Topographic analysis of an empirical human sexual network

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Topographic analysis of an empirical human sexual
network

• Geoffrey Canright and Kenth Engø-Monsen, Telenor
  RI, Norway
• Valencia Remple, U of British Columbia,
  Vancouver, Canada

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Theory meets reality

• Here we will combine two things
• The topographic, or regions-based,
  theoretical approach to analysis of epidemic
  spreading (ECCS04 and ECCS05) (GSC/KEM)
• A detailed empirical network of human sexual
  contacts, based on female sex workers (FSW) in
  Vancouver BC (SNA 2006 2007) (VROrchid)

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Our topographic picture (briefly)

• Eigenvector centrality (EVC) ? spreading power
• High EVC ? well connected to well connected nodes
• EVC is smooth ? a topographic approach makes
  sense for any given graph, we find one or more
  mountains (or regions), each with its most
  central node at the top
• Region membership is determined by
  steepest-ascent path (on the steepest-ascent
  graph or SAG) to the Center (top)
• Spreading within regions is fairly fast and
  predictable
• Spreading between regions may be neither of these

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The Vancouver Orchid dataset

• Based on extensive surveys of female sex workers
  (FSW) and their Clients
• Contacts between these, and with partners (and
  sometimes partners of partners) were recorded
• 553 nodes, 1498 links
• 2 nodes are HIV positive other STIs found in 11
  other nodes

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The Orchid graph regions analysis
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The Orchid graph regions analysis SAG
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A purely heterosexual graph is bipartite!

• Bipartite graph two sets of nodes (eg, M and F)
  all connections are between the two sets (M ? F)
• We are accustomed to finding only a few regions
  in the (non-bipartite) graphs we have studied
  (EX 10 million nodes, 1 region ...)
• In a purely bipartite graph, there are no
  triangles ? the graph is not as well connected
  as it could be otherwise
• The Orchid graph is mostly bipartite (only
  11/1502 links are homosexual) we conjecture that
  this is the reason for the many (17) regions that
  we find
• Nevertheless we find the graph to be dominated by
  3 large regions (totalling 517/553 nodes)

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Conjecture Centers tend to be confined to one
gender (M or F) due to bipartite property
Here we plot all nodes with at least 20 partners
Center large Here, all
Centers are men!
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Our predictions

• When an infection reaches a region, it moves
  towards the Center (uphill), and takes off
  when it reaches the Central neighborhood
• That is, once the infection reaches the Central
  neighborhood of a region, the entire region is
  lost (ie, rapidly infected)
• Movement between regions is heavily dependent on
  how well connected the regions are
• In the Orchid graph, the strongest connections
  are
• Grey ? Red ? Blue
• HIV is found in the Red region (2 hops from
  Centerbad news), and at the Center of a small
  region (also 2 hops from the Center of Red
  region!) ? ?
• We expect it to be difficult to protect the Red
  region also, the strong connections to the other
  two are a problem!

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Spreading simulation start with Red HIV-positive
node 233
Total
Red
Grey
Blue
fast take off
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Protecting the Red region is difficult

• 237 dominates, but either HIV-pos node infects
  the Red region fast
• Simulations with both infected look like those
  with just 237
• ? if we must prioritize one for protection, it
  would be 237
• We have immunized the Red Center no help!
• Reason there remains a very dense Red Central
  neighborhood
• ? we find no easy way to protect the Red region
• However the graph topology suggests that the Grey
  region can be protected from infections coming
  from Red, via protecting the Grey Center (node
  117)
• We also find that infections from the Grey region
  are slowed down by immunizing this same node

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Spreading simulation start with both
HIV-positive nodes immunize Grey Center node
No immunization
Immunize 117
Grey region takes off later
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Spreading simulation start node 306 STI, in
Grey region
Immunize the Grey Center
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Conclusions (thus far)

• The quasi-bipartite nature of the sexual contact
  network has made our regions analysis a bit more
  interesting
• However, the main features we found in earlier
  work are again found here
• The role of the region as a unit of analysis is
  clear
• In particular, the whole region is lost once
  the Central neighborhood is infected
• We find it difficult to protect the (big) Red
  region from the HIV-infected nodesthey are too
  close to its Center
• However, we find that inoculating just one node
  can significantly hinder Grey ? Red spreading

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Future work

• Weight the links with realistic infection
  transmission probabilities per unit time
• Since these weights are disease dependent, we
  will get a distinct adjacency matrix for each
  disease
• The regions analysis is also sensitive to link
  weights
• Thus, using realistic weights will make the
  regions analysis more realistic, and hence more
  practical
• Using realistic link weights, seek and test
  promising protection strategies
• We have not attempted to do that systematically
  here, due to 1.b. above
• Strategies to be tested need not be limited to
  those suggested by our analysis, since the
  simulations are agnostic