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The net reproduction rate and the type-reproduction number in multiregional demography

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  • Hisashi Inaba

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.

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  • Hisashi Inaba, 2009. "The net reproduction rate and the type-reproduction number in multiregional demography," Vienna Yearbook of Population Research, Vienna Institute of Demography (VID) of the Austrian Academy of Sciences in Vienna, vol. 7(1), pages 197-215.
  • Handle: RePEc:vid:yearbk:v:7:y:2009:i:1:p:197-215
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    1. repec:cai:popine:popu_p1986_41n3_0609 is not listed on IDEAS
    2. Francesco Billari & Piero Manfredi & Alessandro Valentini, 2000. "Macro-demographic effects of the transition to adulthood: Multistate stable population theory and an application to Italy," Mathematical Population Studies, Taylor & Francis Journals, vol. 9(1), pages 33-63.
    3. Andrei Rogers, 1966. "The multiregional matrix growth operator and the stable interregional age structure," Demography, Springer;Population Association of America (PAA), vol. 3(2), pages 537-544, June.
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