A practical approach to R0 in continuous‐time ecological models. (17th November 2017)

• Record Type: Journal Article
• Authors: Barril, C.; Calsina, À.; Ripoll, J.
• Other Names: Anguelov Roumen guestEditor.; Banasiak Jacek guestEditor.; Debbouche Amar guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 18(2018)
• Page Start: 8432
• Page End: 8445
• Publication Date: 2017-11-17
• Subjects: next‐generation operator -- population dynamics -- reproduction number; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4673
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.