the anti-virus software needs a period to clean viruses and the external computers need some time to connect to network, a delayed computer virus propagation model is proposed. Critical value of the delay for local stability and occurrence of a Hopf bifurcation are obtained by regarding the delay as a bifurcation parameter and analyzing the distribution of the associated characteristic equation’s roots. Finally, numerical simulations are carried out to support the theoretical predictions. It is proved that the viruses’ propagation can be controlled effectively by postponing occurrence of the Hopf bifurcation.


Key words: computer virus, SIE model, Hopf bifurcation, stability

CLC Number:

TP309.5

SONG Lei1, WANG Chun-lei2. Stability Analysis of Delayed SIE Computer Virus Propagation Model[J]. Computer and Modernization, doi: 10.3969/j.issn.1006-2475.2016.01.010.

References

［1］ Szor P. The Art of Computer Virus Research and Defense［M］. US:Pearson Education, 2005.
［2］ Kephart J O, White S R. Directed-graph epidemiological models of computer viruses［C］// Procceedings of the 1991 IEEE Computer Society Symposium on Research in Security and Privacy. 1991:343-359．
［3］张丽萍,洪龙,王惠南. 一种网络病毒传播的时滞微分方程模型［J］. 南京邮电大学学报(自然科学版), 2007,27(5):78-83.
［4］冯丽萍,王鸿斌,冯素琴. 基于生物学原理的计算机网络病毒传播模型［J］. 计算机工程, 2011,37(11):155-157.
［5］肖丽,包骏杰,冯丽萍. 一种新的计算机病毒模型的稳定性分析［J］. 湘潭大学自然科学学报， 2012,34(2):94-96.
［6］叶晓梦,杨小帆. 基于两阶段免疫接种的SIRS计算机病毒传播模型［J］. 计算机应用, 2013,33(3):739-742.〖HJ1.35mm〗
［7］彭梅,李传东,何兴. 基于直接免疫的SEIR计算机病毒传播模型［J］. 重庆师范大学学报(自然科学版), 2013,30(1):77-80.
［8］盖绍婷,唐功友,于浩,等. 带有免疫的计算机病毒传播模型的稳定性［J］. 中国海洋大学学报， 2013,43(10):110-114.
［9］冯丽萍，王鸿斌，冯素琴. 改进的SIR计算机病毒传播模型［J］. 计算机应用, 2011,31(7):1891-1893．
［10］Chen Jingyun, Yang Xiaofan, Gan Chenquan. Propagation of computer virus under the influnce of external computers: A dynamical model ［J］. Journal of Information & Computational Science, 2013,10(16):5275-5282.
［11］杨斌. 具有时滞的SIQR计算机病毒模型分析［J］. 重庆工商大学学报（自然科学版）, 2013,30(9):70-73.
［12］Ren Jianguo, Yang Xiaofan, Yang Luxing, et al. A delayed computer virus propagation model with its dynamics［J］. Chaos Solitons and Fractals, 2012,45(1):74-79.
［13］Feng Liping, Liao Xiaofeng, Li Huaqing, et al. Hopf bifurcation analysis of a delayed viral infection model in computer networks［J］. Mathematical and Computer Modelling, 2012,56(7-8):167-179.
［14］Mishra B K, Saini D K. SEIRS epidemic model with delay for transmission of malicious objects in computer network［J］. Applied Mathematics and Computation, 2007,188(2):1476-1482.
［15］Muroya Y, Enatsu Y, Li Huaxing. Global stability of a delayed SIRS computer virus propagation model［J］. International Journal of Computer Mathematics, 2014,91(3):347-367.
［16］Hassard B D, Kazarinoff N D, Wan Y H. Theory and Applications of Hopf Bifurcation［M］. Cambridge University Press, 1981.

[1]	PENG Sui, XU Liang, ZHANG Zhi-qiang, LOU Yuan-yuan, YU Hao, QIN Xiao-hui. Probabilistic Voltage Stability Evaluation Algorithm Based on Mixed Vine Copula and ILHS [J]. Computer and Modernization, 2022, 0(12): 6-12.
[2]	HUI Fei, XI Hui, ZHANG Kai-wang, WEI Si. Car-following Model Considering Multi-preceding Vehicles’ Information Feedback and Backward Looking Effect [J]. Computer and Modernization, 2022, 0(08): 70-77.
[3]	CHEN Peng-fei1，2， FENG Jin-zhi1，2， LIU Shu-fan1，2， WANG Bin1，2. Research on Car’s Suspension Performance Based on Computer Virtual Prototype Technology [J]. Computer and Modernization, 2019, 0(09): 112-.
[4]	LUO Min1,2, LI Chang-you3, DAI Huan1,2. Using SPSS and Matlab to Study Stability of Rodent Community [J]. Computer and Modernization, 2017, 0(6): 116-121.
[5]	SONG Lei1, WANG Chun-lei2. Hopf Bifurcation of Delayed Computer Virus Propagation Model [J]. Computer and Modernization, 2016, 0(11): 79-82.
[6]	CAO Wen-jun, XUE Shan-liang. An Improved AODV Routing Protocol for Urban Vehicular Ad Hoc Networks [J]. Computer and Modernization, 2016, 251(07): 98-102.
[7]	CAI Ya-su. Improved Optimal Link State Routing Protocol Algorithm [J]. Computer and Modernization, 2014, 0(8): 106-109.
[8]	LIU Wei. Dynamics and Stability of Trust Model in ECommerce [J]. Computer and Modernization, 2014, 0(4): 138-142.
[9]	HOU Ning1,2， FEI Shu-min2. Ceramic Kiln Temperature Control Based on Predictive Functional Control Algorithm [J]. Computer and Modernization, 2014, 0(11): 106-109.
[10]	ZHAO Chun-li;WANG Ai-hui;. Precision Position Control for IPMC Artificial Muscle Based on Operator [J]. Computer and Modernization, 2012, 203(7): 68-71.
[11]	CHEN Dong-li;TAN Guan-zheng;WU Gao-liang. Analysis of NCS Network Protocol [J]. Computer and Modernization, 2012, 1(6): 85-88.
[12]	LI Qi;WANG Bo. Positioning Algorithm Using Digital Camera Based on Linear Model [J]. Computer and Modernization, 2012, 1(1): 57-60,7.
[13]	WU Shi-yun;WANG Yi-yan. Typical Applications of Matlab for Teaching “Digital Signal Processing” [J]. Computer and Modernization, 2011, 1(8): 185-189.
[14]	WANG Ji-bing;WU Wei-hua. Satellite Formation Keeping in Considering Nonlinearity [J]. Computer and Modernization, 2009, 1(7): 159-162.