×

zbMATH — the first resource for mathematics

Further notes on the basic reproduction number. (English) Zbl 1206.92038
Bauer, Fred (ed.) et al., Mathematical epidemiology. Berlin: Springer (ISBN 978-3-540-78910-9/pbk). Lecture Notes in Mathematics 1945. Mathematical Biosciences Subseries, 159-178 (2008).
Summary: The basic reproduction number, \(R_0\) is a measure of the potential for disease spread in a population. Mathematically, \(R_0\) is a threshold for stability of a disease-free equilibrium and is related to the peak and final size of an epidemic. The purpose of these notes is to give a precise definition and algorithm for obtaining \(R_0\) for a general compartmental ordinary differential equation model of disease transmission. Several examples of calculating \(R_0\) are included, and the epidemiological interpretation of this threshold parameter is connected to the local and global stability of a disease-free equilibrium.
For the entire collection see [Zbl 1159.92034].

MSC:
92D30 Epidemiology
93A30 Mathematical modelling of systems (MSC2010)
37N25 Dynamical systems in biology
PDF BibTeX XML Cite
Full Text: DOI