Strategic Synchronous Snowball Sampling Immunization (NetSci 2020)

Transcript

1. Improving Acquaintance Immunization via Strategic Synchronous Snowball Sampling Samuel F.

   Rosenblatt1,2, Jeffrey A. Smith3, G. Robin Gauthier3, & Laurent Hébert-Dufresne1,2 • Acquaintance Immunization: Immunize random neighbors of random nodes [1] • Leverages the “friendship paradox” to select node proportional to their degree, leading to selection of high degree nodes with no prior network data [2] 1 Department of Computer Science, University of Vermont, 2 Vermont Complex Systems Center, University of Vermont, 3 Department of Sociology, University of Nebraska-Lincoln Correspondence: sfrosenb@uvm.edu 0.0 0.5 1.0 1.5 2.0 0 25 50 % Outbreak Reduction vs. Classic Acquaintance Hamilton-Like Networks - Assortativity = 0.429 Avg Outbreak Size w/ Classic Acquaintance (% of Network) 0.0 0.5 1.0 1.5 2.0 0 25 50 % Outbreak Reduction vs. Classic Acquaintance Bowdoin-Like Networks - Assortativity = 0.261 Avg Outbreak Size w/ Classic Acquaintance (% of Network) 0.0 0.5 1.0 1.5 2.0 0 25 50 % Outbreak Reduction vs. Classic Acquaintance Haverford-Like Networks - Assortativity = 0.257 Avg Outbreak Size w/ Classic Acquaintance (% of Network) 0.0 0.5 1.0 1.5 2.0 0 25 50 % Outbreak Reduction vs. Classic Acquaintance Amherst-Like Networks - Assortativity = 0.253 Avg Outbreak Size w/ Classic Acquaintance (% of Network) 0.0 0.5 1.0 1.5 2.0 0 25 50 % Outbreak Reduction vs. Classic Acquaintance USFCA-Like Networks - Assortativity = 0.251 Avg Outbreak Size w/ Classic Acquaintance (% of Network) 0.0 0.5 1.0 1.5 2.0 0 25 50 % Outbreak Reduction vs. Classic Acquaintance Swarthmore-Like Networks - Assortativity = 0.180 Avg Outbreak Size w/ Classic Acquaintance (% of Network) 0.0 0.5 1.0 1.5 2.0 0 25 50 % Outbreak Reduction vs. Classic Acquaintance Simmons-Like Networks - Assortativity = 0.124 Avg Outbreak Size w/ Classic Acquaintance (% of Network) • In assortative networks, neighbors of neighbors of random nodes can have even higher degree than random neighbors because of both the friendship paradox and assortativity • Thus, beginning with a small subsample and adding any (previously unknown) neighbors of nodes encountered during the acquaintance immunization process to the sample leads to a positive degree bias in the sampling frame • Forming the sample can be done synchronously with immunization for rapid response and efficient resource allocation • This leverages work already necessary in classic acquaintance immunization yet yields an immunized portion with a much higher average degree • Unlike acquaintance immunization, this method requires no complete sampling frame (census) of the population prior to beginning [3] References: 1. Cohen, Havlin, and Ben-Avraham, Physical Review Letters (2003). 2. Christakis and Fowler, PLoS ONE (2010). Concurrent Sampling Process 1. Start with a small percent of all nodes as seeds. 2. Interview a random node in your sample and ask them to list all* their contacts. 3. If any named contacts are unknown to your sample, add them. 4. Immunize a random one of the nodes given by the node in step 2. 5. Repeat steps 2-4 till you reach your desired immunization level. *Alternative variant tested as well with asking for 1 contact, with interesting, but more nuanced, results • Used the CCM model from [4] to create 1000 random networks for each of our seed networks • Hard constraint on degree distribution seed network, soft constraint on degree-degree correlation matrix, which allows us to create random networks with positive assortativity • Used networks between 1K and 2K nodes from FB100 dataset, plus PGP network Synthetic Networks The increased degree of nodes selected for immunization leads to substantially lower outbreak sizes. In the figures above and to the right, we measure the percentage difference between classic acquaintance immunization and our method over a range of infection rates, β, with fixed to 1. (B) (A) 0 500 1000 1500 2000 Position in Immunization Sequence 8 10 12 14 16 18 20 22 Degree Average Degree of the xth Immunized Node: 0.1 % Starting Sample Classic Acquaintance Updating Sample Acquaintance (B) 100 101 102 Degree, k 10 5 10 4 10 3 10 2 10 1 100 CCDF Degree Distributions PGP-like Networks All nodes: < k >=4.48 Classic Acquaintance immunized nodes: < k >=11.4 (A) 3. Rosenblatt et al., PLoS Computational Bio. (2020). 4. Newman, Physical review letters. (2002). 2 4 6 8 0 20 40 60 % Outbreak Reduction vs. Classic Acquaintance PGP-Like Networks - Assortativity = 0.238 % Reduction in outbreak size Avg Outbreak Size w/ Classic Acquaintance (% of Network)