The Influence of Social Network Graph Structure on Disease Dynamics in a Simulated Environment Page: 51
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VACCINATION STRATEGIES BASED ON CENTRALITY MEASURES
Although epidemics are inevitable, it is possible to reduce their impact on society. Ideally,
enough individuals could be vaccinated to stop an outbreak from ever reaching epidemic status, a
concept referred to as herd immunity. In most cases, however, this is not a practical solution. Herd
immunity is achieved if the effective basic reproductive number is brought to a level below unity.
Unfortunately, large intrinsic values of R0, require very high levels of vaccination. In a paper
published in 1982 by Anderson and May, it is reported that the proportion, p, of the population that
must be vaccinated to achieve herd immunity is given by Equation 19 . Therefore, a disease
with an intrinsic Ro = 3 would require that more than 2of the population be vaccinated. Data
from the Centers for Disease Control (See Appendix 5.2.1) indicates that even the yearly influenza
vaccine, in anticipation of expected outbreaks, is distributed in much lower quantities. It is highly
unlikely that an adequate vaccine supply would be available in the event of an unforeseen disease
(19) p> 1-
The experiments in this chapter explore vaccination methods based on centrality. The results
found previously imply that small world graphs effectively facilitate disease spread in a simulated
environment even when the neighborhood size and probability of contacts outside the neighbor-
hood are relatively small. Discussing similar results, a research article by Watts and Strogatz states,
"Infectious diseases are predicted to spread much more easily and quickly in a small world; the
alarming and less obvious point is how few short cuts are needed to make the world small" .
In the previously presented experiments, no intervention strategies are implemented and a large
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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/m1/61/: accessed May 25, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .