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How community structure a ects epidemics - Clara Stegehuis

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QUANTITATIVE LAWS June 13 -June 24

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How community structure a ects epidemics - Clara Stegehuis

  1. 1. How community structure affects epidemics Clara Stegehuis joint work with Remco van der Hofstad and Johan van Leeuwaarden Eindhoven University of Technology
  2. 2. How does community structure affect epidemics? Hierarchical configuration model Epidemics
  3. 3. Configuration model [Bollob´as 1980]
  4. 4. Configuration model [Bollob´as 1980]
  5. 5. Configuration model [Bollob´as 1980]
  6. 6. Configuration model [Bollob´as 1980]
  7. 7. Community structure is lost! Original network Configuration model
  8. 8. Hierarchical configuration model Instead of pairing vertices, pair communities with half-edges Start Possible result
  9. 9. Easy to analyze Use that on community level still a configuration model to obtain: clustering component sizes degree correlations ... ... ... ... · · · · · · · · · ... ...
  10. 10. Easy to analyze Use that on community level still a configuration model to obtain: clustering component sizes degree correlations ... ... ... ... · · · · · · · · · ... ...
  11. 11. HCM* Randomize also edges within communities Start Possible result
  12. 12. Different models CM Fixed degrees HCM* Fixed sets of communities HCM Fixed community structure Increasing randomness
  13. 13. Hierarchical configuration model Epidemics
  14. 14. Bond percolation Infect neighbor with probability p
  15. 15. Bond percolation Infect neighbor with probability p S: fraction of vertices in largest component
  16. 16. Bond percolation results Email network 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 edge occupation probability p Sizeoflargestcomponent data HCM HCM* CM Internet router network 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 edge occupation probability p Sizeoflargestcomponent data HCM HCM* CM
  17. 17. SIR epidemic Email network 0 5 10 15 20 25 30 0.00 0.05 0.10 0.15 time infectednodes data HCM HCM* CM Internet router network 0 5 10 15 20 25 30 0.00 0.10 0.20 0.30 time infectednodes data HCM HCM* CM
  18. 18. Conclusion Communities are important for how epidemics spread across networks Exact community shapes are less important Communities may inhibit or enforce epidemics
  19. 19. Open problem Overlapping communities

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