IDEAS home Printed from https://ideas.repec.org/a/vid/yearbk/v7y2009i1p197-215.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

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
    as

    Download full text from publisher

    File URL: https://epub.oeaw.ac.at/0xc1aa500d_0x0022ebe6
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. repec:cai:popine:popu_p1986_41n3_0609 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Leroy Stone, 1968. "Stable migration rates from the multiregional growth matrix operator," Demography, Springer;Population Association of America (PAA), vol. 5(1), pages 439-442, March.
    2. Josefine Koebe & Jan Marcus, 2022. "The Length of Schooling and the Timing of Family Formation [Income Taxes and the Timing of Marital Decisions]," CESifo Economic Studies, CESifo Group, vol. 68(1), pages 1-45.
    3. Francesco C. Billari & Hans-Peter Kohler, 2002. "Patterns of lowest-low fertility in Europe," MPIDR Working Papers WP-2002-040, Max Planck Institute for Demographic Research, Rostock, Germany.
    4. Tomáš Sobotka & Laurent Toulemon, 2008. "Overview Chapter 4: Changing family and partnership behaviour," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 19(6), pages 85-138.
    5. Mohammad Jalal Abbasi-Shavazi & Rasoul Sadeghi & Hossein Mahmoudian & Gholamreza Jamshidiha, 2012. "Marriage and Family Formation of the Second-Generation Afghans in Iran: Insights from a Qualitative Study," International Migration Review, Wiley Blackwell, vol. 46(4), pages 828-860, December.
    6. Josefine Koebe & Jan Marcus, 2020. "The Impact of the Length of Schooling on the Timing of Family Formation," Discussion Papers of DIW Berlin 1896, DIW Berlin, German Institute for Economic Research.
    7. Kiyosi Hirosima, 2010. "Another tempo distortion: analyzing controlled fertility by age-specific marital fertility rate," MPIDR Working Papers WP-2010-003, Max Planck Institute for Demographic Research, Rostock, Germany.
    8. Dalkhat M Ediev & Mustafa Murat Yüceşahin, 2016. "Contribution of migration to replacement of population in Turkey," Migration Letters, Migration Letters, vol. 13(3), pages 377-392, September.
    9. Coste, Christophe F.D. & Austerlitz, Frédéric & Pavard, Samuel, 2017. "Trait level analysis of multitrait population projection matrices," Theoretical Population Biology, Elsevier, vol. 116(C), pages 47-58.
    10. Sample, Christine & Bieri, Joanna A. & Allen, Benjamin & Dementieva, Yulia & Carson, Alyssa & Higgins, Connor & Piatt, Sadie & Qiu, Shirley & Stafford, Summer & Mattsson, Brady J. & Semmens, Darius J., 2019. "Quantifying source and sink habitats and pathways in spatially structured populations: A generalized modelling approach," Ecological Modelling, Elsevier, vol. 407(C), pages 1-1.
    11. Cáceres, Manuel O. & Cáceres-Saez, Iris, 2013. "Calculating effective growth rate from a random Leslie model: Application to incidental mortality analysis," Ecological Modelling, Elsevier, vol. 251(C), pages 312-322.
    12. James Nichols & James Hines, 2002. "Approaches for the direct estimation of u , and demographic contributions to u , using capture-recapture data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(1-4), pages 539-568.
    13. Marcia Castro, 2007. "Spatial Demography: An Opportunity to Improve Policy Making at Diverse Decision Levels," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 26(5), pages 477-509, December.
    14. Francesco Billari, 2004. "Becoming an Adult in Europe: A Macro(/Micro)-Demographic Perspective," Demographic Research Special Collections, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 3(2), pages 15-44.
    15. A Rogers, 1973. "The Mathematics of Multiregional Demographic Growth," Environment and Planning A, , vol. 5(1), pages 3-29, February.
    16. A Rogers, 1980. "Introduction to Multistate Mathematical Demography," Environment and Planning A, , vol. 12(5), pages 489-498, May.
    17. Luciano Fanti & Mimmo Iannelli & Piero Manfredi, 2010. "Endogenous Age Structure in Descriptive Macroeconomic Growth Models: A General Framework and Some Steady State Analysis," Chapters, in: Neri Salvadori (ed.), Institutional and Social Dynamics of Growth and Distribution, chapter 9, Edward Elgar Publishing.
    18. Eva Beaujouan & Anne Solaz, 2013. "Racing Against the Biological Clock? Childbearing and Sterility Among Men and Women in Second Unions in France," European Journal of Population, Springer;European Association for Population Studies, vol. 29(1), pages 39-67, February.
    19. Pianese, Augusto & Attias, Anna & Bianchi, Sergio & Varga, Zoltàn, 2020. "On the asymptotic equilibrium of a population system with migration," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 115-127.
    20. Andrel Rogers, 1974. "The multiregional net maternity function and multiregional stable growth," Demography, Springer;Population Association of America (PAA), vol. 11(3), pages 473-481, August.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    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.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Bernhard Rengs (email available below). General contact details of provider: https://www.oeaw.ac.at/vid/ .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.