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The replacement number

By Winfried Just1, Hannah Lea Callender2, Drew LaMar3, Ying Xin1

1. Department of Mathematics, Ohio University 2. University of Portland 3. College of William and Mary

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Abstract

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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Cite this work

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.

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