Strategic Synchronous Snowball Sampling Immunization (NetSci 2020)

(Virtual) Poster for NetSci 2020. Describes preliminary research on an improvement to acquaintance immunization which leverages properties of snowball sampling , completed synchronously with immunization, to reduce outbreak sizes compared to acquaintance immunization in manner which is often more logistically feasible than acquaintance immunization.

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)
   

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