Virus propagation model and stability analysis of heterogeneous backup network

doi:10.11772/j.issn.1001-9081.2022030409

Journal of Computer Applications ›› 2023, Vol. 43 ›› Issue (4): 1176-1182.DOI: 10.11772/j.issn.1001-9081.2022030409

• Cyber security • Previous Articles

Virus propagation model and stability analysis of heterogeneous backup network

Yingqi LI, Weifeng JI(), Jiang WENG, Xuan WU, Xiuyu SHEN, Yan SUN

School of Information and Navigation，Air Force Engineering University，Xi’an Shaanxi 710077，China

Received:2022-04-02 Revised:2022-06-07 Accepted:2022-06-22 Online:2023-04-11 Published:2023-04-10
Contact: Weifeng JI
About author:LI Yingqi， born in 1999， M. S. candidate. His research interests include complex network， game theory.
WENG Jiang， born in 1986， Ph. D.， lecturer. His research interests include cryptography.
WU Xuan， born in 1998， M. S. candidate. His research interests include virtual network， 5G.
SHEN Xiuyu， born in 1993， M. S. candidate. His research interests include cyberspace security.
SUN Yan， born in 1995， M. S. His research interests include moving target defense.
Supported by:
Natural Science Foundation of China(61902426)

异构备份网络的病毒传播模型及稳定性分析

李映岐, 姬伟峰(), 翁江, 吴玄, 申秀雨, 孙岩

空军工程大学信息与导航学院，西安 710077

通讯作者: 姬伟峰
作者简介:李映岐（1999—），男，河南南阳人，硕士研究生，主要研究方向：复杂网络、博弈论；
翁江（1986—），男，陕西西安人，讲师，博士，主要研究方向：密码学；
吴玄（1998—），男，安徽阜阳人，硕士研究生，主要研究方向：虚拟网络、5G；
申秀雨（1993—），男，河北馆陶人，硕士研究生，主要研究方向：网络空间安全；
孙岩（1995—），男，黑龙江北安人，硕士，主要研究方向：移动目标防御。
基金资助:
国家自然科学基金资助项目(61902426)

Abstract

Abstract:

Concerning the secondary attack problem of virus in cloud computing， data center and other virtual network-based environments， the virus propagation and immune mechanism under the background of dynamic platform defense was studied， and a heterogeneous backup based network virus defense method was proposed. Firstly， the process of secondary attack of redundant backup was analyzed， and the law of virus action was summarized. At the same time， combined with the idea of dynamic platform defense， the heterogeneous platform state node was introduced， and a Susceptible-Escaped-Infected-Removed-Heterogeneous-Susceptible （SEIRHS） virus propagation model was proposed. Secondly， the local stability at the equilibrium point of the model was proved by using the Routh-Hurwitz stability criterion， and the basic reproductive number was solved. Finally， the proposed model was compared with the traditional Susceptible-Infected-Removed （SIR） and Susceptible-Escaped-Infected-Removed （SEIR） models through simulation analysis， the stability of the model was verified， and the effect of virus propagation influencing factors on virus spread scale was discussed. The simulation results show that the proposed model can objectively reflect the propagation law of virus in the network， and effectively improve the network’s defense effect against the virus by reducing the node degree， increasing the Infected-Heterogeneous （I-H） state transition probability， and reducing the probability of being hidden by the virus during backup， etc.

Key words: heterogeneous backup, virus propagation, dynamic platform defense, stability analysis, network defense

摘要：

针对云计算、数据中心等基于虚拟网络的环境中病毒二次攻击的问题，研究了平台动态防御背景下的病毒传播及免疫机理，并提出一种异构备份式的网络病毒防御方法。首先，分析冗余备份发生二次攻击的过程，并总结病毒作用规律；同时，结合平台动态防御的思想，引入异构平台状态节点，并提出了易感?潜伏?感染?免疫?异构?易感（SEIRHS）病毒传播模型；其次，运用劳斯?赫尔维茨稳定性判据证明了模型平衡点处的局部稳定性，并求解基本再生数；最后，通过实验仿真分析对比了所提模型与传统易感?感染?免疫（SIR）模型、易感?潜伏?感染?免疫（SEIR）模型，并验证了所提模型的稳定性，探讨了病毒传播影响因子对病毒扩散规模的作用结果。仿真结果表明，所提模型能客观反映病毒在网络中的传播规律，并通过降低节点度、提高感染?异构（I-H）状态转移概率、降低备份时已被病毒潜伏的概率等有效提升网络对病毒的防御效果。

关键词: 异构备份, 病毒传播, 平台动态防御, 稳定性分析, 网络防御

CLC Number:

TP393

Yingqi LI, Weifeng JI, Jiang WENG, Xuan WU, Xiuyu SHEN, Yan SUN. Virus propagation model and stability analysis of heterogeneous backup network[J]. Journal of Computer Applications, 2023, 43(4): 1176-1182.

李映岐, 姬伟峰, 翁江, 吴玄, 申秀雨, 孙岩. 异构备份网络的病毒传播模型及稳定性分析[J]. 《计算机应用》唯一官方网站, 2023, 43(4): 1176-1182.

Figures/Tables 8

Fig. 1 SEIRHS model

Fig. 2 Comparison of state variable evolution of different models

Tab. 1 Initial state grouping

分组序号	不同状态节点数
分组序号	易感节点	潜伏节点	感染节点
1	950	0	50
2	900	0	100
3	900	50	50
4	800	0	200

Fig. 3 Nodes of different initial groups changing with time

Fig. 4 Node states corresponding to different k

Fig. 5 Node states corresponding to different θ

Fig. 6 Node states corresponding to different a and b

Fig. 7 Node states corresponding to b=0

References 19

1	王斌锋，苏金树，陈琳. 云计算数据中心网络设计综述［J］. 计算机研究与发展， 2016， 53（9）： 2085-2106. 10.7544/issn1000-1239.2016.20150962
	WANG B F， SU J S， CHEN L. Review of the design of data center network for cloud computing［J］. Journal of Computer Research and Development， 2016， 53（9）： 2085-2106. 10.7544/issn1000-1239.2016.20150962
2	汪小帆，李翔，陈关荣. 复杂网络理论及其应用［M］. 北京：清华大学出版社， 2006： 72-98.
	WANG X F， LI X， CHEN G R. Complex Network Theory and Its Application［M］. Beijing： Tsinghua University Press， 2006： 72-98.
3	XIE Y K， WANG Z. Transmission dynamics， global stability and control strategies of a modified SIS epidemic model on complex networks with an infective medium［J］. Mathematics and Computers in Simulation， 2021， 188：23-34. 10.1016/j.matcom.2021.03.029
4	王刚，冯云，陆世伟，等. 多操作系统异构网络的病毒传播模型和安全性能优化策略［J］. 电子与信息学报， 2020， 42（4）：972-980. 10.11999/JEIT190360
	WANG G， FENG Y， LU S W， et al. Virus propagation model and security performance optimization strategy of multi-operating system heterogeneous network［J］. Journal of Electronics and Information Technology， 2020， 42（4）： 972-980. 10.11999/JEIT190360
5	WANG X， NI W， ZHENG K F， et al. Virus propagation modeling and convergence analysis in large-scale networks［J］. IEEE Transactions on Information Forensics and Security， 2016， 11（10）：2241-2254. 10.1109/tifs.2016.2581305
6	张伟，王汝传，李鹏. 基于云安全环境的蠕虫传播模型［J］. 通信学报， 2012， 33（4）： 17-24. 10.3969/j.issn.1000-436X.2012.04.003
	ZHANG W， WANG R C， LI P. Worm propagation modeling in cloud security［J］. Journal on Communications， 2012， 33（4）：17-24. 10.3969/j.issn.1000-436X.2012.04.003
7	许荣飞，范通让. 云计算网络中的主动免疫隔离传播模型［J］. 计算机工程， 2012， 38（19）：96-99. 10.3969/j.issn.1000-3428.2012.19.027
	XU R F， FAN T R. Active immunization and isolation propagation model in cloud computing network［J］. Computer Engineering， 2012， 38（19）： 96-99. 10.3969/j.issn.1000-3428.2012.19.027
8	GAN C Q， FENG Q D， ZHANG X L， et al. Dynamical propagation model of malware for cloud computing security［J］. IEEE Access， 2020， 8：20325-20333. 10.1109/access.2020.2968916
9	HOAN L V C， AKINLAR M A， INÇ M， et al. A new fractional-order compartmental disease model［J］. Alexandria Engineering Journal， 2020， 59（5）： 3187-3196. 10.1016/j.aej.2020.07.040
10	YANG F F， ZHANG Z Z. Hopf bifurcation analysis of SEIR-KS computer virus spreading model with two-delay［J］. Results in Physics， 2021， 24： No.104090. 10.1016/j.rinp.2021.104090
11	ALOTA C P， PILAR-ARCEO C P C， DE LOS REYES V A A. An edge-based model of SEIR epidemics on static random networks［J］. Bulletin of Mathematical Biology， 2020， 82（7）： No.96. 10.1007/s11538-020-00769-0
12	TORQUATO M， VIEIRA M. Moving target defense in cloud computing： a systematic mapping study［J］. Computers and Security， 2020， 92： No.101742. 10.1016/j.cose.2020.101742
13	周余阳，程光，郭春生，等. 移动目标防御的攻击面动态转移技术研究综述［J］. 软件学报， 2018， 29（9）：2799-2820.
	ZHOU Y Y， CHENG G， GUO C S， et al. Survey on attack surface dynamic transfer technology based on moving target defense［J］. Journal of Software， 2018， 29（9）：2799-2820.
14	季新生，赵硕，艾健健，等. 异构备份式的虚拟网映射方法研究［J］. 电子与信息学报， 2018， 40（5）： 1087-1093. 10.11999/JEIT170730
	JI X S， ZHAO S， AI J J， et al. Research on heterogeneous-backup virtual network embedding［J］. Journal of Electronics and Information Technology， 2018， 40（5）： 1087-1093. 10.11999/JEIT170730
15	关治洪，亓玉娟，姜晓伟，等. 基于复杂网络的病毒传播模型及其稳定性［J］. 华中科技大学学报（自然科学版）， 2011， 39（1）：114-117.
	GUAN Z H， QI Y J， JIANG X W， et al. Virus propagation dynamic model and stability on complex networks［J］. Journal of Huazhong University of Science and Technology （Natural Science Edition）， 2011， 39（1）：114-117.
16	虞亚平，刘玉梅，李大治. 矩阵具有正实部特征值的判定［J］. 数学的实践与认识， 2009， 39（3）：231-234.
	YU Y P， LIU Y M， LI D Z. The criteria for positive real part of matrix eigenvalue［J］. Mathematics in Practice and Theory， 2009， 39（3）：231-234.
17	TANG W， LIU Y J， CHEN Y L， et al. SLBRS： network virus propagation model based on safety entropy［J］. Applied Soft Computing， 2020， 97（Pt A）： No.106784. 10.1016/j.asoc.2020.106784
18	HOSSEINI S， AZGOMI M A. Dynamical analysis of a malware propagation model considering the impacts of mobile devices and software diversification［J］. Physica A： Statistical Mechanics and its Applications， 2019， 526： No.120925. 10.1016/j.physa.2019.04.161
19	宋娟，潘欢，马晓. 带安全检测的云数据中心虚拟机迁移策略［J］. 重庆邮电大学学报（自然科学版）， 2021， 33（2）：311-318.
	SONG J， PAN H， MA X. A virtual machine migration strategy with secure checking for cloud data centers［J］. Journal of Chongqing University of Posts and Telecommunications （Natural Science Edition）， 2021， 33（2）：311-318.

[1]	Kaiwang ZHANG, Fei HUI, Guoxiang ZHANG, Qi SHI, Zhizhong LIU. Car-following model of intelligent connected vehicles based on time-delayed velocity difference and velocity limit [J]. Journal of Computer Applications, 2022, 42(9): 2936-2942.
[2]	WU Sanzhu, LI Peng, WU Sanbin. Virus propagation suppression model in mobile wireless sensor networks [J]. Journal of Computer Applications, 2020, 40(1): 129-135.
[3]	JI Yi, SHI Xin, ZHAO Xiangmo. Car-following model for intelligent connected vehicles based on multiple headway information fusion [J]. Journal of Computer Applications, 2019, 39(12): 3685-3690.
[4]	LI Hongbo JIANG Lin WANG Haitang. Simulation on low speed stable operation of full-order observer for induction motor [J]. Journal of Computer Applications, 2014, 34(4): 1213-1216.

Virus propagation model and stability analysis of heterogeneous backup network

异构备份网络的病毒传播模型及稳定性分析

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 8

References 19

Related Articles 4

Recommended Articles

Metrics