Sexual N etworks: Implications for the T ransmission of S exually T ransmitted I nfections

1. Sexual Networks: Implications for the Transmissionof Sexually Transmitted Infections İlker BEKMEZCİ CMPE 588 Presentation

2. Outline • Introduction • Standard Epidemiological Model • Heterogeneity in the Standard Model • Network Models • The Empirical Study of Sexual Networks • New Approaches to the Study of Epidemics • Discussion

3. Introduction • Standard epidemiological models largely disregard the complex patterns and structures of intimate contacts.

4. Introduction • Classic epidemiological models assume random contacts. • In reality, sex interactions much more complex

5. Introduction • Social network analysis (SNA) offers important insight into how to conceptualize and model social interaction. • Network analysis provides important implications also for the epidemiology of sexually transmitted infections (STI).

6. Standard Epidemiological Model • Three states of people are • Susceptible (S), • Infected (I), • Resistant (R).

7. Standard Epidemiological Model • Random interactions are described as differential equations. S: # of susceptible people in Dt c: # of potentially infected contact b : probability of infection transmission D: mean duration of infection N = S+I

8. Standard Epidemiological Model • dS/dt + dI/dt = 0. Because population size is assumed as constant.

9. Standard Epidemiological Model • A critical notion in disease epidemiology is the basicreproduction number, R0. R0= cbD. c: # of contacts D: duration of relationships b: prob. of infection in a contact

10. Standard Epidemiological Model Epidemic R0= cbD. Bigger than one Exactly one Extinct Extinct To reduce R0, reduce one of them Less than one

11. Standard Epidemiological Model What is your interaction number? Unforunately only three • This model is heterogeneous across persons. • Number of contacts for all persons is the same. Acc. to standart model, it must be five I know, I know. I have to hurry up.

12. Standard Epidemiological Model • Standard model works for flu or measles. • Differential equations can give useful conclusions; • Will epidemic occur? • How big? • Portion of population that has to be vaccinated.

13. Heterogeneity in Standard Model • Sex is not random, randomness is not suitable for sexual networks. • A solution to non-randomness is to define subpopulations based on gender, sexual activity level. • And then to model interactions of subpopulations.

14. Heterogeneity in Standard Model • Sexually very active group can be modeled as subgroups (core groups) • Core group approach is used to study the difference of assortative and disassortative Core group

15. Assortative Sexually active persons interact with the active persons Most interactions within the group Faster initial spread, small-size epidemic Disassortative Sexually active persons interact with low active persons Most interactions between the groups Slow initial spread, large-size epidemic Heterogeneity in Standard Model

16. Assortative Disassortative Heterogeneity in Standard Model Closest match to empirical studies

17. Heterogeneity in Standard Model • Assortive model is used to explain age, ethnicity and other sociological variables. • People tend to interact within the same age, ethnicity or social groups. • The classical cliché is ‘We are from different worlds’.

18. Heterogeneity in Standard Model • The most known exception of this rule is prostitutes and their clients. • They can be thought as bridges between subgroups. “BRIDGE” Younger people Older people

19. Heterogeneity in Standard Model • In standard approach c (number of contacts for each persons) was constant. • Acc. to heterogeneity, it can be vary person to person. • Empirical measurements shows that standard variation of c is very large.

20. Heterogeneity in Standard Model • Reproduction number in heterogeneity and non-constant c. standard deviation of contact numbers avg. # of infections from an infected person mean of contact numbers the higher s2, the higher reproduction number

21. Network Model • Although heterogeneity is more realistic than standard approach, it is not good enough to explain the while picture. • Focus should be shifted from persons to relationships and to the patterns of relationships.

22. Network Model Potterat, J. J., Phillips-Plummer, L., Muth, S. Q., Rothenberg, R. B., Woodhouse, D. E., Maldonado-Long, T. S., Zimmerman, H. P., and Muth, J. B., Risk network structure in the early epidemic phase of HIV transmission in Colorado Springs, Sexually Transmitted Infections 78, i159–i163 (2002).

23. Network Model • Social network analysis is a good tool in this context. • Persons are vertex and relationships are edges. • Network can be constructed as ego network or from the whole population at once.

24. A Brief Review • Sex interactions and STI epidemic can be modeled as • Homogeneous: Assume random interactions and homogeneity across persons • Heterogeneous: Model the population as core groups and contact numbers may vary • Network: Focus on relationships instead of persons, explain all details of the population.

25. Empirical Study of Sexual Nets • The most common tool to collect sexual network information is contact tracing. • Contact tracing means that a person diagnosed with an STI isasked to list all of his or her sexual partners. • These in turn arecontacted, tested, and asked to reveal the same information.

26. Empirical Study of Sexual Nets • Sexual networks consist of many relatively small sexual clusters (components) Too many small components Very few large components

27. Empirical Study of Sexual Nets • Acc. to contact tracing studies, there are two types of components: • Radial: There is one high degree node, the other’s degree is 1 or 2. • Linear : The degree varies from 1 to 4. Radial Linear

28. Empirical Study of Sexual Nets • Two main drawbacks of contact tracing are; • It produces a subset (infected) of population, • It cannot discards non-sexual contacts.

29. Empirical Study of Sexual Nets • Sexual networks are not static and STI may be transmitted on current relations. Lusi Ceyar (dead) Culi Suelın Bobi A network of DALLAS (only a joke)

30. Empirical Study of Sexual Nets • An alternative approach is line graph to analyze concurrent relations • In line graphs, • Nodes are relations, • Edges exist whenever a person has a concurrent relation.

31. Empirical Study of Sexual Nets • Line graph vs. Contact network • Different concurrent relations, • Same network density • Different concurrent relations, • Different network density

32. Empirical Study of Sexual Nets • A ratio for concurrent relations for line graphs b: #. of nodes (concurrent relations) c: # of links

33. Empirical Study of Sexual Nets • Problem of line graphs : SYI can be transmitted on non-concurrent relations • Solution : To keep the edge in line graph for a certain period of time, even if the relation between two persons is over.

34. New Approaches • New studies have shown that sexual networks are scale free. Number of high degree of nodes can not be neglected.

35. New Approaches • Sample sexual networks Potterat, J. J., Phillips-Plummer, L., Muth, S. Q., Rothenberg, R. B., Woodhouse, D. E., Maldonado-Long, T. S., Zimmerman, H. P., and Muth, J. B., Risk network structure in the early epidemic phase of HIV transmission in Colorado Springs, Sexually Transmitted Infections 78, i159–i163 (2002). High school dating: Data drawn from Peter S. Bearman, James Moody, and Katherine Stovel, Chains of Affection, American Journal of Sociology110, 44-91 (2004)

36. New Approaches • Sample sexual networks Potterat, J. J., Phillips-Plummer, L., Muth, S. Q., Rothenberg, R. B., Woodhouse, D. E., Maldonado-Long, T. S., Zimmerman, H. P., and Muth, J. B., Risk network structure in the early epidemic phase of HIV transmission in Colorado Springs, Sexually Transmitted Infections 78, i159–i163 (2002). High school dating: Data drawn from Peter S. Bearman, James Moody, and Katherine Stovel, Chains of Affection, American Journal of Sociology110, 44-91 (2004)

37. Web of Human Sexual Contacts • The analyzed the data were gathered in a 1996 Swedish survey of sexual behavior. • The survey involved a random sample of 4,781 Swedes (aged 18–74 years) and used structured personal interviews and questionnaires.

38. Web of Human Sexual Contacts Cumulative interaction number in the last 12 month for male and female Note that, males has reported larger number of contacts than females !!!!  Cumulative interaction number in lifetime for male and female

39. Implications of Scale-Free Nets • In a scale-free network contagiousnessneeds only to be very low for an epidemic process todevelop. • Remember reproduce number in heterogeneous approach. This ratio is very high in scale-free structures

40. Implications of Scale-Free Nets • Scale-free networks are very sensitive to strategic removal of nodes • If highly connected nodes are removed, network will be disconnected Think of the removal of this node

41. Conclusion • Homogeneous or heterogeneous conventional social models cannot model the real society. • Social networks are a new tool to model and interpret the real societies. • Social network analysis can be very powerful tool for sexual networks.

42. Conclusion • In this context, simulation will be the most important analyzing tool. • The simulation parameters must be set very carefully. • … And sexual network data must be collected correctly.

43. Epidemic Conclusions • Partner notification, • Message development; promoting to have one partner at a time, • Community dialog, • Focus on venues which facilitate sexual mixtures

44. Questions ? ? ?

45. Standard Epidemiological Model • Three distinct model based on three states are • SI, • SIS, • SIR. Most appropriate for STI In Western population, HIV model