A Biological Growth Model using Continued Fraction of Straight Lines

Abstract

S-shaped curves are ubiquitous in biology especially when it comes to growth of a population or even an individual. Growth models such as the classical Verhulst-Pearl logistic growth equation and its extensions effectively model such S-shaped growth curves. Most of these models are parametrised by three or more parameters. In this work, continued fraction of straight lines has been applied to model S-shaped curves of biological growth through the use of only two parameters a and m. Here, m is the maximum growth rate and a is the parameter restricting the growth rate. The parameters a and m help to better interpret the data when compared to the logistic growth model since m represents factors promoting growth while a represents the constraints on growth. This model is effective for modeling both population as well as individual growth, especially around the phase of rapid growth.