Towards an analytic model of epidemic spreading in heterogeneous systems

Mathematical models have been utilized to help understand the epidemic spreading of malicious codes (e.g., computer virus and worms). However, existing such models are either adapted from the ones developed to capture the epidemic spreading of biologically infectious diseases in homogeneous systems, or suitable only for a very specific class of heterogeneous systems. In this paper we present an attempt at building an analytic model of epidemic spreading of malicious codes in arbitrary heterogeneous systems.

[1]  Alexander Grey,et al.  The Mathematical Theory of Infectious Diseases and Its Applications , 1977 .

[2]  J. Doob.  Stochastic processes , 1953 .

[3]  Donald F. Towsley,et al.  The effect of network topology on the spread of epidemics , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[4]  Jiang Wu,et al.  An Effective Architecture and Algorithm for Detecting Worms with Various Scan , 2004, NDSS.

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

[6]  P. Rousseeuw,et al.  Wiley Series in Probability and Mathematical Statistics , 2005 .

[7]  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.

[8]  Donald F. Towsley,et al.  Monitoring and early warning for internet worms , 2003, CCS '03.

[9]  Richard E. Barlow,et al.  Statistical Theory of Reliability and Life Testing: Probability Models , 1976 .

[10]  Kevin A. Kwiat,et al.  Modeling the spread of active worms , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[11]  Vern Paxson,et al.  Very Fast Containment of Scanning Worms , 2004, USENIX Security Symposium.

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

[13]  N. Bailey,et al.  The mathematical theory of infectious diseases and its applications. 2nd edition. , 1975 .

[14]  N. Ling.  The Mathematical Theory of Infectious Diseases and its applications , 1978 .

[15]  Alessandro Vespignani,et al.  Epidemic dynamics in finite size scale-free networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Vern Paxson,et al.  How to Own the Internet in Your Spare Time , 2002, USENIX Security Symposium.

[17]  Stefan Bornholdt,et al.  Handbook of Graphs and Networks: From the Genome to the Internet , 2003 .

[18]  Alessandro Vespignani,et al.  Epidemics and immunization in scale‐free networks , 2002, cond-mat/0205260.

[19]  Andrew A. Chien,et al.  Tolerating denial-of-service attacks using overlay networks: impact of topology , 2003, SSRS '03.

[20]  Evangelos Kranakis,et al.  DNS-based Detection of Scanning Worms in an Enterprise Network , 2005, NDSS.

[21]  Moshe Shaked,et al.  Stochastic orders and their applications , 1994 .

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

[23]  Y. Moreno,et al.  Epidemic outbreaks in complex heterogeneous networks , 2001, cond-mat/0107267.

[24]  Jeffrey O. Kephart,et al.  Measuring and modeling computer virus prevalence , 1993, Proceedings 1993 IEEE Computer Society Symposium on Research in Security and Privacy.

[25]  Donald F. Towsley,et al.  Code red worm propagation modeling and analysis , 2002, CCS '02.

[26]  Ibrahim Matta,et al.  BRITE: an approach to universal topology generation , 2001, MASCOTS 2001, Proceedings Ninth International Symposium on Modeling, Analysis and Simulation of Computer and Telecommunication Systems.