## 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
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