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Epidemic spreading in complex networks with degree correlations

Epidemic spreading in complex networks with degree correlations. Authors: M. Boguna, R. Pastor-Satorras, and A. Vespignani. Publish: Lecture Notes in Physics: Statistical Mechanics of Complex Networks, 2003 Presenter: Cliff C. Zou. Background. Limitation of Internet worm models

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Epidemic spreading in complex networks with degree correlations

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  1. Epidemic spreading in complex networks with degree correlations Authors: M. Boguna, R. Pastor-Satorras, and A. Vespignani. Publish: Lecture Notes in Physics: Statistical Mechanics of Complex Networks, 2003 Presenter: Cliff C. Zou

  2. Background • Limitation of Internet worm models • Extended from simple epidemic model • Homogeneous assumption • No topology considered • Suitable for scan-based worms • Not suitable for modeling topological malware • Email viruses • P2P malware

  3. Objective • Provide epidemic analytical models for topological networks • Cover both correlated networks and uncorrelated networks • We only consider uncorrelated networks here

  4. Model Notations • : infection prob. via an edge per unit time • P(k): fraction of nodes with degree k • Only consider SI model • ik(t): fraction of infected in k-degree hosts • hki = k k P(k): average degree

  5. Topological Model I • (t): prob. that any given link points to an infected host • Think each edge has two “end points” • P(k)ik(t)¢ N: # of k-degree infected • P(k)k¢ N: # of end points owned by k-degree nodes

  6. Topological Model II • A newly infected at most has k-1 links to infect others • It is infected through an edge • The edge is useless in infection later

  7. Problems of Models • Implicit assumptions: Homogenous mixing • Assume infected are uniformly distributed • Fact: epidemic spread via topology • Infected are connected (clustered) • Many infectious edges are wasted • Results: • Models overestimate epidemic spreading speed

  8. A Illustration • 16 infectious “end points” • Only 10 effective infection links • Model I: 16, overestimate 60% • Model II: 12, overestimate 20%

  9. Simulation Results Power law network Random network

  10. How to Improve Model? • Remove wasted edges in modeling • Virtual removal hosts • Hosts with few/no links to vulnerable hosts • How to proceed? • I don’t know yet

  11. Security Research Major Conferences • Tier-1: • IEEE Symposium on Security and Privacy (IEEE S&P) • ACM Computer Communication Security (CCS) • Usenix Security Symposium • Annual International Cryptology Conference (CRYPTO) • Tier-2: • NDSS: Network and Distributed System Security • ACSAC: Annual Computer Security Applications Conference • DSN: dependable system and network • ESORICS: European Symposium on Research in Computer Security • RAID: Recent Advances in Intrusion Detection

  12. Technical News • ACM techology news: • http://www.acm.org/technews/articles/2006-8/0130m.html • Information Security Magazine: • http://informationsecurity.techtarget.com/

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