publication . Article . Preprint . 2016

Cyber Epidemic Models with Dependences

Maochao Xu; Gaofeng Da; Shouhuai Xu;
Open Access
  • Published: 28 Mar 2016 Journal: Internet Mathematics, volume 11, pages 62-92 (issn: 1542-7951, eissn: 1944-9488, Copyright policy)
  • Publisher: Internet Mathematics
Studying models of cyber epidemics over arbitrary complex networks can deepen our understanding of cyber security from a whole-system perspective. In this paper, we initiate the investigation of cyber epidemic models that accommodate the {\em dependences} between the cyber attack events. Due to the notorious difficulty in dealing with such dependences, essentially all existing cyber epidemic models have assumed them away. Specifically, we introduce the idea of Copulas into cyber epidemic models for accommodating the dependences between the cyber attack events. We investigate the epidemic equilibrium thresholds as well as the bounds for both equilibrium and non-e...
Persistent Identifiers
ACM Computing Classification System: ComputingMilieux_MISCELLANEOUS
free text keywords: Modelling and Simulation, Applied Mathematics, Computational Mathematics, Computer Science - Cryptography and Security, Computer Science - Social and Information Networks, Cyber-attack, Computer security, computer.software_genre, computer, Complex network, Mathematics
Related Organizations
20 references, page 1 of 2

[1] D. Chakrabarti, Y. Wang, C. Wang, J. Leskovec, and C. Faloutsos. Epidemic thresholds in real networks. ACM Trans. Inf. Syst. Secur. 10 (4), 1-26, 2008.

[2] F. Chung, L. Lu and V. Vu. Eigenvalues of random power law graphs. Annals of Combinatorics, 7, 21-33, 2003.

[3] U. Cherubini, E. Luciano, and W. Vecchiato. Copula methods in finance. New York: Wiley, 2004. [OpenAIRE]

[4] D. Cvetkovic, P. Rowlingson, and S. Simic. An introduction to the theory of graph spectra. Cambridge University Press, UK, 2010.

[5] G. Da, M. Xu, and S. Xu. A New Approach to Modeling and Analyzing Security of Networked Systems. Proc. 2014 Symposium and Bootcamp on the Science of Security (HotSoS'14), to appear.

[6] A. Ganesh, L. Massoulie, and D. Towsley. The effect of network topology on the spread of epidemics. In Proceedings of IEEE Infocom, 2005. [OpenAIRE]

[7] A. Granas and J. Dugundji. Fixed Point Theory. Springer-Verlag, New York, 2003.

[8] H. Joe. Multivariate models and dependence concepts. Monographs on Statistics and Applied Probability, vol. 73. Chapman & Hall, London, 1997.

[9] J. Kephart and S. White. Directed-graph epidemiological models of computer viruses. IEEE Symposium on Security and Privacy, pages 343-361, 1991.

[10] W. Kermack and A. McKendrick. A contribution to the mathematical theory of epidemics. Proc. of Roy. Soc. Lond. A, 115:700-721, 1927.

[11] X. Li, T. Parker, and S. Xu. A Stochastic Model for Quantitative Security Analysis of Networked Systems. IEEE Transactions on Dependable and Secure Computing, 8(1): 28-43, 2011.

[12] C. R. MacCluer. The Many Proofs and Applications of Perron's Theorem. SIAM Review, 42, 487-498, 2000.

[13] A. McKendrick. Applications of mathematics to medical problems. Proc. of Edin. Math. Soceity, 14:98-130, 1926.

[14] A.J. McNeila and J. Nes˘lehova´. Multivariate Archimedean copulas, d-monotone functions and l1-norm symmetric distributions. Annals of Statistics, 37, 3059-3097, 2009.

[15] R. B. Nelsen. An introduction to copulas, second ed. Springer Series in Statistics. Springer, New York, 2006.

20 references, page 1 of 2
Any information missing or wrong?Report an Issue