Volume 62, 2018CIMPA School on Mathematical Models in Biology and Medicine
|Page(s)||123 - 138|
|Published online||17 October 2018|
An Introduction to The Basic Reproduction Number in Mathematical Epidemiology★
UMR 6249 Chrono-environnement - Université Bourgogne Franche-Comtée, 16 route de Gray, F-25030 Besançon cedex FRANCE
This article introduces the notion of basic reproduction number R0 in mathematical epi-demiology. After an historic reminder describing the steps leading to the statement of its mathematical deﬁnition, we explain the next-generation matrix method allowing its calculation in the case of epidemic models described by ordinary diﬀerential equations (ODEs). The article then focuses, through four ODEs examples and an infection load structured PDE model, on the usefulness of the R0 to address biological as well mathematical issues.
© EDP Sciences, SMAI 2018
This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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