The Influence of Social Network Graph Structure on Disease Dynamics in a Simulated Environment Page: 49
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K Percent of Random Contacts
o 0 ,
010 0 30 -, 40' 50I 60- 70 80090 100%
Percent of Random Contacts
FIGURE 3.8. Total infected on population size 500, p = 0.0 to 1.0 for (a) k = 2 to 10 and
(b)k =20 to 100
k beyond which there is negligible difference regardless of the value of p. A probable explanation
for this threshold value is that there is a level of competition for susceptible individuals when
contacts among infected individuals overlap. Once the neighborhood size becomes large enough
to eliminate this competition, there is no longer a gain by increasing the size even larger.
In the interest of public health, it is beneficial to employ intervention strategies that effectively
reduce the neighborhood size to a level below the threshold. To accomplish this, there are several
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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/m1/59/: accessed May 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .