Fitting the Portuguese population from 1850 to 2010 to a logistic growth model

Authors

  • Carlos Francisco Barbosa Oporto British School, Oporto, Portugal
  • Michael Rothwell Oporto British School, Oporto, Portugal

DOI:

https://doi.org/10.47611/jsrhs.v10i2.1415

Keywords:

Portuguese population, Logistic growth model, Logistic equation, Logistic curve

Abstract

This work explores how the Portuguese population fits a logistic growth model. The present study is divided into two main sections. The first one consists on the qualitative and quantitative study of the logistic equation. Qualitatively, I will look at various aspects of the differential equation, such as the equilibria and their stability and possible inflections of solutions. Quantitatively, I will use the separation of variables to find explicit solutions. Given the lack of accuracy in the linear fitting to the proportional growth rate against the population, in second chapter, I attempted a polynomial trendline fitting to the growth rate against the population. This led the focus to creating an adapted form of the logistic curve that fits the Portuguese population from 1850 to 2010. With a certain degree of accuracy, the adapted form of the logistic growth model fits the Portuguese population in the period mentioned.

Downloads

Download data is not yet available.

Author Biography

Michael Rothwell, Oporto British School, Oporto, Portugal

Dr. Micheal Rothwell is an International Baccalaureate Mathematics Teacher at the Oporto British School, Oporto, Portugal.

References or Bibliography

Barrocas, J.M. (2001). Logística (curva). In Enciclopédia Verbo Luso-Brasileira de Cultura (Século XXI ed., pp. 213-214). Editorial Verbo.

Blink, J. and Dorton, I. (2012). Economics (2nd ed.), Oxford University Press.

INE – Instituto Nacional de Estatística. (2008). Revista de Estudos Demográficos, 44, p. 3. https://www.ine.pt/xportal/xmain?xpid=INE&xpgid=ine_publicacoes&PUBLICACOESpub_boui=45180054&PUBLICACOESmodo=2

INE – Instituto Nacional de Estatística. (2014). População residente em Portugal com tendência para diminiuição e envelhecimento. Destaque – Informação à Comunicação Social, p. 7. https://www.ine.pt/ngt_server/attachfileu.jsp?look_parentBoui=218948085&att_display=n&att_download=y

INE – Instituto Nacional de Estatística. (2016). População residente. Estatísticas Demográficas 2015, 75, p. 22. https://www.ine.pt/xportal/xmain?xpid=INE&xpgid=ine_publicacoes&PUBLICACOESpub_boui=275533085&PUBLICACOEStema=55466&PUBLICACOESmodo=2

Kucharavy, D. & De Guio, R. (2011). Application of S-shaped curves. Procedia Engineering, 9, 559–572.

Lipkin, L. & Smith, D. (2004). Logistic Growth Model. Mathematical Association of America. Retrieved January 15, 2019, from https://www.maa.org/press/periodicals/loci /joma/logistic-growth-model-introduction

Moraes, J.J.P. (1945). Sobre o acerto da logística à população portuguesa. Revista do Centro de Estudos Demográficos, 1, 105-118.

Petrescu, E. (2009). A statistical distribution useful in product lifecycle modelling. Management and Marketing, 4(2), 165-170. http://www.managementmarketing.ro/pdf/articole/145.pdf

Seidl, I. & Tisdell, C. A. (1999). Carrying capacity reconsidered: from Malthus’ population theory to cultural carrying capacity. Ecological Economics, 31(3), 395–408. https://doi.org/10.1016/S0921-8009(99)00063-4

Tjørve, K.M.C. & Tjørve, E. (2017). The use of Gompertz models in growth analyses, and new Gompertz-model approach: An addition to the Unified-Richards family. PLoS ONE, 12(6), 1-17. https://doi.org/10.1371/journal.pone.0178691

Verhulst, P.-F. (1838). Notice sur la loi que la population suit dans son accroissement. In A. Quetelet (Ed.), Correspondance Mathématique et Physique de l’Observatoire de Bruxelles, (4th ed., pp. 113-121).

Verhulst, P.-F. (1845). Recherches mathématiques sur la loi d’accroissement de la population. Nouveaux Mémoires de l’Académie Royal des Sciences et Belles-Lettres de Bruxelles, 18, 1-42.5

Verhulst, P.-F. (1847). Deuxième mémoire sur la loi d’accroissement de la population. Mémoires de l’Académie Royal des Sciences, des Lettres des Beaux-Arts de Belgique, 20, 1-32.

The Free Encyclopedia (2019). Generalised logistic function. Retrieved January 16, 2019, from https://en.wikipedia.org/wiki/Generalised_logistic_function

Published

07-01-2021

How to Cite

Barbosa, C. F., & Rothwell, M. (2021). Fitting the Portuguese population from 1850 to 2010 to a logistic growth model. Journal of Student Research, 10(2). https://doi.org/10.47611/jsrhs.v10i2.1415

Issue

Section

HS Research Articles