1. Topographic analysis of an empirical human sexual network Geoffrey Canright and Kenth Engø-Monsen, Telenor R&I, Norway Valencia Remple, U of British Columbia, Vancouver, Canada

2. 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) (VR—’Orchid’)

3. 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 We call the top node for each region the ’Center’

4. 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 STI’s found in 11 other nodes

5. The Orchid graph — regions analysis = male = female = HIV- pos

6. The Orchid graph — regions analysis — SAG = male = female

7. 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)

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

9. 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 Center—bad 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!

10. Spreading simulation start with Red HIV-positive node 233 Total Red Grey Blue fast take off

11. 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

12. Spreading simulation start with both HIV-positive nodes; immunize Grey Center node Immunize 117 No immunization Grey region takes off later

13. Spreading simulation start node 306 = STI, in Grey region Immunize the Grey Center

14. 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 nodes—they are too close to its Center However, we find that inoculating just one node can significantly hinder Grey  Red spreading

15. Future work 1.Weight the links with realistic infection transmission probabilities per unit time a.Since these weights are disease dependent, we will get a distinct adjacency matrix for each disease b.The regions analysis is also sensitive to link weights c.Thus, using realistic weights will make the regions analysis more realistic, and hence more practical 2.Using realistic link weights, seek and test promising protection strategies a.We have not attempted to do that systematically here, due to 1.b. above b.Strategies to be tested need not be limited to those suggested by our analysis, since the simulations are ”agnostic”