Goodness-of-fit testing for the Gompertz growth curve model

Instantaneous maturity rate: a novel and compact characterization of biological growth curve models

Modeling and analysis of biological growth curves are an age-old study area in which much effort has been dedicated to developing new growth equations. Recent efforts focus on identifying the correct model from a large number of equations. The relative growth rate (RGR), developed by Fisher (1921), has largely been used in the statistical inference of biological growth curve models. It is convenient to express growth equations using RGR, where RGR can be expressed as functions of size or time. Even though RGR is model invariant, it has limitations when it comes to identifying actual growth patterns. By proposing interval-specific rate parameters (ISRPs), Pal et al. (2018) appeared to solve this problem. The ISRP is based on the mathematical structure of the growth equations. Therefore, it is not model invariant. The current effort is to develop a measure of growth that is model invariant like RGR and shares the advantages of ISRP. We propose a new measure of growth, which we call instantaneous maturity rate (IMR). IMR is model invariant, which allows it to distinguish growth patterns more clearly than RGR. IMR is also scale-invariant and can take several forms including increasing, decreasing, constant, sigmoidal, bell-shaped, and bathtub. A wide range of possible IMR shapes makes it possible to identify different growth curves. The estimation procedure of IMR under a stochastic setup has been developed. Statistical properties of empirical IMR estimators have also been investigated in detail. In addition to extensive simulation studies, real data sets have been analyzed to prove the utility of IMR.

Gompertz model in COVID-19 spreading simulation

The paper reports on application of the Gompertz model to describe the growth dynamics of COVID-19 cases during the first wave of the pandemic in different countries. Modeling has been performed for 23 countries: Australia, Austria, Belgium, Brazil, Great Britain, Germany, Denmark, Ireland, Spain, Italy, Canada, China, the Netherlands, Norway, Serbia, Turkey, France, Czech Republic, Switzerland, South Korea, USA, Mexico, and Japan. The model parameters are determined by regression analysis based on official World Health Organization data available for these countries. The comparison of the predictions given by the Gompertz model and the simple logistic model (i.e., Verhulst model) is performed allowing to conclude on the higher accuracy of the Gompertz model.

COVID-19 pandemic models revisited with a new proposal: Plenty of epidemiological models outcast the simple population dynamics solution

We have put an effort to estimate the number of publications related to the modelling aspect of the corona pandemic through the web search with the corona associated keywords. The survey reveals that plenty of epidemiological models outcast the simple population dynamics solution. Most of the future predictions based on these epidemiological models are highly unreliable because of the complexity of the dynamical equations and the poor knowledge of realistic values of the model parameters. The incidence time series of top ten corona infected countries are erratic and sparse. But in comparison, the incidence and disease fitness relationships are uniform and concave upward in nature. These simple profiles with the acceleration curves have fundamental implications in understanding the instinctive dynamics of the corona pandemic. We propose a simple population dynamics solution based on the incidence-fitness relationship in predicting that a plateau or steady state of SARS-CoV-2 will be reached using the basic concept of geometry.

Evolution of model specific relative growth rate: Its genesis and performance over Fisher's growth rates

Growth curve models play an instrumental role to quantify the growth of biological processes and have immense practical applications across disciplines. In the modelling approach, the absolute growth rate and relative growth rate (RGR) are two most commonly used measures of growth rates. RGR is empirically estimated by Fisher (1921) assuming exponential growth between two consecutive time points and remains invariant under any choice of the underlying growth model. In this article, we propose a new measure of RGR, called modified RGR, which is sensitive to the choice of underlying growth law. The mathematical form of the growth equations are utilized to develop the formula for model dependent growth rates and can be easily computed for commonly used growth models. We compare the efficiency of Fisher's measure of RGR and modified RGR to infer the true growth profile. To achieve this, we develop a goodness of fit testing procedure using Gompertz model as a test bed. The relative efficiency of the two rate measures is compared by generating power curves of the goodness of fit testing procedure. The asymptotic distributions of the associated test statistics are elaborately studied under Gompertz set up. The simulation experiment shows that the proposed formula has better discriminatory power than the existing one in identifying the true profile. The claim is also verified using existing real data set on fish growth. An algorithm for the model selection mechanism is also proposed based on the modified RGR and is generalized for some commonly used other growth models. The proposed methodology may serve as a valuable tool in growth studies in different research areas.