Analysis of a growth model inspired by Gompertz and Korf laws, and an analogous birth-death process

• Main Authors: Di Crescenzo, Antonio, Spina, Serena
• Format: Journal Article
• Language: English
• Published: 28-10-2016
• Subjects: Mathematics - Probability; Quantitative Biology - Populations and Evolution
• DOI: 10.48550/arxiv.1610.09297

Mathematical Biosciences (2016), Vol. 282, p. 121-134 We propose a new deterministic growth model which captures certain features
of both the Gompertz and Korf laws. We investigate its main properties, with
special attention to the correction factor, the relative growth rate, the
inflection point, the maximum specific growth rate, the lag time and the
threshold crossing problem. Some data analytic examples and their performance
are also considered. Furthermore, we study a stochastic counterpart of the
proposed model, that is a linear time-inhomogeneous birth-death process whose
mean behaves as the deterministic one. We obtain the transition probabilities,
the moments and the population ultimate extinction probability for this
process. We finally treat the special case of a simple birth process, which
better mimics the proposed growth model.