Mathematical Study of the Verhulst and Gompertz Growth Functions and Their Contemporary Applications

Abstract

This study examines the mathematical characteristics of the logistic, the generalized logistic and the Gompertz growth function used in human population analysis. When a population growth is mathematically modeled, it starts with differential equations considered as a preliminary study. Then, a general solution equation is derived. This is the method followed by the mathematicians who developed these models. To prepare for the study, I used the framework of the objectives and adhered to the resources and approaches outlined by mathematicians who developed the growth function. In addition, I wanted to evaluate the methodologies that remain valid in contemporary applications using the current perspectives. Mathematician and actuary Benjamin Gompertz developed the first survivors’ function in 1825 which was used later as a population growth function while systematizing life tables. In his three published articles, the mathematician Pierre-François Verhulst developed a logistic human population growth function based on his economic analysis. In addition, he searched for test opportunities using the limited population statistics of France, Belgium, England, the USA, and Russia. Contemporary authors Richards and, ‘Ricketts and Head’ made very invaluable contributions to logistic growth function.

Keywords

• Verhulst logistic function
• Gompertz growth function
• Generalized logistic growth function
• Differential equations of Growth functions

Project Number

Yok

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