The Influence of Social Network Graph Structure on Disease Dynamics in a Simulated Environment Page: 38
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propagation since an individual can only be infected one time. In contrast, Figure 3.1 illustrates
a representative contact graph and the resulting outbreak graph with k = 6 and p = 1. For this
particular simulation, the resulting contact graph is a near complete graph. In a random graph, such
as this, contacts are not as likely to be repeated. This implies that there is a higher probability that
the disease will transfer to more individuals in the population. Another point regarding Figure 3.1,
is that the neighborhood size is essentially irrelevant. A value of p = 1 indicates that every contact
is random. Each individual is allowed to make contact with any other individual in the population,
thereby effectively eliminating the boundaries of a neighborhood.
FIGURE 3.1. Example of an ordered graph with k = 6, p = 0. (a) Contact graph; (b)
Resulting outbreak graph
With a population of size 30, the minimum average duration is 19 days which occurs with
the smallest neighborhood size and no random contacts, k = 2 and p = 0. This coincides with
the minimum percent infected of 18%, which is an indication that the duration of an outbreak is
relatively short when few individuals become infected. The maximum duration is 34 days which
occurs when k = 10 and p = 0. Although the shortest duration aligns with the fewest infected,
the longest duration does not align with the most infected. Initially, the duration increases as
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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/m1/48/: accessed May 22, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .