Download Disease Cores

Epidemic Potential in Human Sexual
Networks:
Connectivity and The Development of STD Cores
1
Why do Networks Matter?
2
Local vision
Why do Networks Matter?
3
Global vision
Reachability in Colorado Springs
(Sexual contact only)
4
•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)
Centrality example: Colorado Springs
Node size proportional to
betweenness centrality
5
Probability of infection
by distance and number of paths, assume a constant p ij of 0.6
1
10 paths
probability
0.8
5 paths
0.6
2 paths
0.4
1 path
0.2
0
2
6
3
4
Path distance
5
6
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.
7
*John & Curran, 1978; Phillips, Potterat & Rothenberg 1980; Hethcote & Yorke, 1984
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
8
•Gumshoe work on STD outbreaks suggests that small changes in
individual behavior can generate rapid changes in disease spread.
Structural Cohesion provides a natural indicator of STD
cores.
James Moody and Douglas R. White. 2003. “Structural Cohesion
and Embeddedness: A hierarchical Conception of Social Groups”
American Sociological Review 68:103-127
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?
9
Structural Cohesion: Definition
10
The minimum requirement for structural cohesion is
that the collection be connected.
Structural Cohesion: Definition
When focused on one node, the system is still vulnerable to
11 targeted attacks
Structural Cohesion: Definition
Spreading relations around the structure makes it robust.
12
Structural Cohesion: Definition
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.
13
Structural Cohesion: Definition
•Networks are structurally cohesive if they remain
connected even when nodes are removed
0
14
1
2
3
Structural Cohesion = Potential Std Cores?
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
15
•Once disease enters one of these cores, spread is likely robust and
rapid.
Empirical evidence for Structurally Cohesive STD Cores:
Almost no evidence of Chlamydia transmission
16 Source: Potterat, Muth, Rothenberg, et. al.
2002. Sex. Trans. Infect 78:152-158
Empirical evidence for Structurally Cohesive STD Cores:
Epidemic Gonorrhea Structure
17
G=410
Source: Potterat, Muth, Rothenberg, et. al. 2002. Sex. Trans. Infect 78:152-158
Empirical evidence for Structurally Cohesive STD Cores:
Epidemic Gonorrhea Structure
18