The Influence of Social Network Graph Structure on Disease Dynamics in a Simulated Environment Page: 64
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Figure 4.5 describes the organization of the experiments, however, it should be noted that each
simulation in the diagram represents distinct outbreaks after each of the following vaccination
strategies: low contact centrality, high contact centrality, transmission centrality, spread centrality,
and randomness. For comparison purposes, outbreaks are simulated without vaccination as well.
This results in a total of 7, 200 simulated outbreaks (6 strategies, 10 outbreaks on each graph, 10
graphs, 4 values for p, and 3 values for n).
From the experiments discussed in this chapter, results are presented based on observations
regarding graph structure and centrality distribution, graph structure and outbreak analyses, and
graph structure and vaccination methods. Observations in each of these areas provide interesting
findings which will hopefully generate continued research in this area.
4.4.1. Graph Structure and Centrality Distribution
Prior to outbreak simulations, graph analyses are performed to provide a guideline regarding
the number of simulations necessary for statistically significant results. In addition to increasing
the level of confidence regarding further simulations, the results from this preliminary study offer
insight regarding the relationship between graph structure and centrality distribution. The results
are summarized in Tables 4.3, 4.4, and 4.5, in which Data Set 1 is comprised of averages from a
set of 10 graphs and Data Set 2 is comprised of averages from 20 graphs, such that all 30 graphs
are created using the same set of parameters. The consistency between Data Sets 1 and 2 for
each value of N and p over all distributions implies that experimentation over ten distinct graph
structures should produce reliable results.
The average means and standard deviations for contact centrality over population sizes 50, 150,
and 250 are presented in Table 4.3. The average contact centrality has minimal variation across all
values of p for each specific N value as expected. The graphs are created with a specific number
of edges, (N * CR)/2, therefore, the average contact centrality should be equivalent for a given
population size. Due to normalization, which is a division by the total of all edge weights, the
average contact centrality decreases as the population size increases.
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Johnson, Tina V. The Influence of Social Network Graph Structure on Disease Dynamics in a Simulated Environment, dissertation, December 2010; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc33173/m1/74/: accessed May 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .