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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Researchers should cite this work as follows:

• Winfried Just; Hannah Lea Callender; Drew LaMar; Ying Xin (2015), "The preferential attachment model," https://qubeshub.org/resources/384.

  BibTex | EndNote

1. disease transmission
2. epidemiology
3. IONTW
4. module
5. networks
6. power-law degree distribution
7. preferential attachment
8. Resources @ QUBES - Teaching & Reference
9. scale-free degree distribution