IDEAS home Printed from https://ideas.repec.org/a/rrs/journl/v17y2023i2p40-65.html
   My bibliography  Save this article

A Mathematical Model For Population Distribution

Author

Listed:
  • Nicholas Elias

    (Democritus University of Thrace, GREECE)

Abstract

In the present paper, an attempt is made to construct a deterministic mathematical simulation for population systems, by which their temporal (equation of motion) and spatiotemporal (equation of distribution) behaviour can be deduced, as solutions of the constitutional differential equations of the system. The generic formulation of the constitutional equations gives the simulation the possibility to expand to several populations, but also to parameters of different nature (say economic), by applying proper transformations according to the inner properties of each parameter. The introduction of the topographical features of such a system can be reduced to a boundary conditions problem, applied to the constitutional differential equations. Two initial applications are analyzed herein, namely a one-dimensional inertial population system, and a one-dimensional dynamic population system, where the external force corresponds to a space of constant curvature. The theoretically predicted behaviors of the population distribution of these systems are compared qualitatively to actual field data, collected from cities around the World.

Suggested Citation

  • Nicholas Elias, 2023. "A Mathematical Model For Population Distribution," Romanian Journal of Regional Science, Romanian Regional Science Association, vol. 17(2), pages 40-65, DECEMBER.
  • Handle: RePEc:rrs:journl:v:17:y:2023:i:2:p:40-65
    as

    Download full text from publisher

    File URL: https://rjrs.ase.ro/wp-content/uploads/2023/12/Elias.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Daniel Griffith & David Wong, 2007. "Modeling population density across major US cities: a polycentric spatial regression approach," Journal of Geographical Systems, Springer, vol. 9(1), pages 53-75, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nicholas Elias, 2024. "A mathematical model for population distribution II: Linear systems," Romanian Journal of Regional Science, Romanian Regional Science Association, vol. 18(2), pages 1-34, December.

    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. Rafael Henrique Moraes Pereira & Vanessa Nadalin & Leonardo Monasterio & Pedro Henrique Melo Albuquerque, 2012. "Quantifying Urban Centrality: A Simple Index Proposal And International Comparison," Discussion Papers 1675, Instituto de Pesquisa Econômica Aplicada - IPEA.
    2. Nicholas Elias, 2024. "A mathematical model for population distribution II: Linear systems," Romanian Journal of Regional Science, Romanian Regional Science Association, vol. 18(2), pages 1-34, December.
    3. Peng Ji & Lilin Yuan, 2023. "Whether polycentric spatial structure is conducive to regional coordinated development: A study on urban agglomerations in China," Growth and Change, Wiley Blackwell, vol. 54(4), pages 940-961, December.
    4. Joan Carles Martori & Rafa Madariaga & Ramon Oller, 2016. "Real estate bubble and urban population density: six Spanish metropolitan areas 2001–2011," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 56(2), pages 369-392, March.
    5. Mostafa Ghadami & Andreas Dittmann & Taher Safarrad, 2020. "Lack of Spatial Approach in Urban Density Policies: The Case of the Master Plan of Tehran," Sustainability, MDPI, vol. 12(18), pages 1-22, September.
    6. Hugo Badia, 2020. "Comparison of Bus Network Structures in Face of Urban Dispersion for a Ring-Radial City," Networks and Spatial Economics, Springer, vol. 20(1), pages 233-271, March.
    7. Liz Rodríguez-Gámez & Sandy Dallerba, 2012. "Spatial Distribution of Employment in Hermosillo, 1999–2004," Urban Studies, Urban Studies Journal Limited, vol. 49(16), pages 3663-3678, December.
    8. Luca Salvati & Giuseppe Venanzoni & Pere Serra & Margherita Carlucci, 2016. "Scattered or polycentric? Untangling urban growth in three southern European metropolitan regions through exploratory spatial data analysis," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 57(1), pages 1-29, July.
    9. Lv, Ying-Yue & Yan, Xiao-Yong & Jia, Bin & Yang, Yitao & Liu, Erjian, 2024. "Quantifying the overall spatial distribution characteristics of urban heavy truck trips: The case of China," Journal of Transport Geography, Elsevier, vol. 115(C).
    10. Jon Franczyk & Heejun Chang, 2009. "Spatial Analysis of Water Use in Oregon, USA, 1985–2005," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(4), pages 755-774, March.
    11. Tan Lee & Jyh-Bang Jou, 2010. "Urban Spatial Development: a Real Options Approach," The Journal of Real Estate Finance and Economics, Springer, vol. 40(2), pages 161-187, February.
    12. Bumsoo Lee & Peter Gordon, 2010. "Urban Structure: It's Role in Urban Growth, Net New Business Formation and Industrial Churn," Working Paper 8515, USC Lusk Center for Real Estate.
    13. Wenze Yue & Yong Liu & Peilei Fan, 2010. "Polycentric Urban Development: The Case of Hangzhou," Environment and Planning A, , vol. 42(3), pages 563-577, March.
    14. Daniel Arribas-Bel & Arturo Ramos & Fernando Sanz-Gracia, 2015. "The Size Distribution of Employment Centers within the US Metropolitan Areas," Environment and Planning B, , vol. 42(1), pages 23-39, February.
    15. Daniel A. Griffith, 2008. "A comparison of four model specifications for describing small heterogeneous space‐time datasets: Sugar cane production in Puerto Rico, 1958/59–1973/74," Papers in Regional Science, Wiley Blackwell, vol. 87(3), pages 341-355, August.
    16. Xuejun Liu & Qisheng Pan & Lester King & Zhonghua Jin, 2019. "Analysing the changes of employment subcentres: A comparison study of Houston and Dallas," Urban Studies, Urban Studies Journal Limited, vol. 56(12), pages 2532-2548, September.
    17. Yi Qiang & Jinwen Xu & Guohui Zhang, 2020. "The shapes of US cities: Revisiting the classic population density functions using crowdsourced geospatial data," Urban Studies, Urban Studies Journal Limited, vol. 57(10), pages 2147-2162, August.
    18. Luca Salvati & Margherita Carlucci & Pere Serra, 2018. "Unraveling latent dimensions of the urban mosaic: A multi-criteria spatial approach to metropolitan transformations," Environment and Planning A, , vol. 50(1), pages 93-110, February.
    19. Amal Najihah Muhamad Nor & Rohazaini Muhammad Jamil & Hasifah Abdul Aziz & Muhamad Azahar Abas & Kamarul Ariffin Hambali & Nor Hizami Hassin & Muhammad Firdaus Abdul Karim & Siti Aisyah Nawawi & Aaina, 2022. "Spatial Distribution of COVID-19 Infected Cases in Kelantan, Malaysia," Sustainability, MDPI, vol. 14(21), pages 1-14, October.
    20. Jung Hun Yang & Dick Ettema & Koen Frenken & Frank van Oort & Evert-Jan Visser, 2011. "A geosimulation model of economic activity for supporting spatial planning and economic policy," ERSA conference papers ersa10p1016, European Regional Science Association.

    More about this item

    Keywords

    mathematical simulation; constitutional equations; population distribution.;
    All these keywords.

    JEL classification:

    • Y80 - Miscellaneous Categories - - Related Disciplines - - - Related Disciplines

    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:rrs:journl:v:17:y:2023:i:2:p:40-65. 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: Bogdan-Vasile Ileanu (email available below). General contact details of provider: .

    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.