1. Sexual Networks: Implications for the Transmission of 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  t c: # of potentially infected contact  : probability of infection transmission N = S+I D: mean duration of infection

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 basic reproduction number, R0. R0= c  D. c: # of contacts  : prob. of infection in a contact D: duration of relationships

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

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

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. Heterogeneity in Standard Model 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

16. Heterogeneity in Standard Model AssortativeDisassortative 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. Younger people Older people “BRIDGE”

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. avg. # of infections from an infected person standard deviation of contact numbers mean of contact numbers the higher  , 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 is asked to list all of his or her sexual partners. These in turn are contacted, tested, and asked to reveal the same information.

26. Empirical Study of Sexual Nets Sexual networks consist of many relatively small sexual clusters (components) Very few large components Too many small 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. Two main drawbacks of contact tracing are; It produces a subset (infected) of population, It cannot discards non-sexual contacts. Empirical Study of Sexual Nets

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

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 c: # of links  : #. of nodes (concurrent relations)

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 Sociology 110, 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 Sociology 110, 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 Cumulative interaction number in lifetime for male and female Note that, males has reported larger number of contacts than females !!!!

39. Implications of Scale-Free Nets In a scale-free network contagiousness needs only to be very low for an epidemic process to develop. 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