Asadi M, Di Crescenzo A, Sajadi FA, Spina S. A generalized Gompertz growth model with applications and related birth-death processes.
RICERCHE DI MATEMATICA 2020. [PMCID:
PMC7757087 DOI:
10.1007/s11587-020-00548-y]
[Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/2020] [Revised: 10/04/2020] [Accepted: 11/16/2020] [Indexed: 07/30/2023]
Abstract
In this paper, we propose a flexible growth model that constitutes a suitable generalization of the well-known Gompertz model. We perform an analysis of various features of interest, including a sensitivity analysis of the initial value and the three parameters of the model. We show that the considered model provides a good fit to some real datasets concerning the growth of the number of individuals infected during the COVID-19 outbreak, and software failure data. The goodness of fit is established on the ground of the ISRP metric and the \documentclass[12pt]{minimal}
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\begin{document}$$d_2$$\end{document}d2-distance. We also analyze two time-inhomogeneous stochastic processes, namely a birth-death process and a birth process, whose means are equal to the proposed growth curve. In the first case we obtain the probability of ultimate extinction, being 0 an absorbing endpoint. We also deal with a threshold crossing problem both for the proposed growth curve and the corresponding birth process. A simulation procedure for the latter process is also exploited.
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