A generalized Gompertz growth model with applications and related birth-death processes

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 $d_2$-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.

An Analysis of COVID-19 Cases in Nepal: A Modeling Approach

“…The prediction for the total cases till the end of the epidemic made by the model was around a similar figure. Asadi et al (2020) analyzed COVID-19 cases in Spain using the Gompertz model and found a growth coefficient higher than the results of this study. Faranda et al (2020) studied COVID-19 data of different countries.…”

“…According to their results, the MAPE of Gompertz is less than that of Logistic which means the Gompertz model is more accurate than Logistic. Asadi et al (2020) found the generalized Gompertz model as a good fit for measuring the number of individuals infected in Italy and Iran. Kriston (2020) investigated COVID-19 cases by taking data till March 29 from John Hopkins University and made projections for six countries: Hubei in China, South Korea, Germany, United States, Brazil, and South Africa using Hierarchical Logistic model.…”

“…The contact among people of the different populations determines the aspect that characterizes the rate of transmission pattern in civic places and families, and this virus exhibited high transmission rate (Guo et al, 2020;Sarkodie & Owusu, 2020). The COVID-19 mostly attack and damage the respiratory system and alveoli therein (Gautam, 2020;Asadi et al, 2020). The virus enters through the eyes, the nose, or/and the mouth infects the lung, accrues in the kidney, and can cause damage to resident renal cells (Cheng et al,2020;Fan et al 2020;He et al, 2006).…”