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

9. Simulation Results
Random network
Power law network

10. How to Improve Model? Remove wasted edges in modeling How to proceed?
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: Information Security Magazine:
Information Security Magazine: