Reported Female Genital Chlamydia Rates per 100,000 in Canada by Province/Territory, 1997 to 1999

2. Reported Female Genital Chlamydia Rates per 100,000 in Canada by Province/Territory,1997 to 1999 Health Canada, Bureau of HIV/AIDS, STD and TB, 2000

4. Chlamydia network from Qikiqtarjuaq, NunavutCanada, 2003 Data courtesy of Andrea Cuschieri

6. Colorado Springs, Gonorrhea, 1981 Lot 004

7. Colorado Springs, Gonorrhea, 1981, Lot 004

9. Modeling disease transmission A comparison of data from 15 network studies …well, 13, actually….

10. Dramatis personae Theoreticians Empiricists David Bell Sam Friedman Ann Jolly Al Klovdahl Stephen Muth John Potterat Rich Rothenberg Bob Trotter Martina Morris Mark S. Handcock Francesca Chiaromonte Julian Besag David Hunter Steve Goodreau James Moody Philippa Pattison

11. Study sites

12. The Studies—Colorado Springs

13. The Studies—Atlanta

14. The Studies

15. Demographics, Time Frame and Prevalence • Degree distributions • Recursion • Concurrency • Transitivity • Component distribution • Assortativity • Multiplexity

16. Demographic pattern for 13 network studies:Age

17. Demographic pattern for 13 network studies:Age

18. Demographic pattern for 13 network studiesAge, %Male

19. Demographic pattern for 13 network studiesAge, %Male, %African American

20. Time frame for 13 network studies

21. Prevalence of STDs and HIV—13 studies

22. Demographics, Time Frame and Prevalence • Degree distributions • Recursion • Concurrency • Transitivity • Component distribution • Assortativity • Multiplexity

23. Selected Power Law curves from network studies

24. Exponents and R2 associated with power law curves for 13 network studies

25. Degree distributionsCumulative probability distribution for interviewed persons—all 13 studies combined

26. Uninterviewed person • The construction of a sociogram permits examination of the degree distribution for persons named but never interviewed. • Their degree distribution says something about the interconnectedness of the network.

27. Degree distributionsCumulative probability distribution for interviewed and noninterviewed persons—all 13 studies combined

28. Missing LinksWho has not been named? • What does the space between these two curves represent, and how can it be measured? • Assume that the Non-interviewed actually have the same degree distribution as the Interviewed. • Assume that “Recursion” is the same for Non-interviewed and Interviewed persons

29. Demographics, Time Frame and Prevalence • Degree distributions • Recursion • Concurrency • Transitivity • Component distribution • Assortativity • Multiplexity

30. Recursion: definition • Number of persons in network in the absence of interaction (all respondents provide only egocentric information): Respondents + Contacts = Expected nodes • With de-duplication, we get the actual number of nodes in the network • Recursion is the proportionate decrease in network nodes that occurs because of interaction: [Expected nodes – Actual nodes]/Expected nodes

31. Recursion: observations from data--all contacts

32. Gang-Associated STD Outbreak, Colorado Springs, 1990-1991 N=410

33. Rockdale county syphilis epidemic: Late phase

34. Missing Links:Estimation of the missing • Calculate the expected number of partnerships from the number of contacts named and not interviewed by applying the degree distribution of the Interviewed persons. • Calculated the expected number of persons, given no interaction. • Apply the observed proportion of Recursion, to get the expected total of persons associated with the Non-interviewed. • Sum the expected persons associated with the Noninterviewed with the observed persons associated with the Interviewed. • STILL MISSING: The proportion of ties between Noninterviewed persons that occurred with Interviewed persons and their contacts.

35. Missing Links:Calculation Total = Expected * (1-(0.01*Recursion)

36. Missing Links:Graphic display

37. Proportion of Nodes missing from networks

38. Demographics, Time Frame and Prevalence • Degree distributions • Recursion • Concurrency • Transitivity • Component distribution • Assortativity • Multiplexity

39. Calculating Kappa from egocentric data • Determine mean and variance of degree distribution: kappa = (var/mean) + mean – 1 • For these data, sociometric information is available, so the connection formed by Non-interviewed persons can be included (net effect of decreasing estimate of concurrency)

40. Estimate of concurrency by study

41. Concurrency—SEXUAL partners

42. Concurrency—NEEDLE partners

43. Demographics, Time Frame and Prevalence • Degree distributions • Recursion • Concurrency • Transitivity • Component distribution • Assortativity • Multiplexity

44. Transitivity (Clustering) • Using the definition of completed triangles • Algorithm implemented in UCI-6 • Note the absence (by definition) of clustering in sexual networks that are strictly heterosexual • Conversely, networks involving MSM or IDU can demonstrate considerable clustering

45. Transitivity by study(all relationships)

46. Transitivity by study(sexual relationships)

47. Transitivity by study(needle-sharing relationships)

48. Demographics, Time Frame and Prevalence • Degree distributions • Recursion • Concurrency • Transitivity • Component distribution • Assortativity • Multiplexity

49. Distribution of components

50. Distribution of componentsThree exceptions • Rockdale • Contact tracing, single outbreak • Matrix • Snowball design • Manitoba • Contact tracing, multiple isolated areas