The net reproduction rate and the type-reproduction number in multiregional demography
Journal: Vienna Yearbook of Population Research
Volume: 2009, pages 197 - 215
Publisher: Verlag der Österreichischen Akademie der Wissenschaften
DOI: 10.1553/populationyearbook2009s197
Hisashi Inaba (1)
(1) Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku Tokyo, Japan 153-8914. Email: inaba@ms.u-tokyo.ac.jp
Abstract
In order to study effects of migration on demographic changes of multiregional populations, multiregional population modelling is a useful traditional tool. Although multiregional mathematical demography has been extensively explored since the beginning of the 1970s, its key concept, the multiregional net reproduction rate, has been long neglected. In this review, we focus on a multiregional stable population system and elaborate the definition of the multiregional net reproduction rate. Next we introduce the type-reproduction number from mathematical epidemiology and show that it becomes a useful index to formulate a simple control relation for a multiregional population. Mathematical ideas presented here will help us to reconsider multiregional mathematical demography, which is a useful theoretical framework to study effects of interregional migration on population dynamics and composition.