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

• Published in: Mathematical biosciences Vol. 282; pp. 121 - 134
• Main Authors: Di Crescenzo, Antonio, Spina, Serena
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01-12-2016; Elsevier Science Ltd
• Subjects: Animals; Birth; Birth-death process; Data analysis; Data processing; Differential equations; First-passage-time problem; Genetic algorithms; Growth model; Growth models; Growth rate; Inflection point; Lag time; Logistics; Markov processes; Models, Theoretical; Population Growth; Relative growth rate; Stochasticity; Transition probabilities; Ultimate extinction probability; 60J85; Growth model; Inflection point; Ultimate extinction probability; 92D25; Relative growth rate; Birth-death process; First-passage-time problem; 60J80
• ISSN: 0025-5564; 1879-3134
• DOI: 10.1016/j.mbs.2016.10.005

•A new deterministic growth model similar to the Gompertz and Korf laws.•We study the main properties of the new model.•Some data analytic examples and their performance are also considered.•We study a special linear time-inhomogeneous birth-death process.•This process is the stochastic counterpart of the proposed model.
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.