Many empirically studied networks have approximately so-called power-law or scale-free degree distributions. In Section 1 we formally define such distributions and explore some of their properties. We also introduce and briefly compare two methods for constructing random networks with approximately power-law degree distributions: generic scale-free networks and the preferential attachment model. In Sections 2 and 3 we explore disease transmission on networks that are obtained from the preferential attachment model and implications for designing effective vaccination strategies.
Level: Advanced undergraduate students of biology or mathematics.
Requires: This module is fairly self-contained. Subsection 1.1 as well as Sections 2 and 3 require only basic familiarity with network models of disease transmission and IONTW to the extent covered in Module A quick tour of IONTW. Subsections 1.2 and 1.3 reference the construction given in Section 2 of Module Exploring contact patterns between two subpopulations.
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