Modeling and analysis of the effect of network eigenvalue on viral spread

This paper aims to study the effect of network eigenvalue on the spread of computer virus. To this end, a node-based propagation model, which incorporates the impact of external computers, is proposed. A dynamical analysis of the model shows that the network eigenvalue plays a key role in controlling viral spread. Specifically, the global stability of virus-free equilibrium and the global attractivity of viral equilibrium depend on the value of the maximum eigenvalue of the propagation network. This result reveals that computer virus would tend to extinction or persist depending on network eigenvalue. Finally, some numerical examples are given to illustrate the main results.

[1]  Lu-Xing Yang,et al.  The Impact of the Network Topology on the Viral Prevalence: A Node-Based Approach , 2015, PloS one.

[2]  Chenquan Gan,et al.  The spread of computer virus under the effect of external computers , 2013 .

[3]  R. May,et al.  How Viruses Spread Among Computers and People , 2001, Science.

[4]  Xiaofan Yang,et al.  The spread of computer viruses over a reduced scale-free network , 2014 .

[5]  Stefano Longhi.  Spiral waves in optical parametric oscillators , 2001 .

[6]  Bimal Kumar Mishra,et al.  Dynamic model of worms with vertical transmission in computer network , 2011, Appl. Math. Comput..

[7]  George J. Pappas,et al.  Stability analysis of generalized epidemic models over directed networks , 2014, 53rd IEEE Conference on Decision and Control.

[8]  Chunming Zhang,et al.  A New Model for Capturing the Spread of Computer Viruses on Complex-Networks , 2013 .

[9]  Jiming Liu,et al.  A novel computer virus propagation model and its dynamics , 2012, Int. J. Comput. Math..

[10]  Wan-Tong Li,et al.  Global stability of delayed Hopfield neural networks underdynamical thresholds , 2005 .

[11]  Horst R. Thieme,et al.  Asymptotically Autonomous Differential Equations in the Plane , 1993 .

[12]  Alessandro Vespignani,et al.  Immunization of complex networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  José Roberto Castilho Piqueira,et al.  A modified epidemiological model for computer viruses , 2009, Appl. Math. Comput..

[14]  Faryad Darabi Sahneh,et al.  Optimal information dissemination in epidemic networks , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[15]  C. Scoglio,et al.  An individual-based approach to SIR epidemics in contact networks. , 2011, Journal of theoretical biology.

[16]  Navnit Jha,et al.  SEIQRS model for the transmission of malicious objects in computer network , 2010 .

[17]  Paul Waltman,et al.  The Theory of the Chemostat: Dynamics of Microbial Competition , 1995 .

[18]  Shuo Zhu,et al.  Optimal Acquisition and Inventory Control for a Remanufacturing System , 2013 .

[19]  A. Louisa,et al.  コロイド混合体における有効力 空乏引力から集積斥力へ | 文献情報 | J-GLOBAL 科学技術総合リンクセンター , 2002 .

[20]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[21]  M. Markus,et al.  On-off intermittency and intermingledlike basins in a granular medium. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Jeffrey O. Kephart,et al.  Directed-graph epidemiological models of computer viruses , 1991, Proceedings. 1991 IEEE Computer Society Symposium on Research in Security and Privacy.

[23]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[24]  Piet Van Mieghem,et al.  Epidemic processes in complex networks , 2014, ArXiv.

[25]  R. Robinson,et al.  An Introduction to Dynamical Systems: Continuous and Discrete , 2004 .

[26]  Chenquan Gan,et al.  Propagation of computer virus under the influences of infected external computers and removable storage media , 2014 .

[27]  Richard R. Brooks,et al.  A note on the spread of worms in scale-free networks , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[28]  Shun-Yan Ren,et al.  Stability and Passivity of Spatially and Temporally Complex Dynamical Networks with Time-Varying Delays , 2014 .

[29]  S. Bornholdt,et al.  Scale-free topology of e-mail networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Lu-Xing Yang,et al.  A mixing propagation model of computer viruses and countermeasures , 2013 .

[31]  P. Van Mieghem,et al.  Virus Spread in Networks , 2009, IEEE/ACM Transactions on Networking.

[32]  Christos Faloutsos,et al.  Epidemic spreading in real networks: an eigenvalue viewpoint , 2003, 22nd International Symposium on Reliable Distributed Systems, 2003. Proceedings..

[33]  Yurii B. Shvetsov,et al.  Common Genetic Variation In Cellular Transport Genes and Epithelial Ovarian Cancer (EOC) Risk , 2015, PloS one.

[34]  A. Barabasi,et al.  Halting viruses in scale-free networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Kyomin Jung,et al.  Modeling Multi-state Diffusion Process in Complex Networks: Theory and Applications , 2013, 2013 International Conference on Signal-Image Technology & Internet-Based Systems.

[36]  Jianguo Ren,et al.  Stability and Bifurcation of a Computer Virus Propagation Model with Delay and Incomplete Antivirus Ability , 2014 .

[37]  Chenquan Gan,et al.  The combined impact of external computers and network topology on the spread of computer viruses , 2014, Int. J. Comput. Math..

[38]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[39]  J. Yorke,et al.  A Deterministic Model for Gonorrhea in a Nonhomogeneous Population , 1976 .

[40]  Chenquan Gan,et al.  Epidemics of computer viruses: A complex-network approach , 2013, Appl. Math. Comput..

[41]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[42]  Chenquan Gan,et al.  Propagation of computer virus both across the Internet and external computers: A complex-network approach , 2014, Commun. Nonlinear Sci. Numer. Simul..

[43]  Alessandro Vespignani,et al.  Epidemic dynamics and endemic states in complex networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  Mark E. J. Newman,et al.  Technological Networks and the Spread of Computer Viruses , 2004, Science.

[45]  Lu-Xing Yang,et al.  A new epidemic model of computer viruses , 2014, Commun. Nonlinear Sci. Numer. Simul..