On blog post three Network Society - Kim's Contributions I voiced the question: “why do we still fail in eliminating diseases, if we are able to trace these diseases commencing at the base (the hub)?”
Findings of Watts & Strogatz and Kretschmar & Morris with the Small World Theory in mind show that it is not that straightforward to answer this question.
The network model of disease spreading found by Kretschmar & Morris (1996) and Watts & Strogatz (1998) differs slightly from what has been found by other researchers. Kretschmar & Morris’s model illustrates the dynamics as an apparent function of the structure compared to the latter model. By contrast, Watts & Strogatz’s model only synthesizes the network structure that influence the acceleration and extent of disease transmission.
Kretschmar & Morris and Watts & Strogatz use the small world theory to analyze changes in the spreading dynamics, which are due to more structural characteristics rather than based on connectivity. They use connectedness as a fixed parameter in their analysis. Conversely, other researchers based their analysis on disconnected parameters, e.g., graphs and, fix the average number of connections per actor per graph or occurrence.
Watts & Strogatz envision that others will build upon their method of analysis in an attempt to advance the knowledge, but rather to be able to answer the above-mentioned question.
References:
Watts, D.J. & Strogatz, S.H. 1998. Collective dynamics of 'small-world' networks
Nature Vol. 393, pp. 440-442.
Kretschmar, M. & Morris, M. 1996. Measures of concurrency in networks and the spread of infectious disease. Math. Bioscience. Vol. 133, pp. 165–195
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