title: Analysis of a growth model inspired by Gompertz and Korf laws, and an analogous birth-death process.
abstract: 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.
authors: Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II, 132, 84084 Fisciano (SA), Italy. Electronic address: adicrescenzo@unisa.it.
authors: Antonio
authors: A
authors: Di Crescenzo
authors: Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II, 132, 84084 Fisciano (SA), Italy. Electronic address: sspina@unisa.it.
authors: Serena
authors: S
authors: Spina
mesh_terms: D000818:Animals; D008962:Models, Theoretical; D011158:Population Growth
keywords: Birth-death process; First-passage-time problem; Growth model; Inflection point; Relative growth rate; Ultimate extinction probability