The Influence of Social Network Graph Structure on Disease Dynamics in a Simulated Environment Page: 5
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Point of Symptoms Recovered
Infection Appear or Dead
Susceptible Presymptomatic Clinical Disease Removed
Latent State Time
FIGURE 1.2. Disease progression within a host
of those who become infected/infectious increases. Assuming that the disease is acute rather than
chronic, the progression of the outbreak eventually results in a decrease in the number of infectious
individuals and an increase in the number of those who have recovered from the illness or are
otherwise removed, such as through natural immunity or death. The movement of the population
from states of susceptible, infectious, and removed forms a basis for modeling disease spread.
The susceptible-infectious-removed (SIR) paradigm and its counterparts, such as susceptible-
infectious-susceptible (SIS) and susceptible-latent-infectious-removed (SLIR), are recognized stan-
dards for modeling many infectious diseases. The SIR model (discussed more thoroughly in Sec-
tion 2.2) was first introduced by Kermack and McKendrick in a 1927 paper titled "A Contribution
to the Mathematical Theory of Epidemics" . The basic SIR model can be modified as necessary
to more accurately represent the particular disease under question.
Just as the disease model is important to the simulation, so is the underlying social network.
Social networks are complex and graph models used to mimic these networks may vary. Connec-
tions between individuals, and thus disease contacts, are precarious. The research presented in this
dissertation explores the effect of graph structure on the dynamics of disease spread in a simulated
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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/m1/15/: accessed May 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .