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Minimizing Dependency Ratio in Spain through Demographic Variables

Author

Listed:
  • Joan C. Micó

    (Institut Universitari de Matemàtica Multidisciplinar, Universitat Politècnica de València, Camí de Vera s/n, 46022 València, Spain)

  • David Soler

    (Institut Universitari de Matemàtica Multidisciplinar, Universitat Politècnica de València, Camí de Vera s/n, 46022 València, Spain)

  • Maria T. Sanz

    (Departament de Didàctica de la Matemàtica, Universitat de València, Avda. Tarongers 4, 46022 València, Spain)

  • Antonio Caselles

    (IASCYS, Departament de Matemàtica Aplicada, Universitat de València, Dr. Moliner 50, 46100 Burjassot, Spain)

  • Salvador Amigó

    (Departament de Personalitat, Avaluació i Tractaments Psicològics, Universitat de València, Av. Blasco Ibáñez 21, 46010 València, Spain)

Abstract

The population pyramids in Europe have changed in the last decades, particularly in Spain, where population aging is observed and implies an increase in the dependency ratio. The present study aims to modify a mathematical model of population defined by age and sex based on the von Foerster-Mckendrick equations in order to have birth and migration rates as control variables. To achieve this objective, the necessary mathematical changes are made in the model, and the new mathematical model is verified and validated for the case of Spain, in the period 2008–2019, being considered successful both in its deterministic and stochastic formulation. Finally, through the method of strategies and scenarios and a genetic algorithm, a modification of the population pyramid is obtained in the direction of a decrease in the dependency ratio, increasing the birth rate and immigration and decreasing the emigration rate. These changes lead to a modification of the population pyramid in the year 2040; in particular, an increase of the female population in the age range from 20 to 39 years old.

Suggested Citation

  • Joan C. Micó & David Soler & Maria T. Sanz & Antonio Caselles & Salvador Amigó, 2022. "Minimizing Dependency Ratio in Spain through Demographic Variables," Mathematics, MDPI, vol. 10(9), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1471-:d:803509
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    References listed on IDEAS

    as
    1. Cruz, Marcio & Ahmed, S. Amer, 2018. "On the impact of demographic change on economic growth and poverty," World Development, Elsevier, vol. 105(C), pages 95-106.
    2. Carl Schmertmann, 2012. "Stationary populations with below-replacement fertility," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 26(14), pages 319-330.
    3. Simon, C. & Belyakov, A.O. & Feichtinger, G., 2012. "Minimizing the dependency ratio in a population with below-replacement fertility through immigration," Theoretical Population Biology, Elsevier, vol. 82(3), pages 158-169.
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    Cited by:

    1. Joan C. Micó, 2022. "A Population Pyramid Dynamics Model and Its Analytical Solution. Application Case for Spain," Mathematics, MDPI, vol. 10(19), pages 1-20, September.

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