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

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.

Population Projection With The Application of The Differential Equation of The Logistic and Exponential Model (Case Study: Yogyakarta Special Region Province)

“…Some relevant studies that support and strengthen this research are as follows. (Barbosa & Rothwell, 2021) and (Uddin et al, 2019). The research concluded that the logistic model is a good calculation tool in estimating the population, and the results obtained are the environmental carrying capacity of 2.2 billion.…”