In this module we introduce the important notion of the replacement number, which generalizes the basic reproductive number R₀. We investigate how this number behaves near the start of an outbreak in models based on the uniform mixing assumption and in models that assume a contact network that is a random k-regular graph with small k. We also illustrate a method for estimating the value of R₀ from epidemiological data.

Level: Advanced undergraduate and graduate students of mathematics.

Requires: Module Exploring random regular graphs with IONTW.  An optional subsection requires basic familiarity with differential equation models as covered in Module Differential equation models of disease transmission.

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Researchers should cite this work as follows:

• Winfried Just; Hannah Lea Callender; Drew LaMar; Ying Xin (2015), "The replacement number," https://qubeshub.org/resources/376.

  BibTex | EndNote

1. data analysis
2. estimation
3. module
4. random regular graphs
5. replacement number
6. reproductive number
7. Resources @ QUBES - Teaching & Reference
8. uniform mixing