The Influence of Social Network Graph Structure on Disease Dynamics in a Simulated Environment Page: 76

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Investigations presented herein are the result of multiple analyses of disease spread in simu-
lated environments. The creation of social networks and subsequent disease outbreaks are based
on graph theoretical concepts. This design allows the established field of graph theory to be ap-
plied to the area of epidemiology. A well-recognized paradigm, the SIR model, is superimposed
onto the social network graph structure. Initial investigations in this dissertation measure changes
in outbreak severity as a result of modifications to the social structure. Subsequent experiments
explore the efficacy of several vaccination strategies.
Several conclusions are drawn from these experiments. As a social network progresses from
ordered to random, the neighborhood size becomes less important. A small neighborhood size with
a low probability for contact outside of the neighborhood has a significant effect on the severity of a
disease outbreak, however, as the neighborhood size or the probability of random contacts increase,
the variation in severity is very minor. In fact, as the neighborhood size approaches the size of the
population, the structure of the graph inherently moves from ordered to random regardless of the
probability of random contacts.
It is also observed that the duration of an outbreak and the initial number of secondary infec-
tions, R0o, are not reliable indicators of the severity of an outbreak. A short duration may result due
to the lack of progression of the disease throughout the population, infecting very few individuals,
or it may result because the disease spreads very quickly, infecting many. A value of Ro0 > 1
generally indicates that an epidemic is likely to occur, however, this is not always the case. In
circumstances when the neighborhood size is limited and the probability for random contacts is
low, it is observed that Ro0 > 1 is not an accurate indicator. Although duration and Ro0 are useful in
conjunction with the proportion of population infected, they do not provide enough information to
stand alone.
Chapter 4 explores the efficacy of targeted vaccination policies under the assumption of a
limited supply of vaccine. Unlike the earlier experiments in which the contact graph is created
dynamically as the disease spreads, these experiments first create a social contact graph so that


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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. ( accessed June 25, 2019), University of North Texas Libraries, Digital Library,; .

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