基于扩展传染病模型的异质传感网恶意程序传播建模与分析
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摘要
为揭示异质传感网恶意程序传播规律,提出一种基于扩展传染病理论的异质传感网恶意程序传播建模与分析方法。依据异质传感器节点状态的分析,扩展传统SIR(Susceptible-Infected-Removed)传染病模型,得到异质传感器节点状态转换关系模型。以一个异质传感器节点与其通信的节点数反映其异质特性,使用微分方程形式建立能反映异质传感网恶意程序传播过程中具有不同度的异质传感器节点状态动态变化的HSIORD(Heterogeneous Susceptible-Infected-isOlated-Removed-Deceased)模型。依据稳定点的数学特性,计算该模型的稳定点。采用下一代矩阵法计算该模型的基本再生数,并证明该模型稳定点的稳定性。通过实验仿真,验证了异质传感网恶意程序消亡的理论依据,为管理员有效抑制异质传感网恶意程序传播提供理论指导。
To disclose rules of malware spread in Heterogeneous Sensor Networks(HSNs),we propose a method to model and analyze the process of HSN malware spread based on the extended epidemic model. According to analyses on statuses of Heterogeneous sensor Nodes(HNs),we extend the traditional Susceptible-Infected-Removed(SIR)model and attain a model expressing transition relations among all HN statuses. Based on the heterogeneous character that is reflected by the communication node number of an HN,we employ differential equations to construct a Heterogeneous Susceptible-Infected-isOlated-Removed-Deceased(HSIORD)model,which presents dynamic status changes of HNs with different degrees during the process of malware spread in HSNs. We then compute the equilibrium points of the HSIORD model in the light of the mathematical character of an equilibrium point. Further,we compute the basic regeneration number of the HSIORD model using the next generation matrix,and prove the stability of the equilibrium point to indicate that malware in HSNs will die out. Via experimental simulations,we verify the theoretical results about the stability,which can provide administrators with theoretical guidance on suppressing malware spread in HSNs.
To disclose rules of malware spread in Heterogeneous Sensor Networks(HSNs),we propose a method to model and analyze the process of HSN malware spread based on the extended epidemic model. According to analyses on statuses of Heterogeneous sensor Nodes(HNs),we extend the traditional Susceptible-Infected-Removed(SIR)model and attain a model expressing transition relations among all HN statuses. Based on the heterogeneous character that is reflected by the communication node number of an HN,we employ differential equations to construct a Heterogeneous Susceptible-Infected-isOlated-Removed-Deceased(HSIORD)model,which presents dynamic status changes of HNs with different degrees during the process of malware spread in HSNs. We then compute the equilibrium points of the HSIORD model in the light of the mathematical character of an equilibrium point. Further,we compute the basic regeneration number of the HSIORD model using the next generation matrix,and prove the stability of the equilibrium point to indicate that malware in HSNs will die out. Via experimental simulations,we verify the theoretical results about the stability,which can provide administrators with theoretical guidance on suppressing malware spread in HSNs.
引文
[1] 罗军舟,杨明,凌振,等.网络空间安全体系与关键技术[J].中国科学(信息科学),2016,46(8):939-968.
[2] 张焕国,韩文报,来学嘉,等.网络空间安全综述[J].中国科学(信息科学),2016,46(2):125-164.
[3] 沈士根,黄龙军,范恩,等.受恶意程序传染的WSNs可生存性评估[J].传感技术学报,2016,29(7):1083-1089.
[4] 沈士根,刘建华,曹奇英.博弈论与无线传感器网络安全[M].清华大学出版社,2016.
[5] Shen S,Ma H,Fan E,et al.A Non-Cooperative Non-Zero-Sum Game-Based Dependability Assessment of Heterogeneous WSNs with Malware Diffusion[J].Journal of Network and Computer Applications,2017,91:26-35.
[6] 沈士根,周海平,黄龙军,等.基于最优反应均衡的传感网恶意程序传播抑制方法[J].传感技术学报,2017,30(10):1589-1595.
[7] 沈士根,黄龙军,周海平,等.面向恶意程序传播的异质WSNs稳态可用度评估[J].传感技术学报,2017,30(7):1100-1105.
[8] 沈士根,范恩,胡珂立,等.面向恶意程序传播的传感网可靠度评估[J].电子学报,2018,46(1):75-81.
[9] 沈士根,冯晟,周海平,等.基于云计算和动态贝叶斯博弈的WSN恶意程序传播优化抑制方法[J].电信科学,2018,34(9):78-86.
[10] 付帅,王长广,马建峰.无线传感器网络中恶意程序的传播模型[J].计算机工程,2011,37(3):129-131.
[11] 王小明,李成博,李英姝.移动无线传感网恶意数据包传播随机模型[J].电子与信息学报,2013,35(6):1290-1297.
[12] 胡金涛,宋玉蓉.基于旋转有向天线的无线传感器网络恶意软件传播模型[J].计算机工程,2016,42(4):119-125.
[13] 曹玉林,王小明,何早波.移动无线传感网中恶意软件传播的最优安全策略[J].电子学报,2016,44(8):1851-1857.
[14] 周海平,沈士根,黄龙军,等.基于博弈论的无线传感器网络恶意程序传播模型[J].电信科学,2018,34(11):67-76.
[15] Keshri N,Gupta A,Mishra B K.Impact of Reduced Scale Free Network on Wireless Sensor Network[J].Physica A:Statistical Mechanics and its Applications,2016,463:236-245.
[16] Nowzari C,Preciado V M,Pappas G J.Optimal Resource Allocation for Control of Networked Epidemic Models[J].IEEE Transactions on Control of Network Systems,2017,4(2):159-169.
[17] Eshghi S,Khouzani M H R,Sarkar S,et al.Optimal Patching in Clustered Malware Epidemics[J].IEEE/ACM Transactions on Networking,2016,24(1):283-298.
[18] Yang L,Draief M,Yang X.Heterogeneous Virus Propagation in Networks:A Theoretical Study[J].Mathematical Methods in the Applied Sciences,2017,40(5):1396-1413.
[19] Van Den Driessche P,Watmough J.Reproduction Numbers and Sub-Threshold Endemic Equilibria for Compartmental Models of Disease Transmission[J].Mathematical Biosciences,2002,180(1/2):29-48.
[20] Teschl G.Ordinary Differential Equations and Dynamical Systems.Providence:American Mathematical Society,2012.
[21] Li C H,Tsai C C,Yang S Y.Analysis of Epidemic Spreading of an SIRS Model in Complex Heterogeneous Networks[J].Communications in Nonlinear Science and Numerical Simulation,2014,19(4):1042-1054.
[22] Zhang H,Fu X.Spreading of Epidemics on Scale-Free Networks with Nonlinear Infectivity[J].Nonlinear Analysis:Theory,Methods and Applications,2009,70(9):3273-3278.
[23] Zhu G,Fu X,Chen G.Global Attractivity of a Network-Based Epidemic SIS Model with Nonlinear Infectivity[J].Communications in Nonlinear Science and Numerical Simulation,2012,17(6):2588-2594.沈士根(1974-),男,汉族,绍兴文理学院计算机科学与工程系教授,博士,主要研究方向为无线传感器网络、物联网、博弈论,shigens@126.com;周海平(1977-),男,汉族,绍兴文理学院计算机科学与工程系教授,博士,主要研究方向为复杂网络、推荐算法、博弈论,hpzhou2885@163.com;刘建华(1978-),男,汉族,绍兴文理学院计算机科学与工程系副教授,博士,主要研究领域为无线传感器网络、云计算、博弈论,ljh_541@163.com;曹奇英(1960-),男,汉族,东华大学计算机科学与技术学院教授,博士生导师,博士,主要研究方向为普适计算、智能信息处理,caoqiying@dhu.edu.cn。
[2] 张焕国,韩文报,来学嘉,等.网络空间安全综述[J].中国科学(信息科学),2016,46(2):125-164.
[3] 沈士根,黄龙军,范恩,等.受恶意程序传染的WSNs可生存性评估[J].传感技术学报,2016,29(7):1083-1089.
[4] 沈士根,刘建华,曹奇英.博弈论与无线传感器网络安全[M].清华大学出版社,2016.
[5] Shen S,Ma H,Fan E,et al.A Non-Cooperative Non-Zero-Sum Game-Based Dependability Assessment of Heterogeneous WSNs with Malware Diffusion[J].Journal of Network and Computer Applications,2017,91:26-35.
[6] 沈士根,周海平,黄龙军,等.基于最优反应均衡的传感网恶意程序传播抑制方法[J].传感技术学报,2017,30(10):1589-1595.
[7] 沈士根,黄龙军,周海平,等.面向恶意程序传播的异质WSNs稳态可用度评估[J].传感技术学报,2017,30(7):1100-1105.
[8] 沈士根,范恩,胡珂立,等.面向恶意程序传播的传感网可靠度评估[J].电子学报,2018,46(1):75-81.
[9] 沈士根,冯晟,周海平,等.基于云计算和动态贝叶斯博弈的WSN恶意程序传播优化抑制方法[J].电信科学,2018,34(9):78-86.
[10] 付帅,王长广,马建峰.无线传感器网络中恶意程序的传播模型[J].计算机工程,2011,37(3):129-131.
[11] 王小明,李成博,李英姝.移动无线传感网恶意数据包传播随机模型[J].电子与信息学报,2013,35(6):1290-1297.
[12] 胡金涛,宋玉蓉.基于旋转有向天线的无线传感器网络恶意软件传播模型[J].计算机工程,2016,42(4):119-125.
[13] 曹玉林,王小明,何早波.移动无线传感网中恶意软件传播的最优安全策略[J].电子学报,2016,44(8):1851-1857.
[14] 周海平,沈士根,黄龙军,等.基于博弈论的无线传感器网络恶意程序传播模型[J].电信科学,2018,34(11):67-76.
[15] Keshri N,Gupta A,Mishra B K.Impact of Reduced Scale Free Network on Wireless Sensor Network[J].Physica A:Statistical Mechanics and its Applications,2016,463:236-245.
[16] Nowzari C,Preciado V M,Pappas G J.Optimal Resource Allocation for Control of Networked Epidemic Models[J].IEEE Transactions on Control of Network Systems,2017,4(2):159-169.
[17] Eshghi S,Khouzani M H R,Sarkar S,et al.Optimal Patching in Clustered Malware Epidemics[J].IEEE/ACM Transactions on Networking,2016,24(1):283-298.
[18] Yang L,Draief M,Yang X.Heterogeneous Virus Propagation in Networks:A Theoretical Study[J].Mathematical Methods in the Applied Sciences,2017,40(5):1396-1413.
[19] Van Den Driessche P,Watmough J.Reproduction Numbers and Sub-Threshold Endemic Equilibria for Compartmental Models of Disease Transmission[J].Mathematical Biosciences,2002,180(1/2):29-48.
[20] Teschl G.Ordinary Differential Equations and Dynamical Systems.Providence:American Mathematical Society,2012.
[21] Li C H,Tsai C C,Yang S Y.Analysis of Epidemic Spreading of an SIRS Model in Complex Heterogeneous Networks[J].Communications in Nonlinear Science and Numerical Simulation,2014,19(4):1042-1054.
[22] Zhang H,Fu X.Spreading of Epidemics on Scale-Free Networks with Nonlinear Infectivity[J].Nonlinear Analysis:Theory,Methods and Applications,2009,70(9):3273-3278.
[23] Zhu G,Fu X,Chen G.Global Attractivity of a Network-Based Epidemic SIS Model with Nonlinear Infectivity[J].Communications in Nonlinear Science and Numerical Simulation,2012,17(6):2588-2594.沈士根(1974-),男,汉族,绍兴文理学院计算机科学与工程系教授,博士,主要研究方向为无线传感器网络、物联网、博弈论,shigens@126.com;周海平(1977-),男,汉族,绍兴文理学院计算机科学与工程系教授,博士,主要研究方向为复杂网络、推荐算法、博弈论,hpzhou2885@163.com;刘建华(1978-),男,汉族,绍兴文理学院计算机科学与工程系副教授,博士,主要研究领域为无线传感器网络、云计算、博弈论,ljh_541@163.com;曹奇英(1960-),男,汉族,东华大学计算机科学与技术学院教授,博士生导师,博士,主要研究方向为普适计算、智能信息处理,caoqiying@dhu.edu.cn。
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