Epidemic spreading in complex networks with degree correlations

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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

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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

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Objective

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

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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

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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

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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

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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

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Illustration

• 16 infectious end points
• Only 10 effective infection links
• Model I 16, overestimate 60
• Model II 12, overestimate 20

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Simulation Results
Power law network
Random network
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How to Improve Model?

• Remove wasted edges in modeling
• Virtual removal hosts
• Hosts with few/no links to vulnerable hosts
• How to proceed?
• I dont know yet

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Security Research Major Conferences

• Tier-1
• IEEE Symposium on Security and Privacy (IEEE SP)
• 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

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Technical News

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