Social network and disease spread

1. Social network and disease spread Laurens Bakker, Philippe Giabbanelli

2. Outline ▪ What is a social network? ▪ Measures ▪ Disease spread ▪ Three case studies Social networks and disease spread 1 L Bakker, P Giabbanelli

3. What is a social network?How does it form? Social networks and disease spread 2 L Bakker, P Giabbanelli

4. Social networks and disease spread 3 L Bakker, P Giabbanelli

5. But really, how does it form? People go places… and meet in the process Social networks and disease spread 4 L Bakker, P Giabbanelli

6. But really, how does it form? People want things… and use others Social networks and disease spread 5 L Bakker, P Giabbanelli

7. But really, how does it form? People have things in common… and express their commonalities Social networks and disease spread 6 L Bakker, P Giabbanelli

8. What is a social network?How does it form? Social networks and disease spread 7 L Bakker, P Giabbanelli

9. Fluffy theories Social networks and disease spread 8 L Bakker, P Giabbanelli

10. If we want to do science… Social networks and disease spread 9 L Bakker, P Giabbanelli

11. we need something with teeth! Social networks and disease spread 10 L Bakker, P Giabbanelli

12. Network definition • Actor => Vertex/Node • Boundary • Connection => Edge/Link • Interaction • Dynamic social networks • Observability • Degree (Dombrowski 2007) Social networks and disease spread 11 L Bakker, P Giabbanelli

13. Measures Social networks and disease spread 12 L Bakker, P Giabbanelli

14. Motifs– Clustering – Average distance – Degree distribution Global Degree distribution Average distance Clustering Motifs Local (Giabbanellli 2011) Social networks and disease spread 13 L Bakker, P Giabbanelli

15. Motifs – Clustering – Average distance – Degree distribution 2 1 0 1 3 0 a motif is a subgraph that appears at a ‘very’ different frequence in G than in S. 2 0 Given a graph G… and a set S of random graphs of the same size and average degree, (Milo 2004) Social networks and disease spread 14 L Bakker, P Giabbanelli

16. Motifs – Clustering – Average distance – Degree distribution Social networks and disease spread 15 L Bakker, P Giabbanelli

17. Motifs– Clustering – Average distance – Degree distribution For a given node i , we denote its neighborhood by Ni. The clustering coefficient Ci of i is the edge density of its neighborhood. Here, there are two edges between nodes in Ni. Ci = 2.2/(5.4) = 0.2 If a graph has high clustering coefficient, then there are communities (i.e., cliques) in this graph. At most, it would be a complete graph with Ni.(Ni-1) edges. People tend to form communities so they are common in social networks. Social networks and disease spread 16 L Bakker, P Giabbanelli

18. Motifs– Clustering – Average distance – Degree distribution The distance is the number of edges to go from one node to another. The average distance is the average of the distance between all pairs of nodes. Social networks and disease spread 17 L Bakker, P Giabbanelli

19. Motifs– Clustering – Average distance – Degree distribution The average distance l is: ∙ small if l∝ln(n) ∙ ultrasmall if l∝ln(ln(n)) (Newman 2003) (Cohen 2003) Social networks and disease spread 18 L Bakker, P Giabbanelli

20. History (the Hype) Motifs– Clustering – Average distance – Degree distribution • Milgram (Milgram 1969) • Small world • Watts & Strogatz (Watts 1998) • “Small Worlds” & “6 Degrees” • Barabasi & Albert (Barabasi 1999) • Power Law (scale free) • Newman (Newman 2003) • Review Social networks and disease spread 19 L Bakker, P Giabbanelli

21. Motifs– Clustering – Average distance – Degree distribution Many measured phenomena are centered around a particular value. (Newman 2005) Social networks and disease spread 20 L Bakker, P Giabbanelli

22. Motifs– Clustering – Average distance – Degree distribution Many measured phenomena are centered around a particular value. There also exists numerous phenomena with a heavy-tailed distribution. lets plot it on a log-log scale (Newman 2005) Social networks and disease spread 21 L Bakker, P Giabbanelli

23. Motifs– Clustering – Average distance – Degree distribution We say that this distribution follows a power-law, with exponent α. There also exists numerous phenomena with a heavy-tailed distribution. The equation of a line is p(x) = -αx + c. Here we have a line on a log-log scale: ln p(x) = -α ln x + c apply exponent e c -α p(x) = ecx (Newman 2005) Social networks and disease spread 22 L Bakker, P Giabbanelli

24. Motifs– Clustering – Average distance – Degree distribution We say that this distribution follows a power-law, with exponent α. computer files people’s incomes Keep in mind that this is quite common. visits on web pages moon craters (Li 2005) Social networks and disease spread 23 L Bakker, P Giabbanelli

25. Disease spread Social networks and disease spread 24 L Bakker, P Giabbanelli

26. Thresholds – Variations – Immunization A ‘threshold’ is the extent to which a disease must be infectious before you can’t stop it from spreading in the population. Very famous claim: scale-free networks have no thresholds! It will spread! (Wikipédia: modèles compartimentaux en épidémiologie) Social networks and disease spread 25 L Bakker, P Giabbanelli

27. Thresholds – Variations – Immunization Very famous claim: scale-free networks have no thresholds! It will spread! « in a scale-free network there is no epidemic threshold thus eliminating a sexually transmissible disease is impossible » (Kretschmar 2007, opening of Networks in Epidemiology) That’s actually sort of false… …it needs additional conditions, that may not exist. Social networks and disease spread 26 L Bakker, P Giabbanelli

28. Thresholds– Variations – Immunization Depending on the diseases, there are several epidemiological classes: infected (I), recovered (R), carriers (C)… It may be interesting to see how the properties of the network influences the number of individuals in each class over time. order randomness (Kuperman 2001; Crepey 2006) Social networks and disease spread 27 L Bakker, P Giabbanelli

29. Thresholds– Variations – Immunization There are four broad approaches (Giabbanelli 2011). Is the disease spreading at the same time? Yes No Globalcompetitive Globalpreventive = network game = separator problem We can immunize anybody NP-hard NP-complete (Kostka 2008) (Rosenberg 2001) Localcompetitive Localpreventive We must follow social links Agents that fight… …and explore (Giabbanelli 2009) (Stauffer 2006) Social networks and disease spread 28 L Bakker, P Giabbanelli

30. Case Study #1Measuring what matters Social networks and disease spread 29 L Bakker, P Giabbanelli

31. Example #1: Social networks Measure: distance Property: average distance Social networks and disease spread 30 L Bakker, P Giabbanelli

32. Example #2: Obesity map Measure: Centrality Social networks and disease spread 31 L Bakker, P Giabbanelli

33. Example #3: Backbone network We do not care about clustering or whether the network is scale-free. Measure betweenness and average distance. (Giabbanelli 2010) Social networks and disease spread 32 L Bakker, P Giabbanelli

34. What can we measure in a network? Network Process Measures Social network Disease spread Average distance Factors incluencing obesity Centrality Obesity level Betweenness centrality Average distance Backbone network Deploying equipment Social networks and disease spread 33 L Bakker, P Giabbanelli

35. How do we find out what we should measure? ▪ Know the properties of the network you are studying. → Network analysis ▪ Generate many of them using appropriate stochastic models. → Network generation ▪ Record several measures, and the value of the outcome process. → Possibly optimization ▪ Analyze which measures are linked to the outcome. → Data mining Social networks and disease spread 34 L Bakker, P Giabbanelli

36. Case Study #2Health & Social Networks Social networks and disease spread 35 L Bakker, P Giabbanelli

37. « People are interconnected, and so their health is interconnected. » « … there has been growing conceptual and empirical attention over the past decade to the impact of social networks on health. » (Smith 2008) Christakis&Fowler have used social networks to show that people are correlated in weight status, smoking, and… happiness! http://www.ted.com/talks/lang/eng/nicholas_christakis_the_hidden_influence_of_social_networks.html Social networks and disease spread 36 L Bakker, P Giabbanelli

38. The basic idea A long imbalance between energy intake&output yields obesity. What spread between people are behaviours impacting intake&output. Exercising Eating Social networks and disease spread 37 L Bakker, P Giabbanelli

39. How we modelled it We used social networks. Each individual has a level of physical activity and an energy intake. Social networks and disease spread 38 L Bakker, P Giabbanelli

40. How we modelled it We also modelled human metabolism. Social networks and disease spread 39 L Bakker, P Giabbanelli

41. Results from Phase 1 Social networks and disease spread 40 L Bakker, P Giabbanelli

42. Results from Phase 1 Presented at ICO 8.6% acceptance Positive reactions Journal on its way Social networks and disease spread 41 L Bakker, P Giabbanelli

43. Case Study #3Homeless in the tri-cities Social networks and disease spread 42 L Bakker, P Giabbanelli

44. Homeless in the Tri-Cities (I) • Hope for Freedom Society • Vertex definition • Boundary: existence of client file • Edge definition • Interaction: co-observation • Time! • Connection: repeated interaction Social networks and disease spread 43 L Bakker, P Giabbanelli

45. Homeless in the Tri-Cities (II) • Descriptives: • 2 years • ~250 actors • ~3000 observations • Statistical Models • Static: PNET = ERGM = logitp* (Hunter 2006) • Dynamic: SIENA (Snijders 2006) Social networks and disease spread 44 L Bakker, P Giabbanelli

46. References Barabasi 1999 AL Barabasi, R Albert, Emergence of Scaling in Random Networks, Science, 1999 R Cohen, S Havlin, Scale-free networks are ultrasmall, Physical Review Letters, 2003. Cohen 2003 P Crepey et al, Epidemic variability in complex networks, Phys. Rev. E, 2006. Crepey 2006 K Dombrowski, R Curtis, SR Friedman, Injecting drug user network topologies and infectious disease tranmission: suggestive findings, Working Paper 2007 Drombrowski 2007 Social networks and disease spread 45 L Bakker, P Giabbanelli

47. References PJ Giabbanelli, Self-improving immunization policies for complex networks, MSc Thesis@SFU, 2009 Giabbanelli 2009 Giabbanelli 2010 PJ Giabbanelli, Impact of complex network properties on routing in backbone networks, CCNet 2010 (IEEE Globecom) Giabbanelli 2011 PJ Giabbanelli, JG Peter, Complex networks and epidemics, TSI, 2011, to appear. Hunter 2006 D Hunter, Exponential Random Graph Models for Network Data, Talk, 2006, http://www.stat.psu.edu/~dhunter/talks/ergm.pdf Social networks and disease spread 46 L Bakker, P Giabbanelli

48. References Kostka 2008 J Kostka et al., Word of Mouth : Rumor Dissemination in Social Networks, Lecture Notes in Computer Science, 2008. Kretzschmar 2007 M Kretzschmar, J Wallinga, Networks in Epidemiology, Mathematical Population Studies, 2007 M Kuperman, G Abramson, Small World Effect in an Epidemiological Model, Physical Review Letters, 2001. Kuperman 2001 Li 2005 L Li et al., Towards a Theory of Scale-Free Graphs : Definition, Properties and Implications, Internet Mathematics, 2005. Social networks and disease spread 47 L Bakker, P Giabbanelli

49. References J Travers, S Milgram, An Experimental Study of the Small World Problem, Sociometry, 1969 Milgram 1969 R Milo, et al., Superfamilies of Evolved and Designed Networks, Science, 2004. Milo 2004 MEJ Newman, The structure and function of complex networks, SIAM Review, 2003. Newman 2003 MEJ Newman, Power laws, Pareto distributions and Zipf’s law, Contemporary Physics, 2005. Newman 2005 AL Rosenberg, Graph Separators, with Applications, Kluwer Academic, 2001 Rosenberg 2001 Social networks and disease spread 48 L Bakker, P Giabbanelli

50. References Smith 2008 KP Smith, NA Christakis, Social networks and health, Annu Rev Social, 2008 TAB Snijders, Statistical Methods for Network Dynamics, Proceedings of the XLIII Scientific Meeting of the Italian Statistical Society, 2006 Snijders 2006 AO Stauffer et al, A dissemination strategy for immunizing scale-free networks, Phys. Rev. E, 2006. Stauffer 2006 Watts 1998 DJ Watts, SH Strogatz, Collective dynamics of 'small-world' networks, Nature, 1998 Social networks and disease spread 49 L Bakker, P Giabbanelli