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Strategic Synchronous Snowball Sampling Immunization (NetSci 2020)

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.

Samuel F. Rosenblatt

September 23, 2020
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  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:
    [email protected]
    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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