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A practical approach to R 0 in continuous‐time ecological models
Author(s) -
Barril C.,
Calsina À.,
Ripoll J.
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4673
Subject(s) - mathematics , population model , population , computation , age structure , basic reproduction number , diffusion , unit (ring theory) , space (punctuation) , econometrics , computer science , demography , algorithm , physics , mathematics education , sociology , thermodynamics , operating system
In this paper we study the asymptotic behaviour of the solutions in linear models of population dynamics by means of the basic reproduction number R 0 . Our aim is to give a practical approach to the computation of the basic reproduction number in continuous‐time population models structured by age and/or space. The procedure is different depending on whether the density of newborns per time unit and the density of population belong to the same functional space or not. Three infinite‐dimensional examples are illustrated: a transport model for a cell population, a model of spatial diffusion of individuals in a habitat, and a model of migration of individuals between age‐structured local populations. For each model, we have highlighted the possible advantages of computing R 0 instead of the Malthusian parameter.