IDEAS home Printed from
   My bibliography  Save this article

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


  • Hisashi Inaba


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.

Suggested Citation

  • 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

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    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.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:vid:yearbk:v:7:y:2009:i:1:p:197-215. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Frank Kolesnik). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.