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 Gompertzgrowth function used in human population analysis. When a population growth is mathematically modeled, it startswith differential equations considered as a preliminary study. Then, a general solution equation is derived. This is themethod followed by the mathematicians who developed these models. To prepare for the study, I used the frameworkof the objectives and adhered to the resources and approaches outlined by mathematicians who developed the growthfunction. In addition, I wanted to evaluate the methodologies that remain valid in contemporary applications using thecurrent perspectives. Mathematician and actuary Benjamin Gompertz developed the first survivors’ function in 1825which was used later as a population growth function while systematizing life tables. In his three published articles, themathematician Pierre-François Verhulst developed a logistic human population growth function based on his economicanalysis. 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 tologistic growth function.