1 Epidemic Potential in Human Sexual Networks: Connectivity and The Development of STD Cores

2 Why do Networks Matter? Local vision

3 Why do Networks Matter? Global vision

4 Reachability in Colorado Springs (Sexual contact only) High-risk actors over 4 years 695 people represented Longest path is 17 steps Average distance is about 5 steps Average person is within 3 steps of 75 other people 137 people connected through 2 independent paths, core of 30 people connected through 4 independent paths (Node size = log of degree)

5 Centrality example: Colorado Springs Node size proportional to betweenness centrality

6 Probability of infection by distance and number of paths, assume a constant p ij of Path distance probability 10 paths 5 paths 2 paths 1 path

7 STD Cores Infection Paradox in STD spread: The proportion of the total population infected is too low to sustain an epidemic, so why don’t these diseases simply fade away? The answer, proposed generally by a number of researchers*, is that infection is unevenly spread. While infection levels are too low at large to sustain an epidemic, within small (probably local) populations, infection rates are high enough for the disease to remain endemic, and spread from this CORE GROUP to the rest of the population. If this is correct, it suggests that we need to develop network measures of potential STD cores. *John & Curran, 1978; Phillips, Potterat & Rothenberg 1980; Hethcote & Yorke, 1984

8 STD Cores: A potential STD core requires a relational structure that can sustain an infection over long periods. Suggesting a structure that: is robust to disruption. Diseases seem to remain in the face of concerted efforts to destroy them. Individuals enter and leave the network Diseases (often) have short infectious periods magnifies transmission risk A disease that would otherwise dissipate likely gets an epidemiological boost when it enters a core. can accommodate rapid outbreak cycles Gumshoe work on STD outbreaks suggests that small changes in individual behavior can generate rapid changes in disease spread.

9 James Moody and Douglas R. White “Structural Cohesion and Embeddedness: A hierarchical Conception of Social Groups” American Sociological Review 68: Structural Cohesion provides a natural indicator of STD cores. Intuitively, A network is structurally cohesive to the extent that the social relations of its members hold it together. How many nodes need to be removed to disconnect it?

10 Structural Cohesion: Definition The minimum requirement for structural cohesion is that the collection be connected.

11 When focused on one node, the system is still vulnerable to targeted attacks Structural Cohesion: Definition

12 Spreading relations around the structure makes it robust. Structural Cohesion: Definition

13 Formal definition of Structural Cohesion: A group’s structural cohesion is equal to the minimum number of actors who, if removed from the group, would disconnect the group. Structural Cohesion: Definition

14 Networks are structurally cohesive if they remain connected even when nodes are removed Structural Cohesion: Definition

15 Three requirements for potential STD cores: A structure that: is robust to disruption. Defining characteristic of k-components Allows for a continuous (as opposed to categorical) measure of “coreness” based on the embeddedness levels within the graph. magnifies transmission risk Overlapping k-components act like transmission substations, where high within-component diffusion boosts the likelihood of long-distance transmission from one k-component to other components (lumpy transmission) or to less embedded actors at the fringes (a ‘pump station’). can accommodate rapid outbreak cycles Once disease enters one of these cores, spread is likely robust and rapid. Structural Cohesion = Potential Std Cores?

16 Almost no evidence of Chlamydia transmission Source: Potterat, Muth, Rothenberg, et. al Sex. Trans. Infect 78: Empirical evidence for Structurally Cohesive STD Cores:

17 Epidemic Gonorrhea Structure Source: Potterat, Muth, Rothenberg, et. al Sex. Trans. Infect 78: G=410 Empirical evidence for Structurally Cohesive STD Cores:

18 Epidemic Gonorrhea Structure Empirical evidence for Structurally Cohesive STD Cores:

19 Consider the following (much simplified) scenario: Probability that actor i infects actor j (p ij )is a constant over all relations = 0.6 S & T are connected through the following structure: S T The probability that S infects T through either path would be: Why do Networks Matter?

20 Now consider the following (similar?) scenario: S T Every actor but one has the exact same number of partners The category-to-category (blue to orange) mixing is identical The distance from S to T is the same (7 steps) S and T have not changed their behavior Their partner’s partners have the same behavior But the probability of an infection moving from S to T is: = Different structures create different outcomes Why do Networks Matter?